Quantum computers
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الوثيقة تتناول موضوع الحوسبة الكمومية، مقدمةً نظرية الكم وتطبيقاتها في الحوسبة والتحديات الخاصة بها. تناقش كيف أن الحواسيب الكمومية تتمتع بقدرات معالجة تفوق تلك التي تتمتع بها الحواسيب التقليدية، مما يتيح لها حل مشكلات كان من الصعب حلها سابقًا. بالإضافة إلى ذلك، تستعرض الوثيقة الابتكارات في صناعة الحواسيب الكمومية وتوجهات الشركات التقنية الكبرى نحو تطوير هذه التكنولوجيا.
![33
ﺧوارزﻣﯾﺔ
Grover
اﻟداﻟﺔ ﻋﻠﻰ
f ( x )
اﻟﺗﻲ
اﻟﻣدﺧﻼت ﻋﻠﻰ اﻟداﺋرة ﺗﻘﯾم
{0
∈
x
،
1
n
}
،
ﺗﺷﻐﯾل وﻗت ﻋﻠﻰ اﻟﻔور ﻋﻠﻰ ﻧﺣﺻل
poly ( n ))
n / 2
O (2
ﺣﯾث ،
)
poly ( n)
ﻣن ﯾﺄﺗﻲ
ﻣﻌﯾن ﻣدﺧل ﻋﻠﻰ اﻟداﺋرة ﻟﺗﻘﯾﯾم اﻟﻣﺳﺗﻐرق اﻟوﻗت
.
اﻟﺳﻌﺔ ﺗﺿﺧﯾم
ﺧوارزﻣﯾﺔ ﺗﻘوم
Grover
ﯾﻣﻛ .اﻟﻣﻧظم ﻏﯾر ﻟﻠﺑﺣث اﻟﺳﺎذﺟﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺔ ﺑﺗﺳرﯾﻊ
ن
ًادﺗﻌﻘﯾ اﻷﻛﺛر اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت ﺗﺳرﯾﻊ ًﺎﺿأﯾ اﻟﻛﻣوﻣﯾﺔ ﻟﻠﺧوارزﻣﯾﺎت
.
اﺣﺗﻣﺎﻟﯾﺔ ""ﺗﺧﻣﯾن ﺧوارزﻣﯾﺔ ﺗﻧﻔﯾذ ﻋﻠﻰ اﻟﻘدرة إﻟﻰ ﺑﺎﻟﻧظر
Α
داﻟﺔ ""ﻓﺣص و ،
f
ﻣﺛل ،
Pr [
Α
ﻣﺧرﺟﺎت
w
ﺑﺣﯾث
f ( w ) = 1] = ε
ﺧرج ،
w
ﺑﺣﯾث
f ( w ) = 1 .
اﻟﺗﺟرﯾﺑﻲ اﻟﺑﺣث ﻣﺷﻛﻠﺔ ﻟﺣل اﻟطرق إﺣدى
ﺗﺷﻐﯾل ﺑﺑﺳﺎطﺔ ھﻲ ﻛﻼﺳﯾﻛﻲ ﺑﺷﻛل
A
ﻣﺗﻛرر ﺑﺷﻛل
ﺑﺎﺳﺗﺧدام ﻣرة ﻛل ﻓﻲ اﻹﺧراج ﻣن واﻟﺗﺣﻘﻖ
f
ﺗﻘﯾﯾﻣﺎت ﻋﻧﮫ ﯾﻧﺗﺞ ﻗد ﻣﻣﺎ ،
O (1 / ϵ )
ﻓﻲ
ﻋن ﻧﺎﺗﺟﺔ ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ﺗﺟد أن ﯾﻣﻛن ، ذﻟك وﻣﻊ .اﻟﻣﺗوﺳط
Brassard
و
Høyer
و
Mosca
و
22
Tapp
ھذه ﻣﺛل
f ( w ) = 1
اﺳﺗﺧداﻣﺎت ﻣﻊ
ε)
O (1 /
ﻓﻘ
ﻟـ ط
f
واﺣﺗﻣﺎل ،
ﻣن ًﺎﯾﺗﻌﺳﻔ ﻗرﯾب اﻟﻔﺷل
0
ﺑﺎﺳم اﻟﺧوارزﻣﯾﺔ ھذه ُﻌرفﺗ .اﺳرع ﺗرﺑﯾﻌﻲ ﺗﺣﻘﯾﻖ وﺑﺎﻟﺗﺎﻟﻲ ،
اﻟﻛﻼﺳﯾﻛﻲ اﻻﺣﺗﻣﺎل ﺗﺿﺧﯾم ﻣﻊ اﻟﻘﯾﺎس طرﯾﻖ ﻋن ، اﻟﺳﻌﺔ ﺗﺿﺧﯾم
.
ﺑﺑﺳﺎطﺔ وذﻟك ، اﻹطﺎر ھذا ﻓﻲ أﻋﻼه ﻣﻧﺎﻗﺷﺗﮭﺎ ﺗﻣت اﻟﺗﻲ اﻟﻣﮭﯾﻛﻠﺔ ﻏﯾر اﻟﺑﺣث ﻣﺷﻛﻠﺔ ﺗﺗواﻓﻖ
أﺧذ ﺧﻼل ﻣن
A
ﻟﺗﻛ
ﺳﻠﺳﻠﺔ ُﻧﺗﺞﺗ واﻟﺗﻲ ، اﻟﺧوارزﻣﯾﺔ ون
n -bit
ﻋﻼوة .ﻣوﺣد ﺑﺷﻛل ﻋﺷواﺋﯾﺔ
ﻣدﺧﻼت ھﻧﺎك ﻛﺎن إذا ، ذﻟك ﻋﻠﻰ
{0
∈
k w
،
1
n
}
ﺑﺣﯾث
f ( w ) = 1
ﺛم ،
Pr
[Aoutputswsuchthatf (w) = 1] = kN
إﯾﺟﺎد ﯾﻣﻛﻧﻧﺎ ﻟذﻟك ،
w
ھذه ﻣﺛل
f ( w ) =
1
ﺑﺎﺳﺗﻌﻼﻣﺎت
O (N / k)
إﻟﻰ
f .
ﯾﻣﻛﻧ ، ذﻟك وﻣﻊ
أو ًادﺗﻌﻘﯾ أﻛﺛر اﻟﺧوارزﻣﯾﺔ أن ﻧﺗﺧﯾل أن ﻧﺎ
ﻣن واﺣدة ، اﻟﻣﺛﺎل ﺳﺑﯾل ﻋﻠﻰ .ﺣﻠﮭﺎ ﻧود ﻣﻌﯾﻧﺔ ﻣﺷﻛﻠﺔ وﺗﺳﺗﮭدف اﻷﻣور ﻣﺟرﯾﺎت
اﻟﻘﯾد اﻟرﺿﺎ ﺑﻣﺷﻛﻠﺔ اﻟﻣﻌروﻓﺔ ﻛﻔﺎءة اﻷﻛﺛر اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت
NP-
اﻷﺳﺎﺳﯾﺔ ﻛﺎﻣﻠﺔ
3
-
SAT
اﻟوﻗت ﻓﻲ وﯾﻌﻣل اﻟﻌﺷواﺋﯾﺔ
O ((4/3)
ن
( ن ) ﺑوﻟﻲ
23
).
اﻟﺳﻌﺔ ﺗﺿﺧﯾم ﺗطﺑﯾﻖ ﯾﻣﻛن
اﻟﺗﺷﻐﯾل وﻗت ﻣﻊ ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ﻋﻠﻰ ﻟﻠﺣﺻول اﻟﺧوارزﻣﯾﺔ ھذه ﻋﻠﻰ
n /
O ((4/3)
)
poly ( n )
2
اﻟﺧوارزﻣﯾﺎت ﺗﺳرﯾﻊ ﯾﻣﻛﻧﮭﺎ اﻟﻛﻣوﻣﯾﺔ اﻟﻛﻣﺑﯾوﺗر أﺟﮭزة أن ﯾوﺿﺢ ﻣﻣﺎ ،
إﻛﻣﺎل ﻟﻣﺷﻛﻼت اﻟﺗﺎﻓﮭﺔ ﻏﯾر اﻟﻛﻼﺳﯾﻛﯾﺔ
NP.
ﻟﻠﺧوارزﻣ ﻟﻼھﺗﻣﺎم ﻣﺛﯾر ﻣﺳﺗﻘﺑﻠﻲ اﺗﺟﺎه ﯾﺗﻣﺛل
دﻗﯾﻘﺔ ﺗﻘرﯾﺑﯾﺔ ﺣﻠول إﯾﺟﺎد ﻓﻲ اﻟﻛﻣوﻣﯾﺔ ﯾﺎت
ﻟـ اﻷﺧﯾر اﻟﻌﻣل أﻋطﻰ .اﻟﺗﺣﺳﯾن ﻟﻣﺷﺎﻛل
Farhi
و
Goldstone
و
24
Gutmann
أول
ﻟﺷﻛل اﻟﺧطﯾﺔ اﻟﻣﻌﺎدﻻت ﻣن ﺑﺎﻟﻌدﯾد واﺣد وﻗت ﻓﻲ )ﺗﻔﻲ اﻧدﻣﺎﺟﯾﺔ ﻟﻣﮭﻣﺔ ﻛﻣوﻣﯾﺔ ﺧوارزﻣﯾﺔ
ﺣ ﻣن ﻣﻌروﻓﺔ ﻓﻌﺎﻟﺔ ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ أﻓﺿل ﻋﻠﻰ ﺗﻔوﻗت واﻟﺗﻲ (ﻣﻌﯾن
ھذه ﻓﻲ ؛ اﻟدﻗﺔ ﯾث
ﻟﻧﻔس ﻓﺎﻋﻠﯾﺔ أﻛﺛر ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ ھذا أﻟﮭم .ﺑﺎﻻرﺗﯾﺎح اﻟﻣﻌﺎدﻻت ﻣن ﺟزء ﯾﻘﺎس ، اﻟﺣﺎﻟﺔ](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-33-320.jpg)
![41
اﻟﺜﺎﻟﺚ اﻟﻔﺼﻞ
اﻟﻜﻤﻮﻣﻲ اﻟﺤﺎﺳﻮب ﻋﻤﻞ اﻟﯿﺔ
When building a novel type of computer, like a quantum computer, one can
use an architecture that is based on one of the (presented) classical architectures
[26] to avoid having to design a fundamentally different kind of architecture.
Furthermore, facilitating scalability in quantum computer hardware is one of the
most challenging tasks of quantum computer architectures. In this section, the
quantum von Neumann architecture is introduced which combines the classical
von Neumann architecture with the requirements of the DiVincenzo-criteria in QC
[43] resulting in quantum hardware which incorporates scalability. In a massively
parallel quantum computer, the DiVincenzo criteria have to be fulfilled at every
site that holds a qubit. In order to simplify the hardware of a quantum computer,
one can fabricate hardware specialized on only one criteria and move the
quantum information between these specialized hardware components to
perform QC [20]. The schematic diagram of the quantum von Neumann
architecture is depicted in Fig. 6. Like any quantum computer, it will require a
classical control unit which controls the quantum computer. A quantum bus
system allows moving quantum information between the different parts of the
quantum computer. The manipulation of the quantum information is executed in
the quantum arithmetic logic unit (QALU) which is the most hardware
demanding11 part of the quantum computer as quantum gate operations are
executed here. The quantum information is stored in the quantum memory which
should rely on multiplexing technology for large storage capability. Furthermore,
an input and output region acts as an interface to the classical world in which the
qubit state is initialized and/or detected.
In large-scale quantum computers, one has to achieve big quantum data storage
capacities with low (classical) hardware demand in the quantum memory. If the
hardware demand scaled linearly with the number of qubits that were stored, it
would not obey Rent’s rule and the control hardware would get too complicated
and too expensive for large-scale QC with thousands or millions of qubits.
Reducing the hardware demand can be achieved with multiplexing circuits, as
depicted in Fig. 7 b. Therefore, one needs to have the ability to store quantum
information with a set of constant parameters. For example, to store an ion chain](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-41-320.jpg)
![42
in a segmented Paul trap, one only needs a negative DC voltage at the position of
the ion string and positive DC voltages surrounding it which form an axial
confinement for the ion string. These few voltages can in principle be used to
store arbitrarily many ion strings. During storage, this set of parameters (for
trapped ions that would be a set of DC voltages) is applied to all qubits in the
quantum memory. In order to access a specific memory cell, multiplexing
technology allows a change of this set of parameters to another set which can be
controlled independently. This independent set of parameters enables movement
of the quantum information of an arbitrary memory cell out of the quantum
memory.
Quantum information transport One of the most critical features of this quantum
von Neumann architecture is the quantum bus system for quantum information
transport, which has to be performed with high fidelity to allow fault-tolerant QC.
As quantum information cannot be copied [57], quantum information can only be
transported by physically moving the qubits, quantum teleportation [58] or via
coupling to photons [59, 60]. Atomic or molecular qubit systems enable quantum
information transport via physical movement of the qubit from one location in
space to another. For example in trapped ion systems with segmented Paul traps
[61, 55], ions or ion strings can be moved by changing the confining axial DC
potential. In solid state systems, such movement is not possible in general.
However, there are solid state systems which allow qubit movement, like spins in
silicon [44, 62, 63]. Quantum teleportation [58] requires an entangled qubit pair,
of which one qubit is at the location from where the quantum information is
taken and the second is the qubit at the destination. Furthermore, it requires a
qubit measurement with a classical channel to the destination where a
conditional quantum gate has to be performed. In order to store and read
quantum information in the quantum memory, it implies read-out- and quantum-
gate-capability at every site in the memory. This is in contradiction to a
specialized hardware for each DiVincenzo criteria and, thus, more hardware
demanding than physical movement. But it could be a strategy in many solid-state
systems.
Mapping qubits to photons was demonstrated in atomic or molecular qubit
systems [64, 65] as well as in solid-state systems [60]. Like in quantum
teleportation, this approach requires quantum logic at every site in the memory](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-42-320.jpg)
![43
and is therefore hardware demanding. Quantum information transport with
quantum teleportation or mapping to photons have one advantage over qubit
movement: it is possible to change from one qubit system to another. For
example, QIP could be performed with superconducting circuit QED systems [12,
13] and for long storage in the quantum memory, one could use nitrogen vacancy
centers in diamond [66]. The disadvantage of these technologies compared to
systems, which allow qubit movement, is the high hardware demand in the
memory, as quantum gate operations and quantum state readout are required at
every site in the quantum memory. If this cannot be overcome, quantum
teleportation and mapping to photons will only be applicable to small- and
medium-scale systems. Large-scale systems with low hardware demand per
stored qubit may have to move the qubits in the quantum computer [20]. 4.3.
Parallelism in quantum von Neumann architectures In order to work with an
increasing number of qubits in a quantum von Neumann architecture, one has to
increase the κ value to compensate decoherence in the quantum memory.
Therefore, one can either increase the coherence time or decrease the time per
quantum gate operation. If both options are not feasible, one has to parallelize
QIP. Similar to classical multiprocessor systems, one can use multiple QALUs in
one quantum computer](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-43-320.jpg)
![44
A quantum von Neumann architecture for trapped ion quantum computation
This section covers how one can build the different parts of a quantum von
Neumann architecture in a trapped ion system. The next section will combine
these individual parts to build a model trapped ion quantum computer based on
quantum von Neumann architecture called Quantum 4004. The guideline for
development of the architecture is as follows: (1) Trapped ions QC was chosen
because ion traps are a technology with high κ values. (2) If it is possible, one
should only use operations that have already been demonstrated with high
fidelity. (3) This document covers only the hardware of the quantum computer.
(4) Simplicity of the hardware, especially for scaling of the quantum computer, is
favored over optimization for higher abstraction layer tasks, containing things like
QEC or quantum algorithms, throughout this section. (5) As there is no
functioning fault-tolerant quantum computer yet, one cannot expect a first-
generation quantum computer to work with high computation speed. Thus,
computation speed has low priority in the development of the architecture. If a
fault-tolerant quantum computer can be built and if Moore’s law is applicable to
quantum computer development, the computation speed (and quantum memory
size) will increase exponentially over time. In the quantum charged coupled
device (QCCD) principle [55], shown in Fig. 9, a segmented ion trap is used to
move ions to different positions on the trap by changing the axially confining DC
voltages. This allows using one part of the trap as a quantum memory and
another part as a processing zone, or QALU. The QCCD [55] is a general concept
for trapped ion QC and resembles a quantum von Neumann architecture, as there
are separate regions for the different DiVincenzo criteria [43] and it enables qubit
movement (along the RF rails of the segmented Paul trap). In the following, the
QCCD is used as the underlying principle of a quantum von Neumann architecture
for trapped ion QC
For the QCCD, ideas for QEC and higher level architectures12 have been proposed
[69]. However, trapped ions offer a variety of different gate operations and, thus,
it makes sense to adapt at the abstraction layer scheme for trapped ion QC. Gates
can be performed using local RF fields [70, 23, 71, 72], global RF fields [73] or
optical fields [74, 54]. Even for optical entangling gates, there are multiple types
of gates [75, 76, 77]. Similarly, multiple procedures for efficient ion movement
have been demonstrated [78, 79, 80]. In the following, the lowest abstraction](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-44-320.jpg)
![45
layer of the scheme described in Section 3 (and reference [35]) is split into two.
The new lowest level is then called the hardware layer, and on top of the
hardware layer, a firmware layer is inserted. This new layer contains the firmwire,
such as the type of quantum gates and ion movements. Since the top layers have
only weak hardware dependence, they do not need to be adapted. The quantum
von Neumann architecture, presented in this section, covers only the hardware
abstraction layer. As the exact performance of the hardware is not known and,
thus, the optimum QEC scheme cannot be identified13, it does not make sense to
discuss the higher abstraction layers for this architecture at this point. The
different design challenges for such a quantum von Neumann architecture with
trapped ions are
• vacuum pressure,
• decoherence in the quantum memory,
• multiplexing to enable large quantum memories,
• quantum gates,
• read out and initialization, and
• choice of qubits, which are discussed in the following subsections.
Reduce collisions with background gas In order to maximize the coherence time in
trapped ion systems, collisions with background gas should not limit the
coherence times, as they can lead to ion loss or to loss of quantum information in
the ion chain. Although these losses can be corrected with QEC, it is advisable to
suppress such collisions as much as possible. In room temperature setups,
collisions with residual background gas occur roughly once per hour per ion at
typical UHV pressures of 10−11 mbar [81]. That means when working with, for
example 3600, ions in room temperature setups, one will have approximately one
collision per second. In a cryogenic ion trap experiment at a temperature of 4 K, a
residual background pressure of 10−16 mbar has been observed [82]. Such
pressures reduce the collision rate by 5 orders of magnitude compared to room
temperature setups. Hence in cryogenic experiments, one can work with more
ions than in room temperature setups while at the same time reducing the
collisions with background gas. This suggests that large-scale QC with trapped
ions will have to be performed in a cryogenic environment. Ideally, one wants to](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-45-320.jpg)
![46
be able to neglect collisions with background gas as a source of qubit loss or
decoherence. Therefore, one can look at the two elements with the lowest boiling
point (or triple point), hydrogen and helium. As the exact vacuum pressure in an
experiment strongly depends on the used materials, whether they were baked
before, and so on, one can only perform a worst-case analysis by looking at the
vapor pressure of hydrogen and helium. For the vapor pressure, one assumes at
the whole vacuum chamber is covered with at least one monolayer of the
element in question. Hydrogen has a sublimation equilibrium pressure of 10−6
mbar at a temperature of 4.2 K, and 10−12 mbar at a temperature of 2.6 K [83,
84]. Hence at a temperature around 2 K, hydrogen can no longer sublimate and
will definitely be frozen out. If helium is also a source for collision with the ions,
one will have to cool even further, as 4He has a sublimation equilibrium pressure
of 10−6 mbar at a temperature of 0.46 K, and 10−12 mbar at a temperature of
0.24 K [83]. 3He shows a sublimation equilibrium pressure of 10−6 mbar already
at a temperature of 0.22 K, and 10−12 mbar at a temperature of 0.1 K [83]. This
does not imply that the whole experiment has to be performed at a temperature
of 0.1 K to not be limited by collisions with 3He. But at least one surface in the
cryostat will have to be that cold to exclude collisions with background gas from
the sources of qubit loss or decoherence. 5.2. Decoherence in the quantum
memory and magnetic shielding In trapped ion QC, the qubit can either be
encoded in an optical qubit [85, 74] or a ground state qubit [86, 87, 88]. In the
optical qubit, one state of the qubit is a meta-stable D-state of the ion whereas
the other one is in the ground state. The qubit transition frequency is in the
optical regime and thus it is called optical qubit. As the live-time of this qubit is
limited by the life-time of the meta-stable state, which is typically on the order of
1 s [86], the coherence time will ultimately be limited by its spontaneous decay.
Therefore, to achieve a long coherence time and a high κ value of the system, the
qubit has to be encoded in the ground state of the ion, which does not suffer
from such decoherence. For ground state qubits, the main source of decoherence
is magnetic field fluctuations. Therefore, generating a constant magnetic field and
magnetic shielding are the most critical challenges to achieve long coherence
times in trapped ion systems. Decoherence sources like spin-spin interaction [89]
must be suppressed, e.g. by the choice of an |F1, MF = 0i to |F2, MF = 0i
transition qubit, or by the choice of a qubit at a ’clock transition’, for which the
energy separation does to first order not depend on the magnetic field [86]. Other](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-46-320.jpg)
![47
decoherence sources like leakage of resonant light must be reduced such that
they can be neglected in the quantum memory, which is discussed in Section
5.5.5. Quantum gate operations in trapped ion systems take between 10 and 100
µs [23, 54]. Experimentally, coherence times of more than 100 ms have been
shown with mu-metal magnetic shielding [87] and dressed states [90]. All trapped
ion experiments with coherence times of more than 100 s [22, 24] were
performed with hyperfine qubits at a clock transition [86] and without external
magnetic shielding. Hence 14 with appropriate magnetic shielding, one should be
able to increase the coherence by several orders of magnitude. This results in
coherence times of hours or days and κ values14 greater than 106 . As the main
magnetic field noise in a laboratory environment is from alternating current (AC)
sources, one way to shield against AC magnetic field is using skin-effect in a highly
conducting material surrounding the experiment [91]. Another way is to
encapsulate the experiment in a mu-metal shield [92], which provides shielding
against AC and DC magnetic fluctuations. However, slow magnetic field drifts such
as changes in earth’s magnetic field [93] still penetrate a magnetic shield made
out of a highly conducting material or mu-metal15. Thus, these simple magnetic
shielding schemes will not allow the desired coherence times of hours or days. A
consequence of Meissner effect [94] is that superconductors are perfect
diamagnets and thus perfect magnetic shields. Inside a hollow superconductor,
the magnetic field is constant and shielded from external magnetic fields. When
placing the ion trap (equivalent to the whole quantum computer) in such an
environment, the desired coherence times should be feasible with clock
transitions in hyperfine qubits. In practice, it is not straightforward to define a
certain magnetic field strength inside a superconductor, as required for clock
transitions in hyperfine qubits. During the phase transition into the
superconducting regime, local magnetic flux can get pinned16. To avoid this
pinning, the suggested solution is to have the superconductor undergo the phase
transition in a zero-field environment [95]. For such a cool-down, the experiment
has to be located inside a magnetically shielded room (MSR) [96]. Once the entire
shield is superconducting, external magnetic field changes will no longer be able
to penetrate the shield. Cables, fibers, etc. to operate the Paul trap will have to
enter the superconducting shield through holes to which superconducting tubes
should be attached. The shielding of such superconducting cylinders depends
exponentially on its length (for a given diameter) [97]. Hence, long and thin](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-47-320.jpg)
![48
cylinders are desired for high shielding against the environment. The bias
magnetic field at the position of the ions can be generated by superconducting
coils inside the magnetic shield, as depicted in Fig. 10 a. During the cool-down in a
zero-field environment, the superconducting coils do not contain persistent
current [98]. With additional normally conducting coils, one can generate a
magnetic field inside in the shield, shown in Fig. 10 b. When the superconducting
coils are heated locally, as illustrated in Fig. 10 c, the generated magnetic field can
penetrate the superconducting coils. After they are cooled back down into a
superconducting regime, the magnetic field produced by the normally conducting
coils can be switched off. The resulting persistent current in the superconducting
coils will generate an ultra-stable magnetic field inside the superconducting
shield.
The zero-field environments in MSRs with a residual field of less than 1.5 nT have
been demonstrated [99]. If the pinning of magnetic flux in the superconductor
were to increase the residual magnetic field by a factor of 100, the magnetic field
strength would be on the order of 100 nT. The magnetic field strength for clock
transitions in hyperfine qubits is generated by the superconducting coils inside
the superconducting shield and is on the order of 10 mT [100, 23]. Hence, the
pinned magnetic field in the center of the superconducting coils (at the position
of the ion trap) can only produce a relative offset of 14As previously discussed,
one will only be able to use a small fraction of the stated coherence time, which is
typically a 1/e value of a coherence measure. Although the exact κ value depends
on the logical qubit encoding, a stated coherence time of about 105 s with gate
times of about 10 to 100 µs may lead to κ ≈ 106 . 15A typical value of the DC
attenuation of magnetic field of a mu-metal shield is about 30 dB. 16This local flux
can get pinned to grain boundaries, strains, etc. inside the superconductor which
alters the magnetic field inside the superconductor [95]. The measured magnetic
field strength inside a superconducting cylinder can reach 100 times the
externally applied magnetic field strength. 15 10−5 of the total magne c field,
which leaves hyperfine qubits safely in the regime with only quadratic Zeeman
shift. Such a setup will provide a temporally stable magnetic field to reach the
desired coherence times of hours or days. In general, it is not necessary to
completely eliminate magnetic gradients in trapped ion QC. If the magnetic field
at each storage point is well known, one can calculate the phase evolution of all](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-48-320.jpg)
![49
qubits. However, techniques like decoherence free subspace (DFS) encoding [101]
require the same magnetic field for multiple ions. Therefore, it is desirable but not
necessary to have high homogeneity. Spatial homogeneity is discussed in the
appendix in Appendix A.1 in more detail. 5.3. Local oscillator stability The
transition frequencies of hyperfine transitions are typically on the order of 1-10
GHz [102, 100, 23]. If one wants to achieve coherence times of up to days, a
frequency reference with a stability of about 10−15 will be required. In order to
achieve the required stability of the reference clock, one can sacrifice some ions
of the quantum computer to act as a precise long-term frequency reference.
Although one has to remove some ions from QIP for the clock signal generation,
such a scheme allows stabilizing the local oscillator. It will even enable using the
quantum computer for atomic clock measurements. 5.4. Multiplexing: ion storage
and movement An idling ion string accumulates on the order of 10 quanta/s and
thus about a million phonons during a day of uncooled storage. These high
phonon numbers will cause a melting of the ion crystal and the order in the ion
string will be lost after a refreeze. Hence, ion storage times of hours or days
require sympathetic cooling with a second ion specie
Besides working with two ion species, sympathetic cooling implies that one needs
cooling beams at each storage position. The illumination of each storage zone can
either be accomplished by integrating fibers into the trap [105] or by illuminating
multiple storage zones with a beam parallel to the trap surface, as displayed in
Fig. 11. Integrated fiber optics facilitate cooling of ion strings. However, one fiber
per storage position will complicate the trap design whereas cooling multiple
storage zones with a single beam will simplify the optical setup. These beams
along the surface can even be reused by reflecting the light from one line of
storage zones to the next line of storage zones, similar to the ideas discussed in
reference [106] and shown in Fig. 15 b. One thing that has to be kept in mind
when designing a large-scale quantum computer in a cryogenic environment is
the heat load. Large-scale QC will require thousands of storage sites. If light is
coming from a fiber at every storage site, it will be hard to couple the light back
into fibers to avoid heating the cryostat due to the light absorption. Whereas,
light parallel to the surface cools multiple sites and is easier to couple back into a
fiber. A trap suitable for QIP with thousands of ions will require the control over
thousands of segments and thus over thousands of voltages with digital-to-analog](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-49-320.jpg)
![50
converter (DAC) channels. In order to reduce this hardware demand, one can use
analog multiplexers. By employing such analog switches, one DAC channel can
control multiple segments. An example of how this can be incorporated in ion
movement is shown in Fig. 12. At first, the ion is stored on the left side by
controlling three segment pairs. During the shuttling, one has to control at
maximum four segment pairs. When moving the ion right, the control of an
unused segment pair on the left can be exchanged to control over the next
segment pair on the right17 . Hence, with this multiplexing scheme, it is possible
to move ions in an arbitrarily big segmented trap with DC control over only four
segment pairs and digital multiplexing logic. Furthermore, it is possible to adapt
the voltage ramps for each segment individually which enables the compensation
of stray fields on all parts of the trap
Quantum gates
A major problem with entangling gates which use Coulomb interaction [75, 76],
thus phonons in an ion crystal, is motional heating [109]. A lot of effort has been
made to characterize heating [110], especially its dependence on the distance of
the ion to the surface of the trap, and it has been shown that the heating rate is
reduced in cryogenic environments [111, 112]. Experimentally, heating rates as
low as 0.33 ph/s have been observed in surface traps [113]. Due to sympathetic
cooling in the memory region and short transport times between the quantum 18
memory region and the QALU of less than about 1 ms, heating only affects QIP in
the QALU. The quantum computer based on this quantum von Neumann
architecture for trapped ions has to be operated in a cryogenic environment and,
thus, heating rate should be low enough to allow for fault-tolerant QC.
. RF or optical drive fields RF fields enable qubit operations with the lowest
infidelity in trapped ion systems to date [23]. Entangling operations via Coulomb
interaction require high field gradients due to the low Lamb-Dicke parameter of
RF fields. These high field gradients are typically generated with high RF
amplitudes. If the QALU is surrounded by memory zones, one must protect the
qubits in the quantum memory from the resonant and near-resonant RF fields.
There is research on minimizing RF surrounding the processing zones of traps.](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-50-320.jpg)
![51
However, it is unclear how well this RF field suppression would work for a large-
scale quantum computer with tens of thousands of qubits or more surrounding
the QALU. Experimentally, one has to stabilize the phase of the RF in QALU for
high fidelity operation such that the length between the RF source and the ion
does not fluctuate on a (tens of) micrometer scale. On the other hand, high
fidelity quantum operations can be performed with optical drive fields as well [54,
36]. There, the demonstrated infidelity is about one order of magnitude worse
than with RF fields. However, unwanted fields can be avoided by inhibiting direct
line of sight between the quantum memory and surfaces of the QALU that scatter
light, see the Section 5.5.5 for details. Experimentally, the most challenging part is
amplitude and phase control of the light field at the position of the ion. Given that
optical frequencies are much higher than the RF frequencies, one has to stabilize
the phase of the light with sub-nanometer precision. Suggestions on the phase
stabilization is given in Appendix A.3. Furthermore, in order to avoid long
distances between the quantum memory region and the QALU, the processing
zone will be in the center of the trap. Single ion addressing with laser beams will
require a numerical aperture (NA) of 0.2 or higher for ion-to-ion distances of
about 5 µm. Therefore, the trap needs to be slotted in the region of the QALU to
allow high NA addressing perpendicular to the trap surface. 5.5.3. Physical
requirements for the gate operations So far, this architecture requires (at least)
two ion chains to be loaded into the QALU for QIP, where gate operations are
performed. The type of gates [76, 77, 70, 23] that are executed is defined in the
firmware layer of the architecture. For a full set of quantum operations, single ion
addressing capability is required. As the length of path between the drive field’s
source and the ions should not fluctuate for a stable phase reference, vibration
isolation of the superconducting magnetic shield will be required, e.g. by
suspending the shield with ropes from the vacuum chamber. Please, refer to
Appendix A.2 for more details. With RF gates, the trap can be used as part of the
transmission line which simplifies the setup. For optical gates, light can be guided
via fibers into the magnetic shield and optical alignment in the shield will enable
enough optical access to perform the required gate operations. Furthermore,
vibration isolation will reduce beam pointing instabilities and thus undesired
varying optical crosstalk between the ions. The tight focusing, required for single
ion addressing, results in a high local light intensity at the position of the ion. In
reference [114], the authors state that between 1 and 10 mW optical power is](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-51-320.jpg)
![52
required for single qubit gates with a gate infidelity of 10−4 employing Raman
transitions. Moreover, between 100 mW and 1 W optical power is required for
entangling gates21 using a Gaussian beam with w0 = 20 µm. If all gates in a
quantum von Neumann setup are performed with highly focused Gaussian beams
with w0 ≈ 1 µm, the required total optical power will drop by a factor of 400
compared to their stated values. This lower optical power reduces problems like
bleaching of fibers, which is worse at higher powers. The crosstalk onto
neighboring ions is a coherent process and thus can be eliminated by calibration
and composite pulses [74]. If the crosstalk on all ions is known, one can construct
a pulse sequence that performs all single qubit operations required by the
quantum algorithm and at the same time corrects for the crosstalk [41]. Such
calibration requires precise control over the amplitude of the driving field at the
position of the ion. For operation with RF gates, this implies a clever segment
structure of the trap. For operation with optical gates, beam pointing instabilities
and imperfections in amplitude and timing control must be negligibly small.
Thermal drifts might still cause spatial drifts on time scales of seconds or minutes.
Therefore, it might be necessary to regularly place ”calibration ions” in the QALU
to track drifts of the crosstalk.
In order to protect idling qubits, it is possible to shelve populations from the clock
state to other states in the Zeeman manifold [74] in which the QIP is performed.
With this scheme, gate operations are not resonant with the clock transition in
which quantum information is stored in the quantum memory. However, the
imperfect shelving operations introduce leakage from the qubit states which
needs to be considered in the employed QEC. 5.5.4. Pipelining Since ions which
arrive in the QALU from the quantum memory are only Doppler cooled, they have
to be groundstate-cooled for high fidelity QIP. If cooling and QIP are executed in
the same processing zone of the QALU, the processing cycle will be slowed down
by the required initial cooling. Following the pipelining approach from classical
computer science, one can use separate regions in the processing zone for the
individual tasks required for efficient QIP. These tasks could be: 1. Combining two
(or more) ion strings to a single string 2. Sympathetic Doppler cooling 3.
Sympathetic ground state cooling: e.g. by using electromagnetically-induced-
transparency (EIT) cooling 4. Qubit decoding, e.g. map from a DFS basis back to a
single ion basis 5. Map ions for QIP from clock states, or dressed states, to](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-52-320.jpg)
![54
region22. Thus, the number of processing regions defines the depth of the
pipeline. The parameters of the cooling and processing time have to be chosen
such that they can be synchronized. The time of one execution cycle defines the
speed of the processing. The distance between
the different processing regions should be short so that ion movement does not
increase the execution time of one pipeline step considerably. In the processing
regions, micromotion [115] has to be compensated for effective cooling and QIP.
This will require many independently controlled voltages in the processing zone.
However, in the shuttling regions between the processing regions, micromotion is
not crucial and one can use multiplexing, as shown in Fig. 13, to reduce the
number of DC voltages which need to be controlled in the QALU. In this general
pipelining approach, there are no restrictions on the ion strings processed in the
QALU. In order to keep the vibrational mode structure of the ion strings simple,
one has to limit the length of the ion strings. By choosing the ion string loaded
from the quantum memory such that the qubit ions are surrounded by the
cooling ions, one can detect ion loss during Doppler cooling. For this, one uses a
camera to detect the number and positions of the cooling ions. From the spacing
between the cooling ions, the number of processing ions can be inferred. Ion loss
can be compensated by adding ions to the ion string either in the QALU or in a
special zone outside the QALU. 5.5.5. Trap constraints In order to minimize axial
micromotion (which cannot be compensated), it is imperative to design the trap
in the processing zone as symmetric as possible, e.g. as illustrated in Fig. 16 a and
b. 21 In both the quantum memory and the QALU, the tracks along ions can be
shuttled will form loops. Hence, inter-layer connectivity (vias) will be required for
the fabrication of such trap structures. Modern traps with vias23 typically route
the signal lines underneath the trap surface to the segment. These traps use vias
to connect the actual segments with the routing tracks. This enables placing
ground planes at areas on the trap surface which are not used for electrodes.
These ground planes shield against electric fields from the lower lying routing
layer, thereby, reduce the cross-talk between segments
For the operation with optical gates, stray light that is (near-)resonant to a qubit
transition is a serious problem for the long coherence times required for a
quantum von Neumann architecture. A main source of stray light is light scatter at
the slot, required for QIP with high NA, in the QALU, and it can be minimized by](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-54-320.jpg)
![55
blocking direct line of sight between the quantum memory and the QALU, for
example with walls on the segmented traps, as depicted in Fig. 17. The height of
the walls should be higher than the distance from an ion to the surface of the
trap. These walls should not be perpendicular to the trap surface but under an
angle so that reflections on the wall’s surface reflect the light away from the trap
surface. If the walls are made of a conducting material, they can be grounded and
will have little impact on the trapping potentials. For the operation with RF gates,
blocking of stray fields is not possible. It can only be minimized by clever segment
structures. 5.6. Detection and initialization For QIP with optical gates on ground
state qubits, Raman transitions are incur
porated to couple the quantum states [114]. These transitions are off-resonant
with a typical detuning in the GHz or low THz regime. Because of this large
detuning, a single photon is very unlikely to affect a qubit. Thus, it is safe it
assume that reflections somewhere in the vacuum chamber can be neglected and
it is sufficient to place a wall around the QIP zone in the QALU to shield the
quantum memory from stray light. However, detection requires resonant light
which causes fluorescence which is resonant as well. Furthermore, initialization
produces resonant fluorescence. In the case of resonant photons, even a single
photon can
affect the information in the qubits, and one should try to avoid photons resonant
with a state used for storing quantum information. This problem can be
circumvented by using a second ion species for detection. For this, the state of
the ion to be detected has to be transferred onto the detection ion of a different
species. Entanglement between two ions of different species has been
demonstrated [116]. The swapping operation, illustrated in Fig. 18 a in the circuit
model representation [11], requires only near-resonant driving fields but no
resonant fields. For detection, it transfers the quantum information to another
ion species, while initializing the main qubit for further processing. Therefore,
both state detection and initialization can be performed with ions of the second
ion species and one does not have to worry about stray light resonant to the
qubits in the quantum memory. This implies that initialization fidelity will depend
on the fidelity of entangling operations. In order to increase the initialization
fidelity for qubits which have a quadrupole transition, one can reinitialize the
qubits additionally by optical pumping via the quadrupole transition.](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-55-320.jpg)
![56
High fidelity state detection needs to be performed fast which requires high
photon collection efficiency. For example, in Ca+, the qubit information is usually
stored in the ground state of the ion and, thus, an electron shelving pulse is
required to transfer the population of one qubit state into the D5/2 state. The
D5/2 state has a limited lifetime and thus spontaneous emission causes errors in
the detection. The life-time of the D5/2 state in Ca+ is about 1 s [117] which
means that the detection has to be performed in 10 µs 24 to achieve it with a
detection infidelity of 10−5 . With a sca er rate of about 10 MHz in Ca+, an ion
emits about 100 photons during 10 µs. If one requires 5 clicks on the detector for
reliable detection, one has to collect about 10 % of the photons with a typical
detector efficiency of about 50 %. A collection efficiency of 10 % requires the
detection optics to have NA > 0.6. QEC requires ancilla qubits which have to be
detected to extract information on the occurred errors, and thus the detection
region has to be close to the QALU on the trap. This might limit the optical access
to the QALU. To increase the number of scattered photons in a certain period of
time, one can use the fluorescence of multiple ions by employing Greenberger-
Horne-Zeilinger (GHZ) states [119], as demonstrated in reference [120]. The
circuit representation of this detection scheme can be seen in Fig. 18 b. The input
state |ψi = α |0i + β |1i is transferred onto N ancilla qubits of a second ion species
to generate the GHZ state α |00 · · · 0i + β |11 · · · 1i. With N ancilla qubits, the
count rate increases by a factor of N compared to the detection with just one
ancilla qubit. For detection in the same time interval, the collection efficiency can
be lower by a factor of N compared to the case with one ancilla qubit. It is also
possible to increase the detection fidelity for longer detection times by
performing a majority vote. As an example, if one chooses a detection time of 100
µs for detection of Ca+, this will result in an infidelity of ≈10−4 due to
spontaneous decay. If one chooses 5 ancilla qubits and one can detect how many
ions are bright, 3 qubits will need to decay from the D-state to the S-state for a
wrong state detection. The probability for this to happen is 10−12. Hence, the
overall detection process will more likely be limited by how efficiently one can
generate the GHZ state than by detection itself. Pipelining can also be
incorporated in the detection/initialization zone, as illustrated Fig. 18 c. The
incoming qubits are cooled to the ground state of motion before they are moved
to the swapping zone.](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-56-320.jpg)
![57
There, the CNOT-gates for GHZ state generation and the swap gate are performed
with initialized ancilla qubits of a second ion species. After the swap operation,
the initialized qubits are moved to another initialization zone where one can
compensate the initialization error due to imperfect gates or leakage into other
states during QIP. After the initialization, the ions are shuttled back to other parts
of the trapped ion quantum computer. During the compensation of the
initialization error, the ancilla qubits of the second ion species are moved to a
detection zone where the (GHZ) state is detected. After detection, the ions are
cooled and initialized in separate zones before they can be reused in the swap
zone. Experimentally, the challenge will lie in protecting the quantum information
between the swap and the detection zone from (resonant) stray light of the
cooling and initialization zones. 5.7. Choice of ion species At first, one has to
decide how many species one needs for this architecture. One ion species is
required for the qubit ions. Another ion species is required for sympathetic
cooling. The ions for detection can either be from the same ion species as the ions
for sympathetic cooling, or one can use a third ion species. If one only uses two
ion species, cooling in the memory region and detection have to be pulsed so that
resonant stray fields from the memory region does not affect the quantum state
in the detection zone. Whereas, using three ion species makes the detection zone
independent from the memory region. In the following, the three ion species
architecture will be discussed
Gold has a work function of 5.3 eV [121], which corresponds to 234 nm.
Aluminum has a work function of 4.08 eV [122], which corresponds to 304 nm.
• Mass ratio: for sympathetic cooling the mass ratio of the ion species in the ion
string should be close to 1 [104, 123, 124], so that all modes of a mixed ion crystal
can be efficiently cooled. Experimentally, sympathetic cooling of two-ion crystals
with a mass ratio of 3 has been demonstrated [125].
• Mass: with the same electric field, lighter ions are accelerated faster, which is
advantageous for ion movement. In the same trapping potential, lighter ions have
higher trap frequencies, which allows faster gate operations and less power is
required for the entangling gate operations [114]. The criteria for the choice of
the ion species of the cooling ions are:
• Mass ratio: as described for the qubit ion species.](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-57-320.jpg)
![58
• Wavelength: as described for the qubit ion species.
• No nuclear spin: this simplifies the level structure and the laser system, if one
does not require two beams with GHz detuning from one another. The criteria for
the choice of the ion species of the detection/initialization ions are:
• Mass ratio: as described for the qubit ion species.
• Wavelength: as described for the qubit ion species.
• No nuclear spin: as described for the cooling ion species.
• Long lived D-state: there are several different detection schemes like electron
shelving [126, 127, 128], or using sigma polarized light to cyclically drive a single
transition [61]. Both schemes allow high-fidelity state detection. But in the same
setup, electron shelving with an ion species which has a long lived D5/2 state
usually yields higher fidelity than a detection scheme which is limited by off-
resonant excitations](https://image.slidesharecdn.com/quantumcomputers-210930071209/85/Quantum-computers-58-320.jpg)
Quantum computers
- 1. 1 اﻟدوﻟﯾﮫ اﻟﻌرﺑﯾﮫ اﻷﻛﺎدﯾﻣﯾﺔ اﻟﻣﻌﻠوﻣﺎت ﺗﻘﻧﯾﺔ ﺑﻛﺎﻟورﯾوس :ﻋن ﺑﺣث اﻟﻛﻣوﻣﯾﮫ اﻟﺣواﺳﯾب اﻟﻛرﯾم ﻋوض ﻋﻠﻲ ﻋﻣر ﻣﺻﻌب :اﻟطﺎﻟب إﻋداد :اﻟﺟﺎﻣﻌﻲ اﻟرﻗم 1812018
- 2. 2 اﻟﻣﺣﺗوﯾﺎت ﻓﮭرس اﻟﺻﻔﺣﮫ اﻟﻌﻧوان ﺗﺳﻠﺳل 1 اﻟﻐﻼف ﺻﻔﺣﺔ 1 2 اﻟﻣﺣﺗوﯾﺎت ﻓﮭرس 2 3 اﻟﻣﻘدﻣﮫ 3 5 اﻟﻔﺻل اﻟﻔﯾزﯾﺎء ﻓﻲ اﻟﻛم ﻧظرﯾﺔ ﺗﻌرﯾف اﻻول 4 19 اﻟﻛﻣوﻣﯾﮫ اﻟﺣوﺳﺑﮫ ﺑﻣﺎھﯾﺔ اﻟﺗﻌرﯾف اﻟﺛﺎﻧﻲ اﻟﻔﺻل 5 22 اﻟﻛﻣوﻣﻲ اﻟﺣﺎﺳب اﺟﻠﮭﺎ ﻣن اﻧﺷﺊ اﻟﺗﻲ واﻟﻐﺎﯾﺎت اﻻھداف اﻟﺛﺎﻟث اﻟﻔﺻل 6 41 اﻟﻛﻣوﻣﻲ اﻟﺣﺎﺳب ﻋﻣل اﻟﯾﺔ 7 59 اﻟﻛﻣﻲ اﻟﺣﺎﺳب ﺗواﺟﮫ اﻟﺗﻲ واﻟﺗﺣدﯾﺎت اﻟﻣﺷﻛﻼت 8 60 اﻻﻗﺗراﺣﺎت واﻟﺗوﺻﯾﺎت 9 61 اﻟﻣراﺟﻊ 10
- 3. 3 :اﻟﻣﻘدﻣﺔ - اﻟﻣﻌﻠوﻣﺎﺗﯾﺔ ﻣﺟﺎل ﻓﻲ اﻟﻘﺎدﻣﺔ اﻟﺛورة أن اﻟﺧﺑراء ﯾرى Informatics اﻟﻛﻣوﻣﯾﺔ اﻟﺣوﺳﺑﺔ ﺳﺗﻘودھﺎ Quantum Computing ﻣﻌﺎﻟﺟﺔ ﻋﻠﻰ ھﺎﺋﻠﺔ ﻗدرة ﻣن اﻟﺗﻛﻧوﻟوﺟﯾﺎ ھذه ﺳﺗوﻓره ﻟﻣﺎ ؛ إﻧﺟﺎزھﺎ ﻋن ﻋﺟزت ﻟطﺎﻟﻣﺎ ،ﻣﮭﺎم وإﻧﺟﺎز ،اﻟﻣﻌﻠوﻣﺎت ﻓﻣﺎ .اﻟﺗﻘﻠﯾدﯾﺔ اﻟﺣواﺳﯾب ھﻲ اﻟﺣوﺳﺑﺔ ﺗطوﯾرھﺎ؟ ﺗﻣﻧﻊ اﻟﺗﻲ اﻟﻌواﺋﻖ أھم وﻣﺎ اﺳﺗﺧداﻣﺎﺗﮭﺎ؟ وﻣﺎ اﻟﻛﻣوﻣﯾﺔ؟ ﺗﺻﻣﯾم ﻓﻲ ﺟدﯾدة طرﯾﻘﺔ ،ﺑﺑﺳﺎطﺔ ،اﻟﻛﻣوﻣﻲ اﻟﺣﺳﺎب أو اﻟﻛﻣﯾﺔ اﻟﺣوﺳﺑﺔ أو ،اﻟﻛﻣوﻣﯾﺔ واﻟﺣوﺳﺑﺔ اﻟدﻗﯾﻘﺔ اﻟﻣﻌﺎﻟﺟﺎت Microprocessors اﻟ اﻟﻛﻣﯾﺔ اﻟﻔﯾزﯾﺎء ﻗواﻧﯾن ﻋﻠﻰ ًاداﻋﺗﻣﺎ ؛ ﻋﻠﻰ ﺗﻧطﺑﻖ ﺗﻲ :وھﻲ ﻗﯾم؛ ﺑﺛﻼث اﻟﻣﻌﻠوﻣﺎت ﺑﺗﺧزﯾن ﺗﺳﻣﺢ اﻟﻘواﻧﯾن وھذه .()اﻟﻧﺎﻧوﯾﺔ اﻟﺻﻐر ﻣﺗﻧﺎھﯾﺔ اﻷﺟﺳﺎم وﺟود ﻓﺳﻧﻔﺗرض ،ھذه اﻟﺗﺧزﯾن طرﯾﻘﺔ وﻟﺗﺑﺳﯾط .ﻧﻔﺳﮫ اﻟوﻗت ﻓﻲ ﻛﻼھﻣﺎ أو ،واﺣد أو ،ﺻﻔر واﻟﺣﺎﻟﺔ .واﺣد آن ﻓﻲ اﻟﺣﺎﻟﺗﯾن ﻓﻲ وإﻣﺎ ،ﻣﺿﻲء ﻏﯾر وإﻣﺎ ،ًﺎﺋﻣﺿﯾ إﻣﺎ ﻓﺳﯾﻛون ،ﻣﺻﺑﺎح اﻷﺧﯾرة اﻟﻛﻣوﻣﻲ ﺑﺎﻟﺗراﻛب اﻟﻔﯾزﯾﺎء ﻓﻲ ُﺳﻣﻰﺗ اﻟﺗﺧزﯾن طرﯾﻘﺔ ﻣن Quantum superposition ، اﻟﺟﺳﯾم ﻣﻼﺣظﺔ ﺧﻼل ﻣن ،أﺣدھﻣﺎ ﺣﺎﻟﺔ ﻋﻠﻰ ﻟﻠﺗﻌرف ﻛﻣﯾﺎ ﺟﺳﯾﻣﯾن رﺑط إﻣﻛﺎﻧﯾﺔ ﻋﻠﻰ وﺗﻧص .ﺑﻌﯾدة ﻣﺳﺎﻓﺔ ﻋﻠﻰ ﻛﺎن وإن ،اﻵﺧر اﻟﺑﺗﺎت ﻋﻠﯾﮫ ُطﻠﻖﯾ ﻣﺎ ﺗﺳﺗﺧدم ،ھدﻓﮭﺎ اﻟﻛﻣوﻣﯾﺔ اﻟﺣواﺳﯾب وﻟﺗﺣﻘﻖ اﻟﻛﻣوﻣﯾﺔ Quantum bits اًاﺧﺗﺻﺎر أو » ﻛﯾوﺑت « Qubit .اﻟﺗﻘﻠﯾدﯾﺔ اﻟﺣﺎﺳﺑﺎت ﻓﻲ ﻣﺛﻠﮭﺎ ﻋن ﻣﺧﺗﻠف ﺑﺷﻛل ﺗﻌﻣل واﻟﺗﻲ ، اﻟﺗﻘﻠﯾدﯾﺔ اﻟﺣواﺳﯾب ﻣن أﺳرع ُﮫﯾﺟﻌﻠ ﻓﮭذا ،ﻣﺗزاﻣن ﺑﺷﻛل ﻣﻌﺎﻟﺟﺗﮭﺎ ﯾﺳﺗطﯾﻊ اﻟﻛﻣوﻣﻲ اﻟﺣﺎﺳب وﻷن اﻟﺗﻘﻠﯾدﯾﺔ اﻟﺣوﺳﺑﺔ ﻓﻲ اﻟﺣﺎﺳوب أن ﻧﺟد ،اﻟﻣﻘﺎﺑل وﻓﻲ .اﻟﻣرات ﺑﻣﻼﯾﯾن ،ﺧوارزﻣﯾﺎت ﻣن ﯾﺗﻛون ﻣﻧطﻘﯾﺔ وﺑواﺑﺎت ،وﺳﺟﻼت ،وﺑﺗﺎت اﻟﺦ ,,, . )وھﻲ اﻟﺗراﻧزﺳﺗرات أن اﻟﺗﻛﻧوﻟوﺟﯾﺎ ھذه ﺗطوﯾر إﻟﻰ اﻟﺳﻌﻲ ﺧﻠف ﺗﻘف اﻟﺗﻲ اﻟرﺋﯾﺳﯾﺔ اﻷﺳﺑﺎب أﺣد ﺣد أﻗﺻﻰ إﻟﻰ ﺳﺗﺻل (اﻻﻋﺗﯾﺎدي اﻟﺣﺎﺳوب داﺧل واﻟﻣﻌﺎﻟﺟﺔ اﻟﺗﺧزﯾن ﻋن اﻟﻣﺳﺋوﻟﺔ اﻟوﺣدات ﺗ ﯾﻣﻛن ﻻ ،ﺛم وﻣن اﻟﺻﻐر؛ ﻣن ﻣﻣﻛن طﺑﯾﻖ » ﻗﺎﻧون ﻣور « ﻣﺿﺎﻋﻔﺔ إﻣﻛﺎﻧﯾﺔ ﻋﻠﻰ ﯾﻧص اﻟذي اﻟﺣﺎﺳوب ﯾﻌﺗﻣد ،ذﻟك ﻋﻠﻰ ﻋﻼوة .اﻟﻌﺎدة ﺟرت ﻛﻣﺎ اًﺷﮭر ﻋﺷر ﺛﻣﺎﻧﯾﺔ ﻛل اﻟﺣﺎﺳوﺑﯾﺔ اﻟﻘدرة ﻧﻣوذج ﺑﺧﻼف ﻟﻠﺣوﺳﺑﺔ آﺧر ﻧﻣوذﺟًﺎ اﻟﻛﻣوﻣﻲ » ﺗورﻧﺞ آﻟﺔ « ،اﻟﻛﻣوﻣﯾﺔ ﺗورﻧﺞ آﻟﺔ ﻧﻣوذج وھو ؛ اﻟﻛوﻧﻲ اﻟﻛﻣوﻣﻲ اﻟﺣﺎﺳوب ًﺎﻧأﺣﯾﺎ ﻋﻠﯾﮫ ﯾطﻠﻖ ﻣﺎ أو . ﻓﻲ اﻟﺳﺎﺑﻖ ﻓﻲ ًﺎﻧﻣﻣﻛ ﺣﻠﮭﺎ ﯾﻛن ﻟم اﻟﺗﻲ اﻟﻣﻌﺿﻼت ﻣن اًﻛﺛﯾر ﺗﺣل أن اﻟﻛﻣوﻣﯾﺔ اﻟﺣوﺳﺑﺔ وﺑﺈﻣﻛﺎن ،اﻟﻣﺎل ﻗطﺎع ﻣﺟﺎل ﻓﻲ وأﻣﺎ .واﻟﻔﺿﺎء ،اﻷﻏذﯾﺔ وإﻧﺗﺎج ،اﻟﻣواد وﻋﻠم ،اﻟﻛﯾﻣﯾﺎء :ﻣﺛل ،ﻣﺟﺎﻻت وﯾ .اﻟﻣﻧﺎخ ﺑﺗﻐﯾرات اﻟﺗﻧﺑؤ ﺣﺗﻰ اﻟﻣﺎﻟﯾﺔ اﻷوراق ﺑﺳوق اﻟﺗﻧﺑؤ ﻓﻲ ﻛﺑﯾر دور ﻟﮭﺎ ﻓﺳﯾﻛون اﻵن ﺟري ﯾدﻋﻰ ﻣﺎ ﺑﻧﺎء » اﻟﻛﻣوﻣﻲ اﻹﻧﺗرﻧت « إذ ﻟﻼﺧﺗراق؛ ﻗﺎﺑل ﻏﯾر ﺳﯾﻛون ﺑﺄﻧﮫ اﻟﺑﺎﺣﺛون ﯾﺻﻔﮫ اﻟذي ، .ﻟﻠﺑﯾﺎﻧﺎت ﻧﻘل ﯾوﺟد ﻻ ،ﺟوﺟل ﻣﺛل اﻟﻌﻣﻼﻗﺔ اﻟﺗﻛﻧوﻟوﺟﯾﺎ ﺷرﻛﺎت ﻓﺈن ،اﻟﺗﻛﻧوﻟوﺟﯾﺎ ھذه ﺑﮭﺎ ُدﺗﻌ اﻟﺗﻲ اﻟﮭﺎﺋﻠﺔ ﻟﻠﻔرص ا ًﻧظر ﺗﺗﻧ ،اﻟﻧﺎﺷﺋﺔ اﻟﺷرﻛﺎت ﺣﺗﻰ ،وإﻧﺗل ،وأﺑل ،إم ﺑﻲ وآي ھذه ﻋﻠﻰ ﻟﻼﺳﺗﺣواذ ﺑﯾﻧﮭﺎ ﻓﯾﻣﺎ ﺎﻓس اﺳم ﻋﻠﯾﮫ ُطﻠﻖ أ ﻛﻣﻲ ﻣﻌﺎﻟﺞ ﺗﺻﻧﯾﻊ ﻓﻲ ﺟوﺟل ﺷرﻛﺔ ﻧﺟﺣت وﻗد .اﻟﺗﻛﻧوﻟوﺟﯾﺎ » ﺑراﯾﺳﺗﻠﻛون «
- 4. 4 Bristlecone ﻋﻠﯾﮫ أطﻠﻘت ﻣﻌﺎﻟﺞ ﺗﺻﻧﯾﻊ ﻓﻲ إﻧﺗل ﺷرﻛﺔ ﻧﺟﺣت ﺣﯾن ﻓﻲ ،ًﺎﺗﻛﯾوﺑ ﺧﻣﺳﯾن ﺑﻘدرة اﺳم » ﻟﯾك ﺗﺎﻧﺟل « Tangle Lake. إم ﺑﻲ آي ﺷرﻛﺔ أن إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ وھذا أﻋﻠﻧت ﻗد ﻛﺎﻧت .اﻟﻛﻣﻲ اﻟﺗﻔوق ﯾﺣﻘﻖ ﻣﻌﺎﻟﺞ ﺗﺻﻧﯾﻊ إﻟﻰ ﺗوﺻﻠﮭﺎ ﻋن اﻟﺳﺎﺑﻖ ﻓﻲ ﻗﺑل ًﺎﻧﻣﻣﻛ اًأﻣر اﻷﺳواق ﻓﻲ وﻋرﺿﮫ ﻛﻣﻲ ﺣﺎﺳوب ﺗﺻﻧﯾﻊ إﻟﻰ اﻟﺗوﺻل ﯾﺻﺑﺢ ﻓﻠن ،ھذا وﻣﻊ ﺗوﻓﯾر ﺿرورة ً ﻣﺛﻼ ﺗﺗطﻠب ﻓﮭﻲ .ﻟﻠﻌﻣل ﻣﻌﯾﻧﺔ ﺷروطًﺎ وﺗﺗطﻠب ﻟﻠﻐﺎﯾﺔ ﺣﺳﺎﺳﺔ ﻓﮭﻲ ﺳﻧوات؛ ﺑﺿﻊ ﻟﺣﺎﺳوب وﻣﻼﺋم ﻣﺳﺗﻘر ﻣﺣﯾط ،اﻟﺛﺎﻧﻲ اﻟﺳﺑب وأﻣﺎ .اﻟﻣطﻠﻖ اﻟﺻﻔر ﻣن ﺣرارﺗﮫ درﺟﺔ ﺗﻘﺗرب ﻛﻣﻲ ﻋدد زﯾﺎدة ﻣﻊ ﺳﻌﺗﮫ زادت ﻓﻛﻠﻣﺎ ﻟﻠﺣﺎﺳوب؛ اﻟﻛﻣﻲ اﻻﺳﺗﻘرار ﻋﻠﻰ اﻟﻣﺣﺎﻓظﺔ ﻛﯾﻔﯾﺔ ﻓﻲ ﻓﯾﻛﻣن ،وﻟذا .اﺳﺗﻘراره اﻧﺧﻔض ،اﻟﻛﯾوﺑﺗﺎت ﯾﻌﻣل ﻟﻠ اﻟﺑﺎﺣﺛون إﻟﻰ اﻟطرﯾﻖ ﻓﻲ اﻟﺗﺣدﯾﺎت ھذه ﻋﻠﻰ ﺗﻐﻠب .اﻟﻛﺎﻣل اﻟﺗﻧﻔﯾذ ان ﻧﺳﺗطﯾﻊ وﻟﻛﻲ ﻟﺷرح رﺋﯾﺳﻲ ﻣدﺧل ﻣن ﻻﺑد دﻗﯾﻖ ﺑﺷﻛل اﻟﻛﻣﻲ ﺑﺎﻟﺣﺎﺳب ﻧﻌﻧﯾﮫ ﻣﺎﻟذي ﻧﻔﮭم .اﻻﺳﺎﺳﻲ ﺑﻣﺳﺗواھﺎ اﻟﻔﯾزﯾﺎء ﻓﻲ اﻟﻛم ﻧظرﯾﺔ
- 5. 5 اﻷول اﻟﻔﺻل اﻟﻔﯾزﯾﺎء ﻓﻲ اﻟﻛم ﻧظرﯾﺔ ﺗﻌرﯾف أﻧﮭﺎ ﻋﻠﻰ اﻟﻛم ﻧظرﯾﺔ ﺗﻌرف ،اﻟﻌﺷرﯾن اﻟﻘرن ﻓﻲ ظﮭرت اﻟﺗﻲ اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟﻧظرﯾﺎت ﻣن ﻣﺟﻣوﻋﺔ ﻋﻠﻰ اﻟظواھر ﻟﺗﻔﺳﯾر وذﻟك اﻟﺧﺎﺻﯾﺔ ﺑﯾن دﻣﺟت وﻗد اﻟذرﯾﺔ دون واﻟﺟﺳﯾﻣﺎت اﻟذرة ﻣﺳﺗوى اﻟﻣوﺟﺔ ازدواﺟﯾﺔ ﻣﺻطﻠﺢ ﻟﯾظﮭر اﻟﻣوﺟﯾﺔ واﻟﺧﺎﺻﯾﺔ اﻟﺟﺳﯾﻣﯾﺔ - ﻣﯾﻛﺎﻧﯾﻛﺎ ﺗﺻﺑﺢ وﺑﮭذا ،اﻟﺟﺳﯾم اﻟﻣﯾﻛﺎﻧﯾﻛﺎ ﻋﻠﻰ ﺗطﺑﻖ ً أﯾﺿﺎ أﻧﮭﺎ ﻛﻣﺎ اﻟذري اﻟﻣﺳﺗوى ﻋﻠﻰ اﻟﻔﯾزﯾﺎﺋﻲ اﻟﺗﻔﺳﯾر ﻋن ﻣﺳﺋوﻟﺔ اﻟﻛم ﻋ ﺗﺄﺛﯾرھﺎ ﻻﺗظﮭر وﻟﻛن اﻟﻛﻼﺳﯾﻛﯾﺔ ﻟﻠﻔﯾزﯾﺎء ﺗﻌﻣﯾم ھﻲ اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻟذﻟك ،اﻟﻣﺳﺗوى ھذا ﻠﻰ إﻟﻰ ﯾﻌود اﻟﻛم ﺑﻣﯾﻛﺎﻧﯾﻛﺎ ﺗﺳﻣﯾﺗﮭﺎ .واﻟﻌﺎدي اﻟذري اﻟﻣﺳﺗوﯾﯾن ﻋﻠﻰ ﺗطﺑﯾﻘﮭﺎ ﻹﻣﻛﺎﻧﯾﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ ّﺔﯾأھﻣ اﻟﻛم ﺗﺑﺎدﻟﮭﺎ ﯾﻣﻛن اﻟطﺎﻗﺔ ﻣن ﻛﻣّﯾﺔ أﺻﻐر ﻟوﺻف ﯾﺳﺗﺧدم ﻓﯾزﯾﺎﺋﻲ ﻣﺻطﻠﺢ )وھو ﺑﻧﺎﺋﮭﺎ ﻓﻲ ﻟﻺﺷﺎ وﯾﺳﺗﺧدم ،اﻟﺟﺳﯾﻣﺎت ﺑﯾن وﻟﯾس ،ﻣﺗﻘطﻊ ﺑﺷﻛل ﺗﻧﺑﻌث اﻟﺗﻲ اﻟﻣﺣددة اﻟطﺎﻗﺔ ﻛﻣﯾﺎت إﻟﻰ رة ﻟﻣﯾﻛﺎﻧﯾﻛﺎ ﻛﻣرادﻓﺎت اﻟﻛﻣﯾﺔ واﻟﻧظرﯾﺔ اﻟﻛم ﻓﯾزﯾﺎء ﻣﺻطﻠﺣﻲ ﯾﺳﺗﺧدم ﻣﺎ ﻛﺛﯾرا .(ﻣﺳﺗﻣر ﺑﺷﻛل اﻟﻧﺳﺑﯾﺔ ﻏﯾر اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ إﻟﻰ ﻟﻺﺷﺎرة اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻣﺻطﻠﺢ ﯾﺳﺗﺧدﻣون ّﺄباﻟﻛﺗ وﺑﻌض .اﻟﻛم اﻟﻘرن ﺑداﯾﺎت ﻓﻲ اﻟﻛم ﻧظرﯾﺔ أﺗت اﻟﻔﯾزﯾﺎء ﺗﺳﺗطﻊ ﻟم إﺷﻛﺎﻟﯾﺎت ﻟﺣل اﻟﻧﺳﺑﯾﺔ اﻟﻧظرﯾﺔ ﻣﺛل اﻟﻌﺷرﯾن ﯾﻠﻲ ﻣﺎ ﻓﻲ اﻹﺷﻛﺎﻟﯾﺎت ھذه ﺗﻠﺧﯾص وﯾﻣﻛن ،ﺗﻔﺳﯾرھﺎ ﻓﻲ اﻟﻛﻼﺳﯾﻛﯾﺔ : ﻛﻣﺟﻣوﻋﺗﻧﺎ إﻋﺗﺑﺎرھﺎ ﯾﺗم ﻛﺎن ﺣﯾث ،اﻟذرة ﻟﺷﻛل ﺣﯾﻧﮭﺎ اﻟﻣوﺿوع اﻟﺗﺻور ﺑﯾن اﻟﺗﻧﺎﺳﻖ ﻋدم .ﺣوﻟﮭﺎ اﻹﻟﻛﺗروﻧﺎت ودوران اﻟوﺳط ﻓﻲ اﻟﻧواة ﺑﺗﻣرﻛز اﻟﺷﻣﺳﯾﺔ اﻟﺷﺣﻧﺎت وﺑﺈﻏﻔﺎل أﻧﮫ ﻏﯾر ﺗﺑدد ﻛﮭروﻣﻐﻧﺎطﯾﺳﯾﺔ طﺎﻗﺔ إﻟﻰ ﻟﻺﻟﻛﺗروﻧﺎت اﻟﺳرﯾﻊ اﻟدوران ﻧﺗﯾﺟﺔ ﺗﺗﺣول اﻟﺗﻲ اﻟﻛﮭرﺑﺎﺋﯾﺔ ﯾؤدي ﻣﻣﺎ طﺎﻗﺗﮭﺎ ﻟﻧﻔﺎذ اﻟﺛﺎﻧﯾﺔ ﻣن ﺟزء ﻓﻲ ﺑﺎﻟﻧواة ﺗﺻطدم ﯾﺟﻌﻠﮭﺎ ﻣﻣﺎ اﻹﻟﻛﺗروﻧﺎت طﺎﻗﺔ ﺗﻌطﻲ ﺟدﯾدة ﻟﻧظرﯾﺔ اﻟﺣﺎﺟﮫ ﺟﺎءت ﻟذا واﻗﻌﻲ ﻏﯾر وھذا ،اﻟذرة إﻧﮭﯾﺎر إﻟﻰ آﺧر ﻧﻣودﺟﺎ اﻟذرة ﻟﺗﻛوﯾن . ﺟﻣﯾﻊ ﺗﻐطﻲ أن ﯾﺟب اﻟذري اﻟطﯾف أﻟوان أن ًأﯾﺿﺎ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻧظرﯾﺔ ﺗﻌﺗﺑر اﻷطوال اﻟﻣوﺟﯾﺔ ﻟﻛ ،اﻟﺷدة ﺑﻧﻔس ﺗﺻدر ﺣﯾث ﺑﺷدة ذﻟك ﺗﻧﺎﻗض اﻟﺗﺟرﯾﺑﯾﺔ اﻟﻧﺗﺎﺋﺞ أن اﻟﻔﯾزﯾﺎﺋﯾﯾن ﻻﺣظ ن ًﺟدا وﻣﺣددة ﺧﺎﺻﺔ ﻣوﺟﯾﺔ أطوال ﺿوﺋﯾﺔ(ﻟﮭﺎ ً)ﻣوﺟﺎتأطﯾﺎﻓﺎ اﻟﻣﺧﺗﻠﻔﺔ اﻟذرات . إﺷﻛﺎﻟﯾﺔ ﻧﺗﺄﻣل ﻋﻧدﻣﺎ أﺧرى ﻣﺷﻛﻠﺔ ﺗﻧﺷﺄ اﻷﺳود اﻟﺟﺳم “ اﻟﺳﺎﻗط اﻹﺷﻌﺎع ﻛﺎﻣل ﯾﻣﺗص ﺟﺳم وھو آﺧرى ﻣرة ﺑﺎﻟﻛﺎﻣل إﺻداره ﻟﯾﻌﯾد ﻋﻠﯾﮫ ” اﻟﻔﯾزﯾﺎء إﻟﻰ اﻟﻣﺳﺗﻧدة اﻟﻣﺣﺎوﻻت ﻛل ﻓﺷﻠت ﺣﯾث إﺷﻌﺎع ﻣﻧﺣﻧﻰ ﺗﻔﺳﯾر ﻓﻲ اﻟﺗﻘﻠﯾدﯾﺔ اﻹﺣﺻﺎﺋﯾﺔ اﻷﺳود اﻟﺟﺳم وھذا اﻟﻌﺎﻟﯾﺔ اﻟﺗرددات ﻋﻧد ً ﺧﺻوﺻﺎ ﺑﺎﺳم ًﻻﺣﻘﺎ ﻋرف ﻣﺎ اﻟﺑﻧﻔﺳﺟﯾﺔ ﻓوق اﻟﻛﺎرﺛﺔ ﻗواﻧﯾﻧ أن ﻟﻠﻌﻠﻣﺎء ظﮭر وﺑﮭذا ﺎﻟدﯾﻧﺎﻣﯾﻛﺎ اﻟﺣرارﯾﺔ اﻟظﺎھره ھذه ﺗﻔﺳﯾر ﻋن ﻋﺎﺟزة أﺻﺑﺣت . ﻋﺎم ﻓﻲ 1900 إﻗﺗرح ﺑﻼﻧك ﻣﺎﻛس ﺑﻔ اﻟظﺎھره ھذه ﻟﺗﻔﺳﯾر ﺣل أن إﻓﺗرض ﻓﻘد ﺛورﯾﺔ ﻛرة ﺳﻣﯾت ﻣﺗﻘطﻌﺔ ﻛﻣﯾﺎت ﺷﻛل ﻋﻠﻰ ﺑل ﻣﺗﺻل ﻣﺳﺗﻣر ﺑﺷﻛل ﻻﺗﺻدر اﻟﻛﮭروﻣﻐﻧﺎطﯾﺳﯾﺔ اﻟﻣوﺟﺎت وﻓﻖ اﻷﺟﺳﺎم ﺑﯾن ﺗﺑﺎدﻟﮫ ﯾﻣﻛن اﻟطﺎﻗﺔ ﻣن ﻣﻌﯾن ﻣﻘدار أﺻﻐر اﻟﻛم ﯾﻌﺗﺑر ﺣﯾث ﻛﻣﺎت ﺗرد د ﻣﻌﯾن اﻟﻛم طﺎﻗﺔ وﺗرﺗﺑط ﺑﺗردد ﻟﮫ اﻟﻣراﻓﻖ اﻹﺷﻌﺎع
- 6. 6 E=hv ﺗﻌﺗﺑر ﺣﯾث E اﻟﺻﺎدر اﻟطﺎﻗﮫ ﻛم ﻋن V , اﻹﺷﻌﺎع ﺗردد ﻋن H ﺑﻼﻧك ﺛﺎﺑت ﻋن زاد ﻛﻠﻣﺎ أﻧﮫ إﻋﺗﺑﺎر ﺗم اﻹﻓﺗراض وﺑﮭذا ﺗردد ﻣن اﻟﺻﺎدر اﻹﺷﻌﺎع اﻷﺳود اﻟﺟﺳم ﻋد ﻗﻠت ﻛﻠﻣﺎ د إﻟﻰ اﻟوﺻول ﻋﻧد ًﺟدا ﻛﺑﯾر ﺑﺷﻛل ﺷدﺗﮫ إﻧﺧﻔﺎض ﯾﻌﻧﻲ ﻣﻣﺎ اﻹﺷﻌﺎع ھذ ﻛﻣﺎت ﺗردد اﻟﻣوﺟﺎت ﻓوق اﻟﺑﻧﻔﺳﺟﯾﺔ ﻟظﺎھرة ﻣﻘﺑول ﺗﻔﺳﯾر ﻗدﻣت ﻗد ﺑﻼﻧك ﻓروض ﺗﻛون وﺑﮭذا اﻷﺳود اﻟﺟﺳم إﺷﻌﺎع وﻓﺳر أﻋﺗﺑرﺗﮫ ﻣﺎ اﻟﺗﻘﻠﯾدﯾﺔ اﻟﻔﯾزﯾﺎء ﻛﺎرﺛﺔ ﺑﻧﻔﺳﺟﯾﺔ ﻓوق . طﺑﯾﻌﺔ ﻓﮭم ﻣن أﺧرى اﺷﻛﺎﻟﯾﺎت ﺗﺄﺗﻲ اﻟﺿوء ﯾؤﻛد ﺣﯾن ﻓﻔﻲ ﻧﯾوﺗن ﺟﺳﯾﻣﯾﺔ اﻟﺿوء طﺑﯾﻌﺔ أن )ﻓﮭو أن ﻧﺟد ،اﻟﺗﺟﺎرب ﻣن اﻟﻌدﯾد ذﻟك ﻓﻲ وﺗؤﯾده ،ﺻﻐﯾرة ﺟﺳﯾﻣﺎت ﻣن ﻣؤﻟف ﯾوﻧﻎ ﺗوﻣﺎس ()ﻋﺎﻟم أن ﯾؤﻛد اﻟﺿوء وﺗؤﻛد ﻣوﺟﯾﺔ طﺑﯾﻌﺔ ذو ﯾوﻧﻎ ﺷﻘﻲ ﺗﺟرﺑﺔ ﺣول ﺗداﺧل وﺣﯾود اﻟﺿوء ﻋﺎم وﻓﻲ ،اﻟﻣوﺟﯾﺔ اﻟطﺑﯾﻌﺔ ھذه 1924 إﻗﺗرح ﺑروي دي ﻟوﯾس اﻟﻣﺎدة ﺟﺳﯾﻣﺎت إﻟﻰ ﯾﻧظر أن ﺑﻼﻧك ﻣﻌﺎدﻟﺔ ﺗﺷﺎﺑﮫ ﻣﻌﺎدﻟﺔ ً ﻣﻘﺗرﺣﺎ أﺣﯾﺎﻧﺎ ًﻣوﺟﯾﺎ ﺳﻠوﻛﺎ ﺗﺳﻠك ﺟﺳﯾﻣﺎت أﻧﮭﺎ ﻋﻠﻰ أﯾﺿﺎ وذراﺗﮭﺎ : ﺣﯾث : λ, اﻟﻣوﺟﺔ طول و ، p اﻟﺣرﻛﺔ ﻛﻣﯾﺔ . اﻟﻣوﺟﯾﺔ واﻟطﺑﯾﻌﯾﺔ اﻟﺟﺳﯾﻣﺔ اﻟطﺑﯾﻌﺔ ﻓﯾﮭﺎ ﺗﺗداﺧل ﻟﻠﻌﺎﻟم ﺟدﯾدة ﺻورة ﻣﻼﻣﺢ ﺗﺗﺿﺢ ھﻧﺎ ﺑدأت اﻟﻛم ﻣﯾﻛﺎﻧﯾك ﻟظﮭور اﻟطرﯾﻖ ﻣﮭد ﻣﺎ ھذا وﻛﺎن ﺑﯾﻧﮭﻣﺎ اﻟﺗﻣﯾﯾز ﯾﺻﻌب ﺑﺣﯾث اﻟدﻗﯾﻘﺔ ﻟﻠﺟﺳﯾﻣﺎت ﻧﯾﻠز وﺿﻊ ﻋﻧدﻣﺎ ﺑور اﻟذرة ﺗرﻛﯾب ﺗﺻور ﻋن ﻧظرﯾﺔ ﻻﺗﺳﻣﺢ اﻟﺗﻲ اﻟزاوي ﻟﻼﻧدﻓﺎع ﻗﯾم ﺑﺄﺧذ ﻟﻠﻘﯾﻣﺔ اﻟﺻﺣﯾﺣﺔ اﻟﻣﺿﺎﻋﻔﺎت ﺳوى : ﺗﻌﺒﺮ ﺣﯿﺚ ، اﻟﺰاوي اﻻﻧﺪﻓﺎع ﻗﯿﻢ ﻋﻦ ﺻﺤﯿﺢ ﻋﺪد (3,2,1,…) ﯾﻣﻛن اﻟﻣﺳﺗﻘرة ﻟﻠطﺎﻗﺔ ﻣﺳﺗوﯾﺎت ظﮭرت ھﻛذا و ﺛﺑﺎت ﻣﻔﺳرة ﻓﯾﮭﺎ اﻟداﺋرة اﻻﻟﻛﺗروﻧﺎت وﺿﻊ ﻋﺎم ﻓﻲ .اﻟﺑداﯾﺔ ﺳوى ﯾﻛن ﻟم ھذا ﻟﻛن ،ﻟﻠذرات اﻟطﯾﻔﯾﺔ واﻟﺧطوط اﻟﺗرﻛﯾب 1927 اﻟﻌﺎﻟم ﻗﺎم اﻷﻟﻣﺎﻧﻲ ھﺎﯾزﻧﺑرغ ﺑﺗﻘدﯾم اﻟﺗﺄﻛد ﻋدم ﻣﺑدأ ﻣوﺿﻊ ﺗﺣدﯾد ﻋﻠﻰ ﻗدرﺗﻧﺎ ﻋدم ﻋﻠﻰ ﯾﻧص اﻟذي ھذه ﻛﺎﻧت .ﻣﺗﻧﺎھﯾﺔ وﺑدﻗﺔ واﺣد ﺑﺂن اﻟﻛﻣﯾﺔ اﻟﺟﺳﯾﻣﺎت وﺳرﻋﺔ اﻟﺗﻲ اﻟﺻدﻣﺎت ﻣن ﺳﻠﺳﻠﺔ ﺑداﯾﺔ ﺳﺎدت اﻟﺗﻲ اﻵﻟﯾﺔ اﻟﻣﯾﻛﺎﻧﯾﻛﯾﺔ اﻟﺻورة ﻛل ﻣﻌﮭﺎ ﺗﺣطﻣت واﻟﺗﻲ ﻟﻠﻌﺎﻟم اﻟﻛﻼﺳﯾﻛﯾﺔ ﻧظرﺗﻧﺎ ﺗﻠﻘﺗﮭﺎ ﻓﯾزﯾﺎء إﻧﺗﺻﺎرات ﺑﻌد اﻟﻌﺎﻟم ﺣول ﻧﯾوﺗن اﻟﻘر ﻓﻲ اﻟﻣدوﯾﺔ ﻗﺎم .اﻟﺳﺎﺑﻘﯾن ﻧﯾن ھﺎﯾزﻧﺑرغ ﺑﺻﯾﺎﻏﺔ ﺑﺻﯾﺎﻏﺔ اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻗواﻋد اﻟﻣﺻﻔوﻓﺎت ﺟﺑر ﺳﻧﺔ اﻟﻣﺻﻔوﻓﺎت ﺑﻣﯾﻛﺎﻧﯾﻛﺎ ذﻟك ﺑﻌد ﻋرف ﻓﯾﻣﺎ
- 7. 7 1926 ظﮭر ، ﺷرودﻧﺟر ﺗطور ﺗﺑﯾن اﻟﺗﻲ اﻟﺷﮭﯾرة اﻟﻣوﺟﯾﺔ ﺑﻣﻌﺎدﻟﺗﮫ ﻣوﺟﺔ داﻟﺔ اﻟﻛﻣﻲ اﻟﺟﺳﯾم رﻏم ﻟﻛن ،اﻟﻣوﺟﯾﺔ ﺑﺎﻟﻣﯾﻛﺎﻧﯾﻛﺎ اﻟﺻﯾﺎﻏﺔ ﺗﻠك وﻋرﻓت اﻟزﻣن ﻣﻊ ﺑﯾن اﻟﻌﻣﯾﻖ اﻟظﺎھري اﻹﺧﺗﻼف ﺑول دﻓﻊ ﻣﺎ ھذا ،ﻣﺗطﺎﺑﻘﺔ ﻛﺎﻧت ﻧﺗﺎﺋﺟﮭﻣﺎ ﻓﺎن اﻟﺻﯾﺎﻏﺗﯾن دﯾراك اطﺎر ﻓﻲ ﻟﺗوﺣﯾدھﻣﺎ ذﻟك ﺑﻌد ﻋرف ﺷﺎﻣل اﻟﺗﺣوﯾل ﺑﻧظرﯾﺔ . ﻟﻠذرة ﺑور ﻧﻣوذج : ﺗﺟﺎرب أظﮭرت رذرﻓورد أن اﻟذرة اﻟﺷﺣﻧﺔ ﻣوﺟب ﻣرﻛز ﻣن ﺗﺗﻛون ﯾﺳﻣﻰ ﻧواة وإﻟﻛﺗروﻧﺎت اﻟﻌﻠﻣﺎء ﺗﺟﺎرب أن ﺣﯾن ﻓﻲ .ﻛﺑﯾرة ﺑﺳرﻋﺎت ﺣوﻟﮭﺎ ﺗدور ﺣول أطﯾﺎف ﻣﺗﻘطﻌﺔ اﻷطﯾﺎف ھذه أن ﻣﺗوﻗﻊ ﻏﯾر ﺑﺷﻛل أوﺿﺣت اﻹﻣﺗﺻﺎص و اﻹﻧﺑﻌﺎث ﺗﻔﺳﯾرھﺎ اﻟذرة ﻋن رذرﻓورد ﺗﺻور ﯾﺳﺗطﻊ ﻟم اﻟﺗﻲ اﻟﻣﺷﺎﻛل أﺣد ﻛﺎﻧت وﻗد ،ﻣﺳﺗﻣرة وﻟﯾﺳت ﻗدم أن إﻟﻰ ﺑور ﻧﯾﻠز ﻋﺎم 1913 ﻓﻲ اﻟظﺎھرة ﻟﮭذه ﺗﻔﺳﯾره ﺑور ﻧﻣوذج . ﻛﺎﻧت أھم ﻓرﺿﯾﺔ ﻟﺑور ﻓﯾﮭﺎ ﯾﻛون ﻣدارات ﻓﻲ اﻟدوران ﺳوى ﯾﻣﻛﻧﮭﺎ ﻻ اﻹﻟﻛﺗروﻧﺎت أن ھﻲ ﺳو اﻟزﻣن ﻣن ﻓﺗرة ﻣرور ﺑﻌد ﻓﺈﻧﮫ وإﻻ ﯾﺷﻊ ﻻ أي ﻣﺳﺗﻘر اﻹﻟﻛﺗرون وﯾﺳﻘط طﺎﻗﺗﮫ ﻛل ﯾﻔﻘد ف طﺎﻗﺗﮫ أن أي ﻣﻌﯾﻧﺔ طﺎﻗﺔ ﻣﺳﺗوﯾﺎت إﻻ ﯾﺣﺗل أن ﯾﻣﻛﻧﮫ ﻻ اﻹﻟﻛﺗرون أن ﯾﻌﻧﻲ ھذا .اﻟﻧواة ﻓﻲ إﻟﻰ ﯾﻧﺗﻘل ﺳوف اﻹﻟﻛﺗرون ﻓﺈن اﻟذرة إﺛﺎرة ﺣﺎﻟﺔ ﻓﻲ .ﻣﻛﻣﻣﺔ طﺎﻗﺔ ﻣﺳﺗوى ﺑﻌد ﯾﻌود ﺛم أﻋﻠﻰ ﯾطﻠﻖ اﻟﻌودة وأﺛﻧﺎء اﻷﺻﻠﻲ طﺎﻗﺗﮫ ﻣﺳﺗوى إﻟﻰ اﻟﺛﺎﻧﯾﺔ ﻣن ﺟزء ﻓوﺗون ًﺗﻣﺎﻣﺎ ﻣﺳﺎوﯾﺔ طﺎﻗﺔ ذو ﻧﺟ وﻗد ،اﻟﻣﺳﺗوﯾﯾن طﺎﻗﺗﻲ ﺑﯾن ﻟﻠﻔرق اﻟﻣﺗﻘطﻊ اﻟذرات طﯾف ﺗﻔﺳﯾر ﻓﻲ اﻟﻔروض ھذه ﺣت ﻧظرﯾﺔ ﻟﺗﺛﺑت اﻟذرة ﻓﻲ اﻹﻟﻛﺗروﻧﺎت ﺣرﻛﺔ ﻋﻠﻰ اﻟﻛم ﻧظرﯾﺔ ﻓروض طﺑﻖ أن ﺑﻌد ،()اﻟﺧطﻲ وﺟﺳﯾﻣﺎﺗﮭﺎ اﻟذرة ظواھر ﺗﻔﺳﯾر ﻓﻲ ﻧﺟﺎﺣﮭﺎ اﻟﻛم . اﻟﻣوﺟﻲ اﻟﺗﺻور ﺣﺳب اﻟﻛم ﻧظرﯾﺔ : دﻗﯾﻘﺔ ﻗﯾﺎﺳﺎت ﺑﺗﻘدﯾم اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﺻﯾﺎﻏﺎت ﺗﻘوم ﻻ اﻟﻣﻘﯾﺳﺔ اﻟﺟﺳﯾﻣﺎت ﻟﺧواص ﺗﻌطﻲ ﺑل أي ﺗﻧﺑؤات ﻣﺣﺗﻣﻠﺔ ﺗوزﯾﻌﺎت ﻓﺎﻟﺣﺎﻟﺔ ،ﻟﻠﺟﺳﯾم ﻣﻌﯾﻧﺔ ﺧﺎﺻﯾﺔ ﺗﺄﺧذھﺎ أن ﯾﻣﻛن اﻟﺗﻲ اﻟﻘﯾم ﻟﺟﻣﯾﻊ ﻟﻠﻘﯾﺎس اﻟﻘﺎﺑﻠﺔ ﻟﺧﺻﺎﺋﺻﮫ إﺣﺗﻣﺎﻻت ﺗﺗﺿﻣن ﻟﻠﺟﺳﯾم اﻟﻛﻣﯾﺔ ﻣﺛل : اﻟﻣوﺿﻊ وﻛﻣﯾﺔ اﻟﺣرﻛﺔ واﻟطﺎﻗﺔ اﻟزاوﯾﺔ اﻟﺣرﻛﺔ وﻛﻣﯾﺔ ﻣﺳﺗﻣرة ﺗواﺑﻊ ﺑﻘﯾﻣﮭﺎ ﺗﺷﻛل أن ﯾﻣﻛن اﻟﺧﺻﺎﺋص ھذه ، اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﺗﻌطﯾك ﻻ وﺑﮭذا ،اﻟطﺎﻗﺔ ﻣﺛل ﻣﺗﻘطﻌﺔ ﺗواﺑﻊ ﺗﺷﻛل أن وﯾﻣﻛن اﻟﻣوﺿﻊ ﻣﺛل ﻣﺳﺎرات ﺗﺣدد ﺣﯾث اﻟﻔراغ ﻣن ﻧﻘطﺔ أي ﻓﻲ وﺟوده اﺣﺗﻣﺎل ﺗﻌطﯾك إﻧﻣﺎ ﻟﺟﺳﯾم اﻟدﻗﯾﻖ اﻟﻣوﺿﻊ ﯾ ﻓﻲ وﺟوده إﻣﻛﺎﻧﯾﺔ ﺗﻠﻐﻲ ﻻ ﻟﻛﻧﮭﺎ (ﻏﯾره ﻣن أﻛﺑر إﺣﺗﻣﺎﻟﯾﺗﮫ )أي ًﻛﺑﯾرا اﻟﺟﺳﯾم ﺗواﺟد ﻓﯾﮭﺎ ﻛون اﻷﺧرى اﻟﺧﺻﺎﺋص ﺟﻣﯾﻊ ﺑﺧﺻوص اﻟﻛﻼم ﻧﻔس ﻗول وﯾﻣﻛﻧك اﻟﻔراغ ﻣن ﻧﻘطﺔ أي . ھذه ﺗدﻋﻰ ,اﻟﺧﺻﺎﺋص ﻟﺑﻌض دﻗﯾﻘﺔ ﻗﯾم ﺗﺣدﯾد ﺗﺗﺿﻣن ﻣﻌﯾﻧﺔ ﺣﺎﻻت ھﻧﺎك ﺗﺑﻘﻰ ﻟﻛن اﻟﺣﺎﻻت اﻟﺧﺎﺻﺔ ﺑﺎﻟﺣﺎﻻت . وﺟود ﻟﻧﻔﺗرض ﻣﻘﯾد ﻏﯾر ﺟﺳﯾم ذات ﺑﻣوﺟﺔ اﻟﻛﻣﯾﺔ ﺣﺎﻟﺗﮫ ﺗﻣﺛﯾل إﻣﻛﺎﻧﯾﺔ ﯾﻌﻧﻲ ﻣﻣﺎ ،اﻟﺣرﻛﺔ ﺣر ﻓﻲ اﻟﺟﺳم ﻗﯾﺎﺳﺎت ،اﻟﻣوﺟﺔ ﺑداﻟﺔ ﻧدﻋوھﺎ اﻟﻔراغ ﻛﺎﻣل ﻋﻠﻰ وﺗﻣﺗد ﻣﻌﯾن ﻏﯾر اﻓﺗراﺿﻲ ﺷﻛل ھ أﺧذت ﻓﻠو ،ﺣرﻛﺗﮫ وﻛﻣﯾﺔ ﻣوﺿﻌﮫ ﺗﺗﺿﻣن اﻟﺣﺎﻟﺔ ذه اﻟﻣوﺟﺔ داﻟﺔ ﻣوﺿﻊ ﻓﻲ ًﺟدا ﻋﺎﻟﯾﺔ ﺳﻌﺔ ﻓﮭذ اﻷﺧرى اﻟﻣواﺿﻊ ﻛل ﻓﻲ ()ﺻﻔر ﻣﻌدوﻣﺔ ﻗﯾﻣﮭﺎ وﻛﺎﻧت ()س ﻟﻠﻣوﺿﻊ ﺧﺎﺻﺔ ﺣﺎﻟﺔ ﯾﻌﺗﺑر ا اﻟﻘدرة ﻋدم ﯾﺗﺿﻣن ھذا أن ﻧﻧﺳﻰ أﻻ ﯾﺟب ذاﺗﮫ اﻟوﻗت ﻓﻲ ،((ﺑدﻗﺔ اﻟﺟﺳﯾم ﻣوﻗﻊ ﺑﮭﺎ ))ﯾﺗﺣدد
- 8. 8 ھذه ﻣﺛل ﺗوﺟد ﻻ اﻟﺣﻘﯾﻘﺔ ﻓﻲ ﻟﻛن ،اﻟﺗﺄﻛد ﻋدم ﻣﺑدأ ﺣﺳب ﺣرﻛﺗﮫ ﻛﻣﯾﺔ ﻗﯾﻣﺔ ﺗﺣدﯾد ﻋﻠﻰ إطﻼﻗﺎ اﻟﺧﺻ ﻣن أي ﻗﯾﺎس ﺑﻌﻣﻠﯾﺔ ﺗدﺧﻠﻧﺎ ﻟﻛن اﻟﻣﻘﺎﺳﺔ ﻟﻠﺧواص اﻟﺧﺎﺻﺔ اﻟﺣﺎﻻت ﺗﺎﺑﻊ ﯾﺣول ﺎﺋص ﯾدﻋﻰ ﻣﺎ وھذا اﻟﺧﺎﺻﯾﺔ ﻟﮭذه ﺧﺎﺻﺔ ﺣﺎﻟﺔ إﻟﻰ اﻷﺻﻠﻲ ﺷﻛﻠﮭﺎ ﻣن ﻣوﺟﺗﮫ اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ إﻧﮭﯾﺎر . دﻗﺔ أﻛﺛر ﺑﺷﻛل اﻷﻣر ﻟوﺻف : ًوﺣﯾدا ًﻛﻣﯾﺎ ًﺟﺳﯾﻣﺎ ﻟﻧﻔﺗرض ﺗﺣدﯾد ﯾﻠزﻣﻧﺎ ﻛﻼﺳﯾﻛﯾﺔ ﻧظر وﺟﮭﺔ ﻣن : ﻣوﺿﻊ وﺳرﻋﺔ اﻟﺟﺳﯾم اﻟﺧﺻﺎﺋص ھذه ﻟﻣﺛل وﺟود ﻻ أن ﻓﺗﻌﺗﺑر ﻟﺷرودﻧﻐر اﻟﻣوﺟﯾﺔ ﺑﺎﻟﺻﯾﺎﻏﺔ اﻟﻛﻣﯾﺔ اﻟﻧظرﯾﺔ أﻣﺎ ﻣﺛل اﻟﻣﻘﺎﺳﺔ : وﻛل ﻣﺣﺗﻣل ﻣوﻗﻊ ھو ﻟﻠﺟﺳﯾم ﻣﺗﺎح ﻣوﺿﻊ ﻓﻛل اﻟطﺎﻗﺔ ،اﻟﺣرﻛﺔ ﻛﻣﯾﺔ ،اﻟﻣوﺿﻊ ﻓﻲ اﺧﺗﻼﻓﺎت ھﻲ وأﺧرى ﻗﯾﻣﺔ ﺑﯾن واﻹﺧﺗﻼﻓﺎت ،ًأﯾﺿﺎ ﻣﻣﻛﻧﺔ ﻗﯾﻣﺔ ھﻲ ﻟﻠطﺎﻗﺔ ﻣﺗﺎﺣﺔ ﻗﯾﻣﺔ ﻓﻲ اﻟﺟﺳﯾم وﺟود ﺳﻌﺔ ﺗدﻋﻰ ﻣﻌﯾﻧﺔ ﻗﯾﻣﺔ (ﻣوﻗﻊ)س ﻛل ﻓﻲ اﻟداﻟﺔ ﻟﮭذه ﯾﻛون ﺣﯾث .اﻹﺣﺗﻣﺎﻻت و إﺣﺗﻣﺎل ﻓﯾﻛون ،()س اﻟﻣوﺿﻊ وﺟود ﺳﻌﺔ ﻣرﺑﻊ ﺑﺑﺳﺎطﺔ ھو ()س اﻟﻣوﻗﻊ ﻓﻲ اﻟﺟﺳﯾم ﺟود إﺟراء إﻟﻰ ھﻧﺎ ﻓﺳﻧﺿطر اﻟﺟﺳﯾم ﺣرﻛﺔ ﻛﻣﯾﺔ ﺣﺎﻟﺔ ﻋن أﻣﺎ ،()س اﻟﻣوﻗﻊ ﻓﻲ اﻟﺟﺳﯾم ﺗﺣﻠﯾ ل ﺗواﻓﻘﻲ اﻟﻣوﺟﺔ ﻟداﻟﺔ ﺗواﻓﻘﯾﺎت وﻣﺟﻣوﻋﺔ ﺣرﻛﺔ ﻟﻛﻣﯾﺔ اﻟﻣﻣﻛﻧﺔ اﻟﺣﺎﻻت ﯾﻣﺛل اﻟﻣوﺟﺔ ھذه ﻋﻠﻰ ﻧﺣﺻل وﺑﮭذا،اﻟﺟﺳﯾم اﻟﺣرﻛﺔ ﻟﻛﻣﯾﺎت إﻓﺗراﺿﻲ ﻓراغ ﺿﻣن اﻟﺣرﻛﺔ ﻟﻛﻣﯾﺔ ﻣوﺟﯾﺔ داﻟﺔ ﻗﻠﯾﻠﺔ أو اﻟﺣرﻛﺔ ﻟﻛﻣﯾﺔ ﻛﺑﯾرة ﺣﺎﻟﺔ ﻋﻠﻰ ﯾدل ﻣﻣﺎ اﻟﺗراص ﺷدﯾد إﻣﺎ أﻣواج ﺑﺷﻛل ًﻏﺎﻟﺑﺎ ﺗﻛون اﻟﺣرﻛﺔ ﻟﻛﻣﯾﺔ ﺻﻐﯾرة ﺣﺎﻻت ﯾﻣﺛل وھذا اﻟﺗراص . ﺗﻘوم ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ اﻟدﻗﯾﻖ ﺑﺎﻟﺗﻧﺑؤ ﺗﻘوم ﻓﮭﻲ وﺑﮭذا اﻟزﻣن ﻣﻊ اﻟﻣوﺟﺔ داﻟﺔ ﺗطور ﺑوﺻف اﻟﻣوﺟﯾﺔ اﻟداﻻت ﺗطور ﯾﺷرح ًﺛﺎﺑﺗﺎ ﻗﺎﻧوﻧﺎ ﻟﻧﺎ ﺗﻘدم وﺑﮭذا ﻟﺣظﺔ أي ﻓﻲ ﻟﻠﺟﺳﯾم اﻟﻛﻣﯾﺔ ﻟﻠﺣﺎﻻت اﻟد ھذه ،دﻗﺔ ﺑﻛل ﻓداﻟﺔ ،اﻟﻣﺣﺗﻣﻠﺔ اﻟﺣرﻛﺔ وﻛﻣﯾﺔ اﻟﻣوﺿﻊ ﻗﯾم ﺟﻣﯾﻊ داﺧﻠﮭﺎ ﻓﻲ ﺗﻛون اﻟﺗﻲ اﻻت ﺑﺳرﻋﺔ اﻟزﻣن ﻣﻊ ﺳﯾﺗﺣرك اﻟﻣوﺟﯾﺔ اﻟﺣزﻣﺔ ﻣرﻛز ﺑﺄن ﺗﺗﻧﺑﺄ اﻟﺣرﻛﺔ ﺣر ﻟﻠﺟﺳﯾم اﻟﺗﺎﺑﻌﺔ اﻟﻣوﺟﺔ ﺗوﺟد ،ﻣﺣدد ﻏﯾر ﻓﺄﻛﺛر أﻛﺛر اﻟﻣوﺿﻊ ﻟﯾﺻﺑﺢ اﻟﻣوﺟﺔ إﻣﺗداد ﺳﯾزداد اﻟوﻗت ﻧﻔس ﻓﻲ و ﺛﺎﺑﺗﺔ اﻟﻛ اﻷﻧظﻣﺔ ﺑﻌض ًأﯾﺿﺎ ذرة ﻓﻲ اﻹﻟﻛﺗرون ﻛﺣﺎﻟﺔ اﻟزﻣن ﻣﻊ ًﺗﻐﯾرا ﺗﺑدي ﻻ اﻟﺗﻲ اﻟﻣﺳﺗﻘرة ﻣﯾﺔ ﺗواﺟد ﯾﻛون داﺋرﯾﺔ ﻣﺳﺗﻘرة إﺣﺗﻣﺎﻟﯾﺔ ﻛﻣوﺟﺔ اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻓﻲ ﯾﺻور واﻟذي اﻟﮭﯾدروﺟﯾن ﻋن إﺑﺗﻌدﻧﺎ ﻛﻠﻣﺎ ًﺗدرﯾﺟﯾﺎ اﻹﺣﺗﻣﺎل ﯾﻘل ﺣﯾن ﻓﻲ اﻟﻧواة ﻣن ﻣﻌﯾن ﺑﻌد ﺿﻣن ًﻛﺑﯾرا اﻹﻟﻛﺗرون ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ ﺗطرح ،اﻟﻧواة ھذا )ﯾدﻋﻰ اﻟﻣوﺟﯾﺔ ﻟﻠداﻟﺔ ًﺣﺗﻣﯾﺎ ًﺗطورا إذن اﻟﺗطور ﺑﺎﻟﺗطور U) ﻟﺣظﺔ أي ﻓﻲ اﻟﻔراغ ﻧﻘﺎط ﺟﻣﯾﻊ ﻓﻲ اﻟداﻟﺔ ﻗﯾم ﺑدﻗﺔ ﺗﺣدد ﻓﮭﻲ ﻟﻛن ،زﻣﻧﯾﺔ اﻟﺧﺻﺎﺋص إﺣدى ﻟﺗﺣدﯾد اﻟﻘﯾﺎس ﻋﻣﻠﯾﺔ ﻓﻲ اﻟﺗدﺧل ﻣن ﺗﻧﺷﺄ اﻟﻛم ﻟﻣﯾﻛﺎﻧﯾﻛﺎ اﻹﺣﺗﻣﺎﻟﯾﺔ اﻟطﺑﯾﻌﺔ ﯾﺣﺻل ﻋﻧدﺋذ ﻟﻠﺟﺳﯾم اﻟﻣﻘﺎﺳﺔ اﻟﺗطور R ﻣن ًأﯾﺎ اﻟﻣﻘﺎﺳﺔ اﻟﺧﺎﺻﯾﺔ ﺑﻣوﺟﺑﮫ ﻓﺗﺄﺧذ إﺣﺗﻣﺎﻟﻲ اﻟﻐﯾر إﺣﺗﻣﺎﻟﮭﺎ ﻗﯾﻣﺔ ﺣﺳب ﻟﮭﺎ اﻟﻣﺗﺎﺣﺔ اﻟﻘﯾم . اﻟﻧظرﯾﺔ ﻧﺗﺎﺋﺞ : إﻧﻣﺎ ﻛﻣوﻣﻲ ﺟﺳﯾم أو ﻛﻣوﻣﯾﺔ ﺟﻣﻠﺔ ﻗﯾﺎس أو رﺻد ﺑﻧﺗﯾﺟﺔ ً دﻗﯾﻘﺎ ًﺗﻧﺑؤا اﻟﻛم ﻣﯾﻛﺎﻧﯾك ﺗﻌطﯾﻧﺎ ﻻ واﻟﻣﺧﺗﻠﻔﺔ اﻟﻣﻣﻛﻧﺔ اﻟﻧﺗﺎﺋﺞ ﻣن ﻣﺟﻣوﻋﺔ ﺑﺈﻋطﺎء ﺗﻛﺗﻔﻲ ﻻ ﻛﻣﺎ .ﻣﻌﯾن وﺟود اﺣﺗﻣﺎل ﻣﻧﮭﺎ ﻟﻛل اﻟرﺻد ﻧﺗﯾﺟﺔ اﻟطﺑﯾﻌﺔ ھذه ﯾﻌﺗﺑر ﻓﮭو ﻣوﺟﯾﺔ أو ﺟﺳﯾﻣﯾﺔ ﻛﺎﻧت ان اﻟﺟﺳﯾم طﺑﯾﻌﺔ ﺗﺣدﯾد ﯾﺳﺗطﯾﻊ ﺗﮭﺗم وﻋﻧدﻣﺎ اﻟﺧواص ﺗﻠك ﺗرﺻد ﻟﻠﺟﻣﻠﺔ اﻟﻣوﺟﯾﺔ ﻟﻠﺧﺎﺻﯾﺔ اھﺗﻣﺎﻣك ﺗوﺟﮫ ﻓﻌﻧدﻣﺎ واﻟﻘﯾﺎس ﺟﺳﯾم ﺑﺷﻛل اﻟﺟﻣﻠﺔ ﺗﺑدو اﻟﺟﺳﯾﻣﯾﺔ ﺑﺎﻟﺧواص .
- 9. 9 ھذه ظﮭرت ﻣﺎ أول ازد اﻟﻣوﺟﺔ واﺟﯾﺔ – اﻟﺟﺳﯾم ﻓﻲ اﻟﺿوﺋﯾﺔ ﯾوﻧﻎ ﺗﺟرﺑﺔ ﻓﺎﺳﺗﺧدام ،اﻟﺷﮭﯾرة )اﻟﺗﻲ اﻟﺟﺳﯾﻣﯾﺔ اﻟﺧﺎﺻﯾﺔ ﯾؤﻛد ﻛﺎن اﻟﺿوء ﻟﻣرور واﺣد ﺛﻘب (اﻟﻔوﺗون دﻋﻲ ﺑﻣﺎ ﺑﻌد ﻓﯾﻣﺎ ﺗﺟﻠت ﻛﺎن اﻟﺿوء اﻧﻌراج .واﻟﻣظﻠﻣﺔ اﻟﻣﺿﯾﺋﺔ اﻟﺗداﺧل ﻣﻧﺎطﻖ ﻟظﮭور ﯾؤدي ﺛﻘﺑﯾن ﻓﺗﺢ ﻛﺎن ﺣﯾن ﻓﻲ ﻣﺎﻛس وﺗﻔﺳﯾر اﻟذرات أطﯾﺎف أﻛدت ﺣﯾن ﻓﻲ اﻟﻣوﺟﯾﺔ اﻟﺿوء طﺑﯾﻌﺔ ﻋﻠﻰ ًأﯾﺿﺎ ًواﺿﺣﺎ ًدﻟﯾﻼ ﻣﺗﺟﺎﻧﺳ ﻣﺗﻘطﻌﺔ ﻛﻣﯾﺎت ﺑﺷﻛل ﺗﺻدر طﺎﻗﺔ ﻋن ﻋﺑﺎرة اﻟﺿوء ﺑﺄن ﻟﮭﺎ ﺑﻼﻧك اﻟﻛﻣوم ﺗدﻋﻰ ﺔ ﻟﻠﺿوء اﻟﺟﺳﯾﻣﯾﺔ اﻟطﺑﯾﻌﺔ (اﻟﻛﮭرﺿوﺋﻲ اﻟﻣﻔﻌول ﺗﺟرﺑﺔ ﻓﻲ ﺑﺎﻟﻔوﺗوﻧﺎت اﻟﻛﻣوم ﺗﻠك )وﺗﻣﺛﻠت . ﺑﺎﺗﺟﺎه اﻟﻣﺛﻧوي اﻟﺗﺻور ھذا ﻟﯾﻣددا ﻟﮭﺎﯾزﻧﺑرغ اﻻرﺗﯾﺎب وﻣﺑدأ ﺑروﻏﻠﻲ دي ﻋﻼﻗﺔ ذﻟك ﺑﻌد أﺗت ﻛ اﻷﺟﺳﺎم ﺗداﺧل ﻋن اﻟﺣدﯾث اﻟﻣﻣﻛن ﻣن وأﺻﺑﺢ اﻟذرﯾﺔ وﺗﺣت اﻟذرﯾﺔ اﻟﺟﺳﯾﻣﺎت ﺟﻣﯾﻊ ﻣﺎ ﺑﮭﺎ اﺳﺗﺧدم ﯾوﻧﻎ ﻟﺗﺟرﺑﺔ ًﺗﻣﺎﻣﺎ ﻣﺷﺎﺑﮭﺔ ﺗﺟرﺑﺔ أﺟرﯾت ﻓﻘد ،اﻷﻣواج ﺗداﺧل ﻋن اﻟﺣدﯾث إﻟﻛﺗروﻧﯾﺔ ﺷدة ذات ﻣﻧﺎطﻖ ﻋﻠﻰ ﺑﺎﻟﻣﻘﺎﺑل وﺣﺻﻠﻧﺎ اﻟﺿوﺋﯾﺔ اﻟﻔوﺗوﻧﺎت ﻣن ًﺑدﻻ اﻹﻟﻛﺗروﻧﺎت ﺗﺗﺻرف اﻟﻔوﺗوﻧﺎت ﻛﻣﺎ اﻻﻟﻛﺗروﻧﺎت أن اﻟﺗﺄﻛﯾد ﻋزز وھذا اﻻﻟﻛﺗروﻧﺎت ﻋﻠﻰ ﻣﺣرﻣﺔ وﻣﻧﺎطﻖ وﺟﺳﯾم ﻛﻣوﺟﺔ ﻟﯾﺳت اﻟﻛﻣوﻣﯾﺔ اﻟﺟﻣل ﻛل ﻓﺈن اﻟﻛم ﻟﻣﯾﻛﺎﻧﯾك ﻛوﺑﻧﮭﺎﺟن ﺗﻔﺳﯾر اﻋﺗﻣدﻧﺎ وإذا .ًﻣﻌﺎ اﻟرﺻد ﻋﻣﻠﯾﺔ ﺗوﺟﮫ ﺣﺳب ﺟﺳﯾم أو ﻛﻣوﺟﺔ ﻧﻔﺳﮭﺎ ﻋن ﺗﻌﺑر ﻣوﺟﯾﺔ داﻟﺔ إﻧﻣﺎ ﺟﺳﯾم وﻻ ﻣوﺟﺔ ﻻ واﻟﻘﯾﺎس اﻟﺑﺷري . واﻟزﻣن اﻟطﺎﻗﺔ ﻓﻲ اﻟﺗﺄﻛد ﻋدم ﻣﺑدأ : ﺗﻘ ﻋﻠﻰ ﻟﮭﺎﯾزﻧﺑرج اﻟﺗﺄﻛد ﻋدم ﻣﺑدأ دور ﯾﻘﺗﺻر ﻻ اﻟﻣوﺿﻊ ﺗﺣدﯾد ﻓﻲ اﻟﻣﻣﻛﻧﺔ اﻟدﻗﺔ ﻣﻘدار ﯾﯾد ًﻣﺛﻼ اﻟﻔوﺗون ﻓطﺎﻗﺔ ،واﻟزﻣن ﻛﺎﻟطﺎﻗﺔ اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟﺧﺻﺎﺋص ﻛﺎﻓﺔ إﻟﻰ ﯾﺗﻌداه ﺑل اﻟﺣرﻛﺔ وﻛﻣﯾﺔ ﺑﺗﺣدﯾد ﺗﺗﺣدد اﻟﺗردد ﻟﻛن اﻟﺿوء أﻣواج ﻋد ﯾﺗطﻠب اﻟﺗردد ھذا ﺗﺣدﯾد اﻹھﺗزازات ﻓﺗرات ﻓﻲ ﻹﻧﺟﺎ زﻣﻧﯾﺔ ﻓﺗرة أﺻﻐر ﯾﻣﺛل اﻟذي ،اﻟﻣوﺟﺔ إھﺗزاز زﻣن ﻣﺿﺎﻋﻔﺎت ﻣن زﻣﻧﯾﺔ إھﺗزاز ز زﻣﻧﯾﺔ ﻓﺗرات وإﺳﺗﺧدام اﻟﺗردد ﻟﺗﺣدﯾد ﻣطﻠوﺑﺔ اﻟزﻣن ﻟﻘﯾﺎس ﺣدود ھﻧﺎك ﺑﺎﻟﺗﺎﻟﻲ ،واﺣد ﺿوﺋﻲ ﻋدم ﻋﻼﻗﺔ ﯾﻧﺷﻲء ﻣﻣﺎ ،ﻣﺣددة ﻏﯾر اﻟﻔوﺗون طﺎﻗﺔ ﯾﺟﻌل اﻟﺿوء ﻣوﺟﺔ إھﺗزاز زﻣن ﻣن أﺻﻐر ﻗﺻﯾرة إﺛﺎرة ﻓﺈﺣداث اﻷطﯾﺎف ظﺎھرة ﻓﻲ اﻟﻌﻼﻗﺔ ھذه ﺗﺗﺟﻠﻰ ،واﻟزﻣن اﻟطﺎﻗﺔ ﺑﯾن ﺟدﯾدة دﻗﺔ اﻟ إﻟﯨ اﻻﻟﻛﺗروﻧﺎت ﺑﻌض ﻧﻘل إﻟﻰ ﯾؤدي اﻟذرات ﻣن ﻣﺗﻣﺎﺛﻠﺔ ﻟﻣﺟﻣوﻋﺔ ﻣدة طﺎﻗﺔ ﻣﺳﺗوﯾﺎت أﻋﻠﻰ ﻋﻠﻰ ﻧﺣﺻل ﺑﺎﻟﺗﺎﻟﻲ (اﻟزﻣﻧﯾﺔ اﻟﻔﺗرة ﻗﺻر )ﺑﺳﺑب ﻣﺣددة ﻏﯾر ﻟﻛن طﯾف ﻓﻲ ﻣﺗﻧوع ﺿوﺋﻲ اﻟﺑﻧﻔﺳﺟﯾﺔ ﻓوق اﻟﻣوﺟﺎت إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ اﻟﺳﺑﻌﺔ ﺑﺄﻟواﻧﮫ اﻟﻣرﺋﻲ اﻟطﯾف )ﯾﻐطﻲ اﻟﻣوﺟﯾﺔ أطواﻟﮫ ﺗﺳﻣﺢ طوﯾﻠﺔ زﻣﻧﯾﺔ ﻟﻔﺗرات ﻟذرات إﺛﺎرة ﺑﻌﻣﻠﯾﺔ ﻧﻘوم ﻋﻧدﻣﺎ ﺑﺎﻟﻣﻘﺎﺑل ،(اﻟﺣﻣراء وﺗﺣت ﺑﻛون اﻟطﺎﻗﺔ اﻟﻣﺳﺗوﯾﺎت ﻋﻠﻰ ﻧﺣﺻل وﺑﺎﻟﺗﺎﻟﻲ ,ﻣﺣددة اﻟﻣﺛﺎرة ﻟﻼﻟﻛﺗروﻧﺎت طﯾف ﺧطوط ذو ﺗﻌﻛس ﻣﻌﯾﻧﺔ ﻣوﺟﯾﺔ اﻟذرات ﻟﺗﻠك اﻟﻣدارﯾﺔ اﻟﺑﻧﯾﺔ . ،ًﺟدا ﻗﺻﯾرة زﻣﻧﯾﺔ ﻓﺗرات ﻓﻲ اﻟطﺎﻗﺔ ﺣﻔظ ﻗﺎﻧون ﺗﻌطﯾل ﻋﻠﻰ ﯾﻌﻣل ﻗد اﻹﺳﺗﻧﺗﺎج ھذا ﻣﺛل زﻣﻧﯾﺔ ﻣدة ﺧﻼل ﯾﻌﯾده أن ﺑﺷرط طﺎﻗﺔ ﻗرض ﻋﻠﻰ اﻟﺣﺻول اﻟﻛﻣﻲ ﻟﻠﻧظﺎم ﯾﻣﻛن أﺧرى ﺑﺻﯾﺎﻏﺔ ﺗﺗﺣدد ،ًﺟدا ﻗﺻﯾرة ﻓﻲ إﻋﺎدﺗﮫ وﺟﺑت اﻟطﺎﻗﺔ ﻣﻘدار إزداد ﻓﻛﻠﻣﺎ اﻟطﺎﻗﺔ ﺑﻛﻣﯾﺔ اﻟطﺎﻗﺔ اﻟﻘرض ﻣدة اﻟﻧﻔﻖ ﺗﺄﺛﯾر ،اﻟذرات ﺑﺗﺄﺛﯾر اﻟﺿوء )ﺗﺷﺗت :ﻣﺛل اﻟﻣﮭﻣﺔ اﻟﻧﺗﺎﺋﺞ ﻣن ﻋدد ھذا ﻋن وﯾﻧﺗﺞ أﻗل زﻣن وﯾﻔﺳر ،طﺎﻗﺔ ﻗروض طرﯾﻖ ﻋن ﻣرﺗﻔﻌﺔ طﺎﻗﺔ ﻟﺣواﺟز اﻟﻛﻣﯾﺔ اﻟﻧظم ﺑﻌض إﺟﺗﯾﺎز ﻋﻣﻠﯾﺔ وھﻲ
- 10. 10 اﻟﻌد ﻗدرة اﻟﻧﻔﻖ ﺗﺄﺛﯾر ﻋدم رﻏم اﻟطﺎﻗﺔ اﻟﺣواﺟز ﺑﻌض إﺟﺗﯾﺎز ﻋﻠﻰ اﻟﻛﻣﯾﺔ اﻟﺟﺳﯾﻣﺎت ﻣن ﯾد اﻟﻣﺷﻌﺔ اﻟﻌﻧﺎﺻر ظﺎھرة ﺗﻔﺳﯾر ﻓﻲ ھذا وﯾدﺧل ،إﺣﺗﻣﺎﻟﯾﺔ ﺑﻧﺳب اﻟﻼزﻣﺔ ﻟﻠطﺎﻗﺔ إﻣﺗﻼﻛﮭﺎ . اﻟﻛم ﻟﻣﯾﻛﺎﻧﯾك دﯾراك ﺻﯾﺎﻏﺔ : ﺑول ﻗﺎم دﯾراك ﺑﺻﯾﻐﺗﯾﮫ اﻟﻛم ﻣﯾﻛﺎﻧﯾك ﺑوﺿﻊ : اﻟﻣﺻﻔوﻓﺎت ﻣﯾﻛﺎﻧﯾك ﺿﻣن اﻟﻣوﺟﻲ واﻟﻣﯾﻛﺎﻧﯾك اﻟﺟوھرﯾﺔ اﻟﻧﺗﺎﺋﺞ ﻣن ﻋدد إﻟﻰ أدى ﻣﺎ وھذا اﻟﺧﺎﺻﺔ اﻟﻧﺳﺑﯾﺔ ﺑﻧظرﯾﺔ ﺟﻣﻌﮭﺎ أﺷﻣل ﺻﯾﺎﻏﺔ أوﻟﮭﺎ : ﻧﻔﺳﮭﺎ ﺣول اﻟذرﯾﺔ اﻷﺟﺳﺎم دوران ﺧﺎﺻﯾﺔ إدﺧﺎل ( ﺑﺎﻹﻧﺟﻠﯾزﯾﺔ : Spin) : ﯾدور ﻓﺎﻻﻟﻛﺗرون ﻟﻠﺳﺑﯾن أﺳﻧد ﻛﻣﺎ .()ﺳﺑﯾن اﻟﻣﻐزﻟﻲ ﺑﺎﻟﻠف دﻋﯾت اﻟﺧﺎﺻﺔ وھذه ﻧﻔﺳﮫ ﺣول ﯾدور ﻛﻣﺎ اﻟﻧواة ﺣول اﻟﺟﺳﯾﻣﻲ اﻟدوران ﺧﺎﺻﯾﺎت ﺗﺷرح ﻋددﯾﺔ ﻗﯾﻣﺔ : اﻟذرة ﺿﻣن طﺎﻗﯾﺔ ﺑﺳوﯾﺎت دﯾراك ﻧظرﯾﺔ ﺗﻧﺑﺄت ﻓﻲ اﻟﻛﺗروﻧﺎ ﯾﺻف ﺣل ﻓﻠﻛل ،ﺑﻌد ﻣﻛﺗﺷﻔﺔ ﻏﯾر طﺎﻗﺗﮫ ﻟﻛن واﻟطﺎﻗﺔ اﻟﺧواص ﻓﻲ ﯾﻣﺎﺛﻠﮫ (اﻟﻣرآة )ﻛﺧﯾﺎل ﺗﻣﺎﻣﺎ ﻧظﯾر ﺣل ﯾوﺟد طﺎﻗﯾﺔ ﺳوﯾﺔ ﺷﺑﯾﮭﺔ اﺟﺳﺎم ﻟظﮭور ﻣﻌﯾﻧﺔ ﺣﺎﻻت ﻓﻲ ﯾؤدي أن ﯾﻣﻛن اﻟﺟﺳﯾم ھذا ﻣﺛل وﺟود ،ﺳﺎﻟﺑﺔ ﺑﺎﻟﺑوزﯾﺗرون دﻋﯾت ﻣوﺟﺑﺔ وطﺎﻗﺔ ﻣوﺟﺑﺔ ﺷﺣﻧﺔ ذات ﺑﺎﻻﻟﻛﺗروﻧﺎت وﻗد : ظﮭور ﺛﺑت ھذه اﻟﺑوزﯾﺗروﻧﺎت اﻛﺗﺷﺎف ﺑداﯾﺔ ھذا وﻛﺎن .اﻟﻧووﯾﺔ اﻟﺗﻔﺎﻋﻼت ﺑﻌض ﻓﻲ اﻟﻣﺿﺎدة اﻟﻣﺎدة اﻟﺗﻲ اﻟﺳﺎﻟﺑﺔ اﻟطﺎﻗﺔ ﺟﺳﯾﻣﺎت ﻋن ﺗﻧﺷﺄ . ﻧﺗﺞ اﻻﻧﺗﻔﺎء ﻣﺑدأ ﻟﺑﺎوﻟﻲ اﻟﺳﺑﯾن ذات اﻟﺟﺳﯾﻣﺎت اﺟﺗﻣﺎع ﯾدرس ﻛﺎن ﻋﻧدﻣﺎ ﻻ اﻧﮫ ﺑﯾن ﺣﯾث : ﻟﻣدار اﻟﻣﺣﺗﻠﯾن اﻹﻟﻛﺗروﻧﯾن ﻓﺣﺗﻰ ،اﻟطﺎﻗﯾﺔ اﻟﺳوﯾﺔ ﻧﻔس ﯾﺣﺗﻼ أن ﻛﻣوﻣﯾﯾن ﻟﺟﺳﯾﻣﯾن ﯾﻣﻛن ا ﺿﻣن واﺣد (طﺎﻗﯾﺔ )ﺳوﯾﺔ + ﺳﺑﯾن ذو أﺣدھﻣﺎ ﯾﻛون أن ﯾﺟب ﻟذرة 2 / 1 واﻵﺧر - 2 / 1 وﺑﮭذا ﻣﺧﺗﻠﻔﺔ اﻟﻛﻣوﻣﯾﺔ ﺣﺎﻟﺗﮭﻣﺎ ﺗﻛون . اﻟﻛﻣوﻣﯾﺔ اﻟﻧظرﯾﺔ ﺗﻔﺳﯾرات : ﻋن وﯾﺑﻌدﻧﺎ ﯾﺻدﻣﻧﺎ اﻟذري ودون اﻟذري اﻟﻌﺎﻟم ﻋن ﻏرﯾب ﺗﺻور ﺑﺗﻘدﯾم اﻟﻛﻣوﻣﯾﺔ اﻟﻧظرﯾﺔ ﺗﻘوم اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻔﯾزﯾﺎء ﺗﻘدﻣﮫ وﻣﺎ اﻟﺣﯾﺎﺗﻲ اﻟواﻗﻊ ﻓﻲ اﻟﻔﻧﺎه ﻣﺎ ﻛل ﻣن ﺑﺎﻟرﻏم ﻟﻛﻧﮭﺎ .ﺗﺻورات ﻣن ﯾوم ﺑﻌد ﯾوﻣﺎ ﺻﺣﺗﮭﺎ وﺗﻌزز اﻟذري دون اﻟﻌﺎﻟم ﺣﻘﺎﺋﻖ ﺗﻔﺳﯾر ﻓﻲ ﺑﻌﯾد ﺣد إﻟﻰ ﺗﻧﺟﺢ ذﻟك ﻛل أدﺧل ھذا ﻛل .اﻟﺗﻧﺑؤات ھذه ﻟﺗؤﻛد ﺑﻌد ﻓﯾﻣﺎ ﺗﺄﺗﻲ اﻟﻌﻠﻣﯾﺔ اﻟﺗﺟﺎرب ﻛل ﻟﻛن ﻏرﯾﺑﺔ ﺗﻧﺑؤات ﺑﺗﻘدﯾم وﻣدى ﺗطرﺣﮫ ﻣﺎ طﺑﯾﻌﺔ ﺣول ﻓﻠﺳﻔﯾﺔ ﻧﻘﺎﺷﺎت ﻋﻣﻖ ﻓﻲ اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ أن ﺣﺗﻰ ،اﻟﺣﻘﯾﻘﺔ ﻣن ﻗرﺑﮫ واﻟﺗﺟﺎرب اﻟﻣﻧﺎﻗﺷﺎت ھذه أھم وﻣن ،ﺳؤال ﻛﻣوﺿﻊ اﻟﺣﻘﯾﻘﺔ ﻗﺿﯾﺔ ﻧﻔس طرﺣت اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ اﻟﻔﻛرﯾﺔ : ﺷرودﻧﻐر ﻗطﺔ ﻓﺎﻏﻧر وﺻدﯾﻖ .
- 11. 11 اﻟﻛﻣوﻣﯾﺔ اﻟﻧظرﯾﺔ واﺳﺗﻧﺗﺎﺟﺎت ﻧﺗﺎﺋﺞ ﻟﺗﻔﺳﯾر ﻧظر وﺟﮭﺎت ﻋدة ﻗدﻣت ﻟﻘد اﻟﻧ ھذه أول : ظرﯾﺎت ﯾﻌرف ﻛوﺑﻧﮭﺎﺟن ﺑﺗﻔﺳﯾر إﻟﻰ أﺳﺎﺳﻲ ﺑﺷﻛل وﯾﻌود ﺑور أن ﯾؤﻛدون اﻟذﯾن ،وزﻣﻼﺋﮫ اﻟطﺑﯾﻌﺔ اﻻﺣﺗﻣﺎﻟﯾﺔ ﻧ ﺑﺄي ﺗﻔﺳﯾرھﺎ ﯾﻣﻛن ﻻ اﻟﻛم ﻧظرﯾﺔ ﻟﺗﻧﺑؤات ظرﯾﺔ ﺣﺗﻣﯾﺔ ﺻﻔﺔ وھﻲ ،أﺧرى .ﻣﻧﮫ ﻧﻌﺎﻧﻲ واﻟﻣﻌﻠوﻣﺎت اﻟﻣﻌرﻓﺔ ﻓﻲ ﻟﻧﻘص ﻧﺗﺎﺟﺎ وﻟﯾﺳت ﺑﮭﺎ ﻧﻌﯾش اﻟﺗﻲ اﻟطﺑﯾﻌﺔ ﻓﻲ أﺻﯾﻠﺔ طﺑﯾﻌ ذات اﻟطﺑﯾﻌﺔ ﻷن اﺣﺗﻣﺎﻟﯾﺔ طﺑﯾﻌﺔ ذات اﻟﻛﻣوﻣﯾﺔ اﻟﻧظرﯾﺔ ﺑﺎﺧﺗﺻﺎر ﻓﻣﺎ أﺳﺎﺳﺎ اﺣﺗﻣﺎﻟﯾﺔ ﺔ ھو ﻛﻣﺎ اﻷﻣر ﺗﺻوﯾر ھو اﻟﻛﻣوﻣﯾﺔ اﻟﻧظرﯾﺔ ﺗﻔﻌﻠﮫ . وﻗف اﻵﺧر اﻟطرف ﻋﻠﻰ أﯾﻧﺷﺗﺎﯾن رﻓﺿﮫ ﻟﯾﻌﻠن اﻟﻛﻣوﻣﯾﺔ ﻣؤﺳﺳﻲ أﺣد ﻟﻼﺣﺗﻣﯾﺔ اﻟﺗﻲ اﻟﻛﻣوﻣﯾﺔ ﺗﻧﺷﺄﻋن اﺣﺗﻣﺎﻟﯾﺔ اﻟﻌﺑﺎرة ھذه ﻛﺎﻧت .اﻟﻧرد ﯾﻠﻌب ﻻ اﻹﻟﮫ )إن ﻗﺎﺋﻼ ،اﻟﻘﯾﺎﺳﺎت ﺑﻣﺛﺎﺑﺔ اﻟﺷﮭﯾرة ﻓﻲ ﻧﻘص ھﻧﺎك ان ﻓﻛرة ﻣرﺟﺣﺎ ،اﺣﺗﻣﺎﻟﯾﺔ أﺻﺎﻟﺔ ﻟﻠطﺑﯾﻌﺔ ﺗﻛون ان ﻟﻔﻛرة ﻗﺎطﻊ رﻓض ﻧﺎﻗﺻﺔ اﻟﻛم ﻓﻧظرﯾﺔ وﻋﻠﯾﮫ ﻟﻠﻧﺗﺎﺋﺞ اﻻﺣﺗﻣﺎﻟﯾﺔ اﻟطﺑﯾﻌﺔ ﺗﻠك إﻟﻰ ﯾؤدي ﻟدﯾﻧﺎ اﻟﻣﺗوﻓرة اﻟﻣﻌﻠوﻣﺎت دﻋﺎه ﻣﺎ وھو ﺑﺎﻟﻣﻌﻠوﻣﺎت اﻟﻧﻘص ﺗﻌوﯾض طرﯾﻖ ﻋن اﻛﻣﺎﻟﮭﺎ ﯾﻧﺑﻐﻲ اﻟﺧﻔﯾﺔ ﺑﺎﻟﻣﺗﻐﯾرات ﻓﻌن ﺣﺗﻣﯾﺔ طﺑﯾﻌﺔ ذات ﻛﺎﻣﻠﺔ ﻧظرﯾﺔ ﺻﯾﺎﻏﺔ ﯾﻣﻛن اﻟﻣﺗﻐﯾرات ھذه طرﯾﻖ . ذﻟ ﺑﻌد ظﮭرت ﻣﺛل اﻟﻛﻣوﻣﯾﺔ وﻧﺑؤات ﻧﺗﺎﺋﺞ ﺑﻐراﺑﺗﮭﺎ ﺗﺿﺎھﻲ اﻟﺗﻲ اﻟﺗﻔﺳﯾرات ﺑﻌض ك ﻧظرﯾﺔ اﻟﻣﺗﻌددة اﻟﻌواﻟم ﻻﯾﻔرﯾت ﻧظرﯾﺔ ﺗطرﺣﮭﺎ اﻟﺗﻲ اﻻﺣﺗﻣﺎﻻت ﺟﻣﯾﻊ ﺑﺄن اﻟﻧظرﯾﺔ ھذه ﺗﻘول ﺣﯾث ، ﯾﻛون وﺑﺎﻟﺗﺎﻟﻲ .اﻟﻣﺗوازﯾﺔ اﻟﻣﺳﺗﻘﻠﺔ اﻟﻌواﻟم ﻣن ﻋدد ﻓﻲ اﻟوﻗت ﺑﻧﻔس ﻓﻌﻠﯾﺎ ﺗﺣﺻل اﻟﻛم اﻟﻛون اﺣﺗﻣﺎﻟﯾﺎ اﻻ ﯾﻛون ﻟن ﻓرﻋﻲ ﻛون ﻛل أن ﺣﯾن ﻓﻲ ﺣﺗﻣﯾﺎ اﻟﻣﺗﺷﻌب . إﻟﻰ ﯾﻌود ﺑوم ﺗﻔﺳﯾر أﯾﺿﺎ ھﻧﺎك ﺑوم دﯾﻔﯾد وﺟود وﯾﻔﺗرض ﻣوﺟﯾﺔ داﻟﺔ ﻋﺎﻟﻣﯾﺔ ﻣﺣﻠﯾﺔ ﻏﯾر ﺗﺳﻣﺢ أن ﺑوم ﯾﺣﺎول اﻟﺗﻔﺳﯾر ھذا ﻋﻠﻰ اﻋﺗﻣﺎدا .ﻓوري ﺑﺷﻛل ﺑﻌﺿﮭﺎ ﻣﻊ ﺗﺗﻔﺎﻋل ﺑﺄن اﻟﺑﻌﯾدة ﻟﻠﺟزﯾﺋﺎت ﯾظﮭر ﻛﻣﺎ ﺑﻌﺿﮭﺎ ﻣﻊ اﻟﻣﺗﻔﺎﻋﻠﺔ اﻟﻣﻧﻔﺻﻠﺔ اﻟﺟﺳﯾﻣﺎت ﻣن ﻣﺟﻣوﻋﺔ ﻟﯾس اﻟﻔﯾزﯾﺎﺋﻲ اﻟواﻗﻊ أن ﯾؤﻛد دوﻣﺎ ﻣﺗﻐﯾرة ﺣرﻛﯾﺔ طﺑﯾﻌﺔ ذو ﻣﻧﻘﺳم ﻏﯾر واﺣد ﻛل ھو ﺑل ﻟﻧﺎ . ﺗﻌرﯾف اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ اﻟﺻﻔﺎت ﻋن رﯾﺎﺿﯾﺎ ُﻌﺑرﺗ ٍةﻣﺗﻐﯾر ٍﺔﻛﻣﯾ ﻋﻠﻰ وﯾدل اﻟﻛم ﻣﯾﻛﺎﻧﯾك ﻓﻲ ُﺳﺗﺧدمﯾ ٌﺢﻣﺻطﻠ ھو ﻣﺣددﯾن ٍوزﻣﺎن ٍﻣﻛﺎن ﻓﻲ ٌدﻣوﺟو ﻣﺎ ٍﻟﺟﺳﯾم اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ ﻗﯾﻣﺔ أن ﯾﻌﻧﻲ وھذا ﻟﻠﺟﺳﯾم اﻟﻣوﺟﯾﺔ ٍدﻣﺣد ٍتوﻗ وﻓﻲ اﻟﻧﻘطﺔ ﺗﻠك ﻓﻲ اﻟﺟﺳﯾم ذﻟك ﺗواﺟد ﺑﺎﺣﺗﻣﺎﻟﯾﺔ ﺗﺗﻌﻠﻖ . ﺧﻼل ﻣن ﺳﻌﺔ ﻋن ُﻌﺑرﺗ أﻧﮭﺎ ﻧﺟد اﻟﺻوﺗﯾﺔ ﻛﺎﻷﻣواج أﺧرى ٍ ﺑﺄﻣواج اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ ﻣﻘﺎرﻧﺔ اﻟداﻟﺔ ﻗﯾﻣﺔ ﻣرﺑﻊ ﻋﻠﻰ ُﻌﺗﻣدﯾ ﺑﯾﻧﻣﺎ ،ﻓﯾزﯾﺎﺋﯾﺎ ٍةﻛﺑﯾر ٍﺔأھﻣﯾ ذات ﻟﯾﺳت اﻟﺳﻌﺔ أن ﻣﻊ ،اﻟﺟﺳﯾم ﻣوﺟﺔ ﻣﺣددﯾن ٍتووﻗ ٍﻣﻛﺎن ﻓﻲ ﺟﺳﯾم ﻹﯾﺟﺎد ﻓﯾزﯾﺎﺋﯾﺎ اﻟﻣوﺟﯾﺔ . اﻟﻣوﺟﯾ اﻟﻣﻌﺎدﻟﺔ أو ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ ﺔ
- 12. 12 ﻋﺎم ﻓﻲ 1926 ﻋﻠم أﺳﺎس ﺷﻛﻠت ٍﺔﻣﻌﺎدﻟ إﻟﻰ ﺷرودﻧﺟر إرﯾون اﻟﻧﻣﺳﺎوي اﻟﻔﯾزﯾﺎء ﻋﺎﻟم ﺗوﺻل ،ﺑﺎﻟﻣﺟﮭر ُرىﺗ ﻻ اﻟﺗﻲ اﻟذري ودون اﻟذري اﻟﻣﺳﺗوى ﻓﻲ اﻟظواھر ﯾدرس اﻟذي اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻗواﻧﯾن أھﻣﯾﺔ ﻛﻣﺎ ﺗﻣﺎﻣًﺎ اﻟﻛﻣوﻣﯾﺔ ﻟﻠﻣﯾﻛﺎﻧﯾﻛﺎ ﺑﺎﻟﻧﺳﺑﺔ ٍةﻛﺑﯾر ٍﺔأھﻣﯾ ﻋﻠﻰ اﻟﻣﻌﺎدﻟﺔ ھذه ﺣﺎزت ﺣﯾث اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻣﯾﻛﺎﻧﯾﻛﺎ ﻓﻲ ﻟﻠظواھر ﺑﺎﻟﻧﺳﺑﺔ ﻟﻧﯾوﺗن اﻟﺣرﻛﺔ . ُﺣددﺗ أﻧﮭﺎ اﻟﻣﺣﺗﻣل اﻷﻣواج ﺷﻛل اﻟﻣوﺟﯾﺔ اﻟﻣﻌﺎدﻟﺔ ﻋﻠﯾﮭﺎ ُطﻠﻖﯾ ﻛﻣﺎ أو ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ ﺗﺗﻧﺎول ٍتﻣؤﺛرا ﻧﺗﯾﺟﺔ اﻷﻣواج ﺗﻠك ﺗﻌدﯾل طرﯾﻘﺔ ﺑﺎﻟﺗﻔﺻﯾل ﺗوﺿﺢ ﻛﻣﺎ ،اﻟﺻﻐﯾرة اﻟﺟﺳﯾﻣﺎت ﺣرﻛﺔ ﻣﻌ ﺻﺣﺔ ﺷرودﻧﺟر أﺛﺑت ﺣﯾث ٍ؛ﺔﺧﺎرﺟﯾ ا ًﻛﺛﯾر ُﺣددﯾﻟ اﻟﮭﯾدروﺟﯾن ذرة ﻋﻠﻰ ّﻘﮭﺎﺑط ﻋﻧدﻣﺎ ﺎدﻟﺗﮫ ﻓﻲ ٍةﺑﻛﺛر ُﺳﺗﺧدمﺗ اﻟﻣﻌﺎدﻟﺔ أﺻﺑﺣت وﻟﮭذا ٍﺔﻣﺗﻧﺎھﯾ ٍﺔﺑدﻗ ﺧﺻﺎﺋﺻﮫ ﻣن اﻟﻔﯾزﯾﺎء واﻟﻧووﯾﺔ اﻟذرﯾﺔ ﺑﺎﻟﺟواﻣد ُدﻋﻰﺗ ﻛﻣﺎ أو اﻟﺻﻠﺑﺔ واﻟﺣﺎﻟﺔ .2 ﺻﻔﺎت اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ ﻟﻠﻘﯾﺎس اﻟﻘﺎﺑﻠﺔ اﻟﺟﺳﯾم ﻣﻌﻠوﻣﺎت ﻛﺎﻓﺔ اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ ُﻘدمﺗ . ﻛﺎن إن ٍﺟﺳﯾم اﻛﺗﺷﺎف اﺣﺗﻣﺎﻟﯾﺔ أن ﯾﻌﻧﻲ ھذا اﻟواﺣد ُﺳﺎويﺗ اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ ﻣرﺑﻊ ﻗﯾﻣﺔ ﻛﺎﻧت إن اﻟواﺣد ﺗﺳﺎوي أن ﯾﺟب ،ﻣﺎ ٍﻣﻛﺎن ﻓﻲ ًادﻣوﺟو . ﻣُﻔردة وﻗﯾﻣﺗﮭﺎ ٌةﻣﺳﺗﻣر اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ . ﻣﻌﺎدﻟﺔ ﺧﻼل ﻣن اﻟﺟﺳﯾم طﺎﻗﺔ ﺣﺳﺎﺑﺎت ﻣﻌرﻓﺔ ٍﺔﺑﺳﮭوﻟ ﯾﻣﻛن ﺷرودﻧﺟر . اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ طرﯾﻖ ﻋن اﻟﺛﻼﺛﺔ اﻷﺑﻌﺎد ﻓﻲ اﻟﻣﺣﺗﻣل اﻟﺗوزع إﯾﺟﺎد ﯾﻣﻛن . ٍدﻣﺣد ٍ ﻟﻣﺗﻐﯾر اﻟﻣﺗوﻗﻌﺔ اﻟﻘﯾﻣﺔ أي اﻟﻔﻌﻠﯾﺔ اﻟوﺳطﯾﺔ اﻟﻘﯾﻣﺔ ﺣﺳﺎب اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ طرﯾﻖ ﻋن ﯾﻣﻛن . ﺗﺗﺿﻣن ٌ ﺟﯾﺑﯾﺔ ٌ ﻣوﺟﺔ ھﻲ ٍّﺣر ٍﻟﺟﺳﯾم اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ ﻏﯾر ٍ وﻣوﻗﻊ ٍﺔﺑدﻗ ٍةﻣﺣدد ٍﺔﺣرﻛ ﻛﻣﯾﺔ ٍدﻣﺣد . 3 اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ أﺳﺎﺳﯾﺎت ﻣﻌرﻓﺔ ﯾﻣﻛن ﻋﻠﻰ اﻟﻘﺎﺋﻣﺔ ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ ﻋﻠﻰ ﺑﺎﻻﻋﺗﻣﺎد اﻟﻣوﺟﯾﺔ ﻟﻠداﻟﺔ اﻟزﻣﻧﻲ اﻟﺗطور اﻟوﻗت . اﻟﺳﮭل ﻣن ُﺻﺑﺢﯾ اﻟﻘوة ﻧظﺎم ﺿﻣن ٍﻣُﻐﻠﻖ ٍﻣﺟﺎل ﻓﻲ ٍدﻣوﺟو ٍﻟﺟﺳﯾم اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ اﺳﺗﺧدام ﻋﻧد اﻟﻧظﺎم ذﻟك طﺑﯾﻌﺔ واﻛﺗﺷﺎف ﻓﮭم . اﻟﻣﺷﻐل ھﻲ اﻟﮭرﻣﯾﺗﯾﺔ Q ﺑﺎﻟﺧﺎﺻﯾﺔ اﻟﻣرﺗﺑط q ﻓﯾزﯾ ﻟﻠﻘﯾﺎس اﻟﻘﺎﺑﻠﺔ ًﺎﯾﺎﺋ .
- 13. 13 ،ﺑﺎﻟﻧظﺎم اﻟﻣرﺗﺑطﺔ اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ اﻻﻋﺗﺑﺎر ﺑﻌﯾن اﻷﺧذ ﻣﻊ اﻟﻣﺗﻛﺎﻣﻠﺔ اﻟﻣﺗوﻗﻌﺔ اﻟﻘﯾﻣﺔ ﺗطﺑﯾﻖ ﻋﻧد ﻟﻠﺧﺎﺻﯾﺔ اﻟﻣﺗوﻗﻌﺔ اﻟﻘﯾﻣﺔ ﺗﺣدﯾد ﯾﻣﻛن q. ﻣﺷﻐل ﯾوﺟد Q ﺧﺎﺻﯾﺔ ﻟﻛل q اﻟﻣرﺗﺑطﺔ اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ ﻋﻠﻰ ُؤﺛرﯾو ﻓﯾزﯾﺎﺋﯾﺎ ﻣﻼﺣظﺗﮭﺎ ﯾﻣﻛن اﻟﺧﺎﺻﯾﺔ ﻟﺗﻠك اﻟﻣﺣددة اﻟﻘﯾﻣﺔ ﻣﻊ .4 اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ اﻧﮭﯾﺎر ﻓﻛرة ّداﻟ ﺣﺎﻟﺔ ﻣن اﻻﻧﺗﻘﺎل ﻋﻧد اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ اﻧﮭﯾﺎر ﯾﺣدث ٍﺟﺳﯾم ﺣﺎﻟﺔ إﻟﻰ اﻟﻣﻧﺗﺷرة اﻟﻣوﺟﯾﺔ اﻟﺔ ﻋن ٍﻛﻣﺛﺎل ﯾوﻧﻎ ﺷﻘﻲ أو اﻟﻣزدوج اﻟﺷﻖ ﺗﺟرﺑﺔ ﻧﺄﺧذ أن ﯾﻣﻛﻧﻧﺎ اﻟﻔﻛرة ھذه وﻟﺗﺗوﺿﺢ ،ٍّ ﻣوﺿﻌﻲ ٍﺔﻟوﺣ ﺑﺎﺗﺟﺎه ٍ ﻟﯾزر ﺟﮭﺎز ﻣن ﻓوﺗون إطﻼق اﻟﺗﺟرﺑﺔ ﺗﺗﺿﻣن ﺣﯾث اﻟﻣوﺟﯾﺔ؛ اﻟدﻟﺔ اﻧﮭﯾﺎر ﻓﯾ ٍ ﺣﺎﺟز ﺧﻼل ﻣن ﯾﻣر أن ﻋﻠﯾﮫ إﻟﯾﮭﺎ ﻟﯾﺻل ﻟﻛﻧﮫ ٍﺔﻓوﺗوﻏراﻓﯾ ﺷﻘﯾن أو ﻓﺗﺣﺗﯾن ﮫ . ،ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ ﻣن ٌ ﻣﺳﺗﻧﺗﺟﺔ ٌ ﻣﻌﺎدﻟﺔ وھﻲ ﻟﻠﻔوﺗون اﻟﺣﺎﺻل اﻟﺗﻐﯾﯾر اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ ﺗوﺿﺢ ٌﺟﺳﯾم ﺑل ٍﺔﻣﻌﺎدﻟ ﻣﺟرد ﻟﯾﺳت اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ أن اﻟﻌﻠﻣﺎء ﯾﻌﺗﻘد ﺣﯾث ﻓﯾزﯾﺎﺋﻲﱞ اﻟذي اﻷﻣر ﺣﻘﯾﻘﻲﱞ اﻟﻣزدوج اﻟﺷﻖ ﺗﺟرﺑﺔ ﻓﻔﻲ اﻟﻛم؛ ﻟﻣﯾﻛﺎﻧﯾﻛﺎ اﻟﻔﯾزﯾﺎﺋﻲ اﻟﻣﻌﻧﻰ وﺗوﺿﯾﺢ ﻓﮭم ﻓﻲ ﺻﻌوﺑﺎت أوﺟد ﺗوﺿﺢ اﺣﺗﻣﺎﻻت ﺣول ﻣﻌﻠوﻣﺎت ُﻘمﺗ ﺑل ﻣﺳﺎره ﺗﺗﻧﺎول وﻻ ﻓﻘط اﻟﻔوﺗون ﺗطور اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ ﻧﺳﺑﺔ ُﺣددﺳﺗ ً ﻓﻣﺛﻼ ،ﻣﺣددﯾن ٍوﻣﻛﺎن ٍزﻣن ﻓﻲ وﺟوده 20 ھذه ﻓﻲ اﻟﻔوﺗون وﺻول ﻻﺣﺗﻣﺎل % وﻧﺳﺑﺔ اﻟﻠوﺣﺔ ﻣن ٍةﻣﺣدد ٍﺔﻧﻘط إﻟﻰ اﻟﺗﺟرﺑﺔ 40 وھﻛذا أﺧرى ٍﺔﻧﻘط ﻓﻲ % . اﻟﻣﺣﺗﻣﻠﺔ اﻟﻔوﺗون ﻣﺳﺎرات ﺗﻛون ﻣﺳﺎرات اﻟﻔوﺗون ﺳﻠوك اﻟﻣﻣﻛن ﻣن أﻧﮫ أي ٍﺔﺗراﻛﺑﯾ ٍﺔﺣﺎﻟ ﻓﻲ ﻓﻛل اﻟﻔوﺗون اﻛﺗﺷﺎف ﻣﻛﺎن اﺣﺗﻣﺎﻻت ﺗﺣدﯾد ﻓﻲ ﻣﻧﮭﺎ ٍ ﻣﺳﺎر ﻛل ُﺳﺎھمﯾو ،ٍﺔﻟﺣظ أي ﻓﻲ ﻛﺛﯾرة اﻻﺣﺗﻣﺎل ﻓﻛرة إﻟﻰ ﺑﺎﻟﻌودة ُﻌﺗﻘدﯾ ﻣﻣﺎ أﻛﺑر ٍﺑﺷﻛل ﯾؤﺛر ﻣﻧﮭﺎ ٍدواﺣ . اﻟﻣو ّاﻟﺔداﻟ اﻧﮭﯾﺎر ﻋن ٍﺔأﻣﺛﻠ ّةدﻋ ﺗظﮭر ﻟﻠﺗﺟرﺑﺔ ًﺎوﻓﻘ ٌ ﻛﺎﻣﻠﺔ ٌةذر ﺗظﮭر اﻟﻔوﺗون ﻣن ً ﻓﺑدﻻ ،ﺟﯾﺔ ﻣن ذﻟك وﻣﻊ ،ﺣﻘﯾﻘﯾﯾن ﻓﯾزﯾﺎﺋﯾﯾن ﺷﯾﺋﯾن ﻛﺄﻧﮭﻣﺎ ﯾﺑدوان اﻟطﺎﻗﺔ ﻣن ﻣﺗراﻛﺑﯾن ﻣﺳﺗوﯾﯾن ُﺑديﺗ اﻟذرة ﺗﺗﻔﺎﻋل ﻋﻧدﻣﺎ .ﻓﯾزﯾﺎﺋﯾﺔ ﺣﻘﯾﻘﺔ اﻋﺗﺑﺎرھﻣﺎ وﻋدم اﻟﻣوﺟﯾﺔ اﻟداﻟﺔ ﺧﻼل ﻣن وﺻﻔﮭﻣﺎ اﻟﻣﺣﺗﻣل ﯾﻣ وﺑﺎﻟﺗﺎﻟﻲ اﻟﻣوﺟﯾﺔ ّاﻟﺔداﻟ ﺗﻧﮭﺎر ﻣﺎ ٍﺟﺳﯾم ﻣﻊ ﻣﺳﺗوﯾﻲ أﺣد ﻋﻠﻰ اﻟﺣﺻول ﺟراء ﻗﯾﺎﺳﮭﺎ ﻛن اﻟﻣﺣﺗﻣﻠﯾن اﻟطﺎﻗﺔ .5 اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ﺗﻌرﯾف ﺣﯾث ﻛﻣوﻣﯾﺎ ﻣﺗﺷﺎﺑﻛﯾن ﻟﺟﺳﻣﯾن ﺗﺣدث اﻟﺗﻲ اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟظﺎھرة ﺗﻠك اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ﯾﺻف اﻟﻣﺳﺎﻓﺎت ﻋن اﻟﻧظر ﺑﻐض ،آﻧﯾﺎ ّﺔﯾاﻟﻔﯾزﯾﺎﺋ ﺻﻔﺎﺗﮭم ﻓﻲ ﻣﺗﺷﺎرﻛﯾن ، ٍ ﻣﺑﺎﺷر ٍاﺗﺻﺎل ﻋﻠﻰ ﯾﺑﻘﯾﺎن ﻓﻘ ﺗﺗﺄﺛر اﻷﺟﺳﺎم أن ﻋﻠﻰ ﯾﻧص )واﻟذي ّﺔﯾاﻟﻣﺣﻠ وﻣﺑدأ ﯾﻧﺎﻗض اﻟواﻗﻊ ﻓﻲ وھذا ،ﺑﯾﻧﮭﻣﺎ اﻟﺷﺎﺳﻌﺔ ط وﻧظرﯾﺔ (ﻣﺑﺎﺷرة ﻟﮭﺎ اﻟﻣﺟﺎور ﺑﻣﺣﯾطﮭﺎ اﻟﺧﺎﺻﺔ اﻟﻧﺳﺑﯾﺔ ﻣن أﯾﻧﺷﺗﺎﯾن أﻟﺑرت .
- 14. 14 ٍتوﻗ ﻓﻲ أﻧﮫ ﯾﻌﻧﻲ ھذا ،ﻛﻣوﻣﯾﺎ ﻣﺗﺷﺎﺑﻛﯾن إﻟﻛﺗروﻧﯾن ھﻧﺎﻟك أن ﺳﻧﻔﺗرض اﻟﺗﺑﺳﯾط أﺟل وﻣن ھذا ﺑﯾن ٍﺔّﺻﺧﺎ ٍﺔﻋﻼﻗ ر ّﺗطو إﻟﻰ اﻻﺻطدام ھذا أدى ﺑﺣﯾث ﺑﺑﻌﺿﮭﺎ اﻹﻟﻛﺗروﻧﯾن ﺻدم ﺗم ٍﺳﺎﺑﻖ ﻓﻲ وذﻛرﻧﺎ .اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ﻣﺻطﻠﺢ ﻋﻠﯾﮭﺎ ُطﻠﻖﻧ ،اﻟزوج اﻟﻣﺗﺷﺎﺑﻛﺔ اﻷﺟﺳﺎم أن اﻟﺗﻌرﯾف ()اﻟﻌزم اﻟدوران ﺟﮭﺔ ﻣن ﻛﻼ أن ﯾﻌﻧﻲ ھذا ،ﺑﯾﻧﮭﺎ ﻓﯾﻣﺎ آﻧﯾﺎ اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟﺻﻔﺎت ﺗﺗﺷﺎرك ﻛﻣوﻣﯾﺎ ٍ ﻣﺑﺎﺷر ٍﺑﺷﻛل اﻟﻣﺗﺷﺎﺑﻛﯾن اﻟزوﺟﯾن ﺑﯾن ﺗﺷﺎرﻛﮭﺎ ﯾﺗم اﻟﺻﻔﺎت ھذه ﻛل ،اﻟﻣﻛﺎن وﺣﺗﻰ واﻟﺷﺣﻧﺔ .1 ھذا ،اﻟﺳﺎﻋﺔ ﻋﻘﺎرب ﺑﺎﺗﺟﮭﺎه اﻷول اﻹﻟﻛﺗرون دوران اﺗﺟﺎه أﺻﺑﺢ اﻟﺗﺻﺎدم وﺑﻌد أﻧﮫ وﺑﻔرض ﯾدو اﻵﺧر اﻹﻟﻛﺗرون أن ﺑﺎﻟﺿرورة ﯾﻌﻧﻲ اﻻﺗﺟﺎه ذﻟك ﺑﻌﻛس ر . اﺗﺟﺎه واﻛﺗﺷﺎف اﻷول اﻹﻟﻛﺗرون ﺧﺻﺎﺋص ﻹﺣدى ﻗﯾﺎﺳﻧﺎ دّوﺑﻣﺟر ّﮫﻧأ اﻷﻣر ﻓﻲ واﻟﻣُﻠﻔت ﻟو ﺣﺗﻰ ًةﻣﺑﺎﺷر ﻟﻸوﻟﻰ ﻣﻌﺎﻛﺳﺔ ﺧﺻﺎﺋص ﯾﺗﺧذ اﻟﻣُﺗﺷﺎﺑك اﻵﺧر اﻹﻟﻛﺗرون ﻓﺈن ،ﺣرﻛﺗﮫ دوران ﯾﻛ ﻓﺈﻧﮭﻣﺎ ﻣﺗﺷﺎﺑﻛﯾن ﺟﺳﻣﯾن أي ﻗﯾﺎس ﻗﺑل أﻧﮫ أي !اﻟﻛون ﻣن اﻵﺧر اﻟطرف ﻓﻲ ﻛﺎﻧت ﻓﻲ وﻧﺎن اﺗﺟﺎه ﺗﺣدﯾد ﻗﺑل ،اﻹﻟﻛﺗروﻧﯾن ﻛﻼ ﻓﺈن اﻹﻟﻛﺗروﻧﺎت ﻋﻠﻰ ﻣﺛﺎﻟﻧﺎ وﻓﻲ ،ٍﺔوﻣﺗذﺑذﺑ ٍﺔﻣﺟﮭوﻟ ٍﺔﺣﺎﻟ ٍآن ﻓﻲ اﻟﺳﺎﻋﺔ ﻋﻘﺎرب وﻋﻛس ﻣﻊ ٍدوران ﺣﺎﻟﺔ ﻓﻲ ﯾﻛوﻧﺎن ،ٍﺔّﺻﺧﺎ ٍةأﺟﮭز ﺑواﺳطﺔ دوراﻧﮭﻣﺎ ﻛذﻟك؟ أﻟﯾس ٌﻏرﯾب ھذا !ًﺎﻣﻌ اﻹﻟﻛﺗر ﻓﺈن اﻹﻟﻛﺗروﻧﯾن أﺣد دوران ﺟﮭﺔ ﺗﺣدﯾد ﻋﻧد ﻟﻛن ﯾﺗﺧذ ﻛﻣوﻣﯾﺎ اﻟﻣﺗﺷﺎﺑك اﻵﺧر ون ،اﻷول اﻹﻟﻛﺗرون ﻋن ًةﺑﻌﯾد ﻣﺳﺎﻓﺗﮫ ﻛﺎﻧت وﻣﮭﻣﺎ ﻛﺎن أﯾﻧﻣﺎ ٍّآﻧﻲ ٍﺑﺷﻛل ﻟﻸول ًﺎﺳﻣﻌﺎﻛ ًﺎھاﺗﺟﺎ اﻟﺗﺷﺎﺑك ظﺎھرة ﻓﻲ أﯾﻧﺷﺗﺎﯾن ﻗﺎل ﻟذﻟك .اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك وﺟوھر ُﻠبﺻ اﻟواﻗﻊ ﻓﻲ وھذا اﻟﻛﻣوﻣﻲ “ ٍﺔﻣﺧﯾﻔ ٍتﺑﺳرﻋﺎ ﺗﺣدث ٌ ﻏرﯾﺑﺔ ٌظواھر إﻧﮭﺎ ”. ﺑ ﯾﻌﺗﻘد إﻟﻰ ﻣﺎ ٍﺔﺑطرﯾﻘ اﻷول اﻟﺟﺳﯾم ﺻﻔﺔ ﻣﻌرﻓﺔ ﻋﻧد آﻧﯾﺎ ﺗﻧﺗﻘل اﻟﺗﻲ اﻟﻣﻌﻠوﻣﺎت أن اﻟﻌﻠﻣﺎء ﻌض اﻟﻌﻠﻣﺎء ﻣن ٌةوﺟﻣﮭر أﯾﻧﺷﺗﺎﯾن رﻓﺿﮫ ﻣﺎ اﻟواﻗﻊ ﻓﻲ وھذا ،اﻟﺿوء ﺳرﻋﺔ ﺗﻔوق ﻗد اﻵﺧر اﻟﺟﺳﯾم اﻵﺧرون .2 ﻋﺛرت ﻣﺎ ﻓﺈذا ،اﻟﻘﻔﺎزات ﺑزوﺟﻲ ﻣﺎ ٍّدﺣ إﻟﻰ ﻛﻣوﻣﯾﺎ اﻟﻣﺗﺷﺎﺑﻛﺔ اﻟﺟﺳﯾﻣﺎت ﺣﺎﻟﺔ ﺗﺷﺑﯾﮫ ﯾﻣﻛﻧﻧﺎ ﺗﻣﺎﻣًﺎ ًﺎواﺛﻘ ﻓﺳﺗﻛون اﻷﯾﻣن ّﺎزاﻟﻘﻔ ﻋﻠﻰ ﻣﻼﺑﺳك ﺧزاﻧﺔ ﻓﻲ ًﺎﺿﻓر ّﺎزاﻟﻘﻔ ھو اﻵﺧر ّﺎزاﻟﻘﻔ ﺑﺄن اﻛﺗﺷﺎﻓك ﻟﺣظﺔ ٍّآﻧﻲ ٍﺑﺷﻛل اﻵﺧر ّﺎزاﻟﻘﻔ ﻋن اﻟﻣﻌﻠوﻣﺔ ھذه ﻣﻌرﻓﺔ ﻣن ﺳﺗﺗﻣﻛن ّكﻧأ أي ،اﻷﯾﺳر ٍدﺑﻌﯾ ٍبﻛوﻛ ﻋﻠﻰ اﻵﺧر ﻛﺎن ﻟو ﺣﺗﻰ ﺧزاﻧك ﻓﻲ ّﺎزاﻟﻘﻔ ﻟﺻﻔﺔ ! أن ّ إﻻ ،ﻛﻣوﻣﯾﺎ اﻟﻣُﺗﺷﺎﺑﻛﺔ اﻷﺟﺳﺎم ﺣﺎﻟﺔ ﻣﻌﺎﻟﻣﮫ ﻓﻲ ُﺷﺑﮫﯾ اﻟﺗﺷﺑﯾﮫ ھذا أن ﻣن ﺑﺎﻟرﻏم ﻟﯾس اﻷﻣر اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ﻧظرﯾﺔ أﺛﺎرﺗﮫ اﻟذي اﻟﺟدل ھو ﻓﻣﺎ .ّﺔﯾاﻟﻛﻣوﻣ اﻟﻔﯾزﯾﺎء ّﺧﺿم ﻓﻲ اﻟﺑﺳﺎطﺔ ﺑﺗﻠك اﻟﻔﯾزﯾﺎﺋﯾﯾن؟ أوﺳﺎط ﺑﯾن ھذه 3 اﻟﻛﻣوﻣﻲ ﻟﺗﺷﺎﺑك ﻧظرﯾﺔ ﺣول اﻟﻘﺎﺋم اﻟﺟدل ﺣﯾﻧﻣﺎ ،اﻟﻌﺷرﯾن اﻟﻘرن ﻣن اﻷول اﻟﻧﺻف إﻟﻰ اﻟﻌﺟﯾﺑﺔ اﻟﻧظرﯾﺔ ھذه ﺣول اﻟﻘﺎﺋم اﻟﺟدل ﯾﻌود ٌ ﻣﺧﯾﻔﺔ ﺑﺄﻧﮭﺎ ووﺻﻔوھﺎ اﻟظﺎھرة ھذه أﺳس وروزﯾن وﺑودوﻟوﺳﻛﻲ أﯾﻧﺷﺗﺎﯾن ﻣن ﻛل وﺿﻊ
- 15. 15 “Spooky” ﺑﻣﻌﺿﻠﺔ ذﻟك ﻣﻧذ ُﻋﯾتدو ، EPR ّﻧواﯾوﺑ .اﻟﻣذﻛورﯾن اﻟﻌﻠﻣﺎء ﻣن ﻛل إﻟﻰ ً ﻧﺳﺑﺔ ﺗﻛون ﻗد ّﺔﯾاﻟﻛﻣوﻣ ﻟﻠﻔﯾزﯾﺎء اﻟﻔﯾزﯾﺎﺋﻲ اﻟﻣﺟﺗﻣﻊ ﻓﻲ ﻋﻠﯾﮭﺎ ّﻔﻖاﻟﻣﺗ اﻟﺻﯾﻐﺔ أن اﻟﻣﻌﺿﻠﺔ ھذه ﺑطرح ٍﺔﻛﺎﻣﻠ ﻏﯾر . ﺗﻔوق ٍﺔﺑﺳرﻋ اﻟﻣﺗﺷﺎﻛﺑﯾن اﻟزوﺟﯾن ﺑﯾن ﻟﻠﻣﻌﻠوﻣﺎت ٍّآﻧﻲ ٍﻧﻘل وﺟود ﻓﻛرة أﯾﻧﺷﺗﺎﯾن رﻓض وﻗد ﻋن اﻟﺑﻌﯾدة اﻟﻣﺗﺷﺎﺑﻛﺔ اﻷﺟﺳﺎم ﺑﯾن اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟﺣﺎﻟﺔ ﻟﺗواﻓﻖ ﺗﻔﺳﯾره ﻓﻲ وﻟﺟﺄ ،اﻟﺿوء ﺳرﻋﺔ اﻟﻣﺣﻔوظﺔ اﻟﻣﻌﻠوﻣﺎت ﺑﻧظرﯾﺔ دﻋﺎه ﺑﻣﺎ ﺑﻌﺿﮭﺎ (Hidden variables theory) واﻟﺗﻲ ًﺎﻣﺳﺑﻘ ً ﻣﺣﻔوظﺔ ﺗﻛون ﻣﺗﺷﺎﻛﺑﯾن ﺟﺳﯾﻣﯾن ﻛل ﺣﺎﻟﺔ ﻋن اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟﻣﻌﻠوﻣﺎت أن ﻋﻠﻰ ّ ﺗﻧص اﻟزوﺟﯾ اﻧﻔﺻﺎل ﻟﺣظﺔ ﺑﻌﺿﮭﻣﺎ ﻋن ن . ﻋﺎم اﻟﻔرﯾدة ﺑﺗﺟرﺑﺗﮫ أرﺳﻰ ﺑﯾل ﺟون اﻟﺷﮭﯾر اﻟﻔﯾزﯾﺎﺋﻲ اﻟﻌﺎﻟم أن إﻻ 1964 ﻓﻲ ﻧظره وﺟﮭﺔ أن ﯾﻣﻛن أﺣدھﻣﺎ ﻗﯾﺎس ﻋﻧد اﻟزوﺟﯾن ﻓﻲ ﻧﺷﮭدھﺎ اﻟﺗﻲ اﻟﺗﻐﯾرات ﺑﺄن ً ﻗﺎﺋﻼ اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ًﻔﻣﺧﺎﻟ !اﻟﺿوﺋﯾﺔ اﻟﺳﻧﯾن ﻣﻼﯾﯾن ﺑﻌﺿﮭﻣﺎ ﻋن ﺑﻌﯾدﯾن اﻟزوﺟﺎن ﻛﺎن ﻟو ﺣﺗﻰ ،آﻧﯾﺎ ﯾﺣدث ﺑذﻟك ﺎ اﻟﻧﺳﺑﯾﺔ ّﺗﮫﯾوﻧظر أﯾﻧﺷﺗﺎﯾن .4 اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ظﺎھرة اﺧﺗﺑﺎر إﻣﻛﺎﻧﯾﺔ اﻟواﻗﻊ أرض ﻋﻠﻰ اﻟﺗﺟﺎرب ﻣﻌظم ّوﻟﻛن ،ﺑﯾل ﻧظرﯾﺔ ﻣن ﻟﻠﺗﺄﻛد اﻟﺗﺟﺎرب ﻣن اﻟﻌدﯾد اﺟراء ﺗم اﻟﻣﺎﺿﻲ اﻟﻘرن ﻓﻲ اﻟﺣﺳﺎﺳﯾﺔ ذات اﻟﺗﺟﮭﯾزات ﺑﻧﺎء ﺻﻌوﺑﺔ إﻟﻰ ﯾرﺟﻊ وذﻟك ٍﺔدﻗﯾﻘ َﻧﺗﺎﺋﺞ إﻋطﺎء ﻋن ًةﻗﺎﺻر ﻛﺎﻧت اﻟﻛﺎﻓﯾﯾن واﻷداء . ﻋﺎم ﻓﻲ وﻓﻲ 2015 ٍﺔﻗرﯾﺑ َﻧﺗﺎﺋﺞ إرﺳﺎء ﻣن ٍبﺗﺟﺎر ﺛﻼث ﺗﻣﻛّﻧت ،ﺑﯾل ﻧظرﯾﺔ ﺗﺄﻛﯾد ﻣن ًادﺟ ﻋﻠﻰ ﺗﺟرﺑﺗﮫ ﻓﻲ اﻋﺗﻣد واﻟذي ،ﺷﺎﻟم ﻛرﯾﺳﺗن اﻟﺑروﻓﯾﺳور ﺑﺈﺷراف ﻛﺎﻧت اﻟﺗﺟﺎرب ﺗﻠك إﺣدى ﻟﯾﻘوم ،اﻟﺗﺟﻣﯾد درﺟﺔ إﻟﻰ ﺗﺑرﯾده ﺗم اﻟﻧﺎﻗﻠﯾﺔ ﻋدﯾم ﺧﺎص ٍّﻣﻌدﻧﻲ ٍﺑﺷرﯾط ﻣﺗﺷﺎﺑﻛﯾن ﻓوﺗوﻧﯾن ﺻدم ّﻣﻛ ﺑدوره ھذا ،ٍﻧﺎﻗل ٍ ﻣﺳﺎر إﻟﻰ ﺑﺗﺣوﯾﻠﮭﺎ ﺑﮭﺎ اﺻطداﻣﮫ ﻋﻧد اﻟﻔوﺗون ﻣن اﻟﺗﺟرﺑﺔ ﻋﻠﻰ اﻟﻘﺎﺋﻣﯾن ن ﺑﯾﻧﮭﻣﺎ اﻟﺗﺷﺎﺑك ھذا ﻗﯾﺎس إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ اﻟﻣﺗﺷﺎﺑﻛﯾن اﻟﻔوﺗوﻧﯾن ﺑﯾن ٍارﺗﺑﺎط أي وﺟود ﻣن اﻟﺗﺄﻛد . أرض ﻋﻠﻰ اﻟﻛﻣوﻣﻲ اﻟﺗﺷﺎﺑك ظﺎھرة ﺗﺳﺧﯾر أﻣﺎم ًﺎواﺳﻌ اﻟﺑﺎب ﻓﺗﺣت اﻟواﻗﻊ ﻓﻲ اﻟﺗﺟرﺑﺔ وھذه اﻟﻧﺎﻗﻠ ﻓﺎﺋﻘﺔ اﻟﻧﺎﻧوﯾﺔ اﻷﺳﻼك ﻣﺳﺗﺷﻌرات ﺧﻼل ﻣن وذﻟك اﻟواﻗﻊ ّﺔﯾ (Superconducting Nanowire Single Photon Detectors) وﻗد ،ﻣﻌﮫ وﻣن ﺷﺎﻟم اﻟﻌﺎﻟم اﺑﺗﻛرھﺎ واﻟﺗﻲ اﻟﻔﺿﺎﺋﯾﺔ اﻻﺗﺻﺎﻻت ﺗﺷﻔﯾر ﻓﻲ اﻻﺧﺗراع ذﻟك ﺗﺳﺧﯾر ﺑﺎﻹﻣﻛﺎن ﯾﻛون ﻗد ﺑﺄﻧﮫ ﻧﺎﺳﺎ ﺣتّﺻر ً ﻣﺳﺗﻘﺑﻼ اﻟﺑﻌﯾدة .5 : اﻷﺳود اﻟﺟﺳم اﺷﻌﺎع • ﻋﻧدﻣﺎ اﻟﺟﺳم إن اﻟﻣﻌروف وﻣن , ﻋﻠﯾﮫ اﻟﺳﺎﻗط اﻹﺷﻌﺎع ﻛل اﻷﺳود اﻟﺟﺳم ﯾﻣﺗص اﻻﺳﺗﻘرار ﺣﺎﻟﺔ إﻟﻰ ﯾﺻل إن ﺑﻌد اﻟﺣرارة ھذه اﻟﺟﺳم ﯾﺑﻌث اﻟﺣرارة ﻣن ﻛﻣﯾﺔ ﯾﻣﺗص اﻟﻌﻠﻣﺎء دھﺷﺔ ﻛﺎﻧت وﻗد. ﺛﺎﺑﺗﺔ اﻟﺳطﺢ ﺣرارة درﺟﺔ ﺗﻛون ﻋﻧدﻣﺎ اﻟﺣﺎﻟﺔ وھﻲ اﻟﺣراري
- 16. 16 ﻛل ﯾﻣﺗص اﻟﺳود اﻟﺟﺳم أن ﻻﺣظوا ﻋﻧدﻣﺎ ھذا ﯾﺑﻌث ﻓﺗرة وﺑﻌد ﻋﻠﯾﮫ اﻟﺳﺎﻗطﺔ اﻷﻟوان ﺻﻐﯾرة ﻓﺗﺣﺔ ﺑﮫ ﺗﺟوﯾف اﻧﮫ ﻋﻠﻰ اﻷﺳود اﻟﺟﺳم ﺗﺻور وﯾﻣﻛن. أﺧرى ﻣرة اﻹﺷﻌﺎع أن إﻟﻰ ﺑداﺧﻠﮫ اﻟﻣﺳﺗﻣرة ﺑﺎﻻﻧﻌﻛﺎﺳﺎت اﻹﺷﻌﺎع وﯾﺑدأ اﻹﺷﻌﺎع ﻣﻧﮭﺎ ﯾدﺧل طﺎﻗﺗﮫ ﻛل ﯾﻔﻘد ﺑﺎﻟداﺧل • ﺷدة ﺗوزﯾﻊ ﻟﻣﻧﺣﻧﯾﺎت اﻟﺗﺟرﯾﺑﯾﺔ اﻟﻧﺗﺎﺋﺞ اﻟﺗﺎﻟﻲ اﻟﺷﻛل وﯾوﺿﺢ طﯾف ﻓﻲ اﻹﺷﻌﺎع ﻟﮭﺎ ﺗﻔﺳﯾر وﺟود دون ﻣن ﻣﺧﺗﻠﻔﺔ ﺣرارة درﺟﺎت ﻋﻧد اﻷﺳود اﻟﺟﺳم درﺟﺔ ﺑزﯾﺎدة ﺗزداد اﻷﺳود ﻟﻠﺟﺳم (اﻟطﺎﻗﺔ )ﻛﺛﺎﻓﺔ اﻹﺷﻌﺎﻋﯾﺔ اﻟﺷدة أن ﻣﻧﮭﺎ وﻧﻼﺣظ ﻋﻠﻰ وﯾﻧص اﻟزﯾﺎدة ھذه ﻟﺗﻔﺳﯾر ﺗﺟرﯾﺑﻲ ﻗﺎﻧون ﺳﺗﯾﻔﺎن اﻟﻌﺎﻟم وﺿﻊ وﻟﮭذا اﻟﻣطﻠﻘﺔ اﻟﺣرارة اﻹﺷﻌﺎﻋ اﻟﺷدة : أن اﻷﺳود ﻟﻠﺟﺳم ﯾﺔ U اﻟﺣرارة ﻟدرﺟﺔ اﻟراﺑﻊ اﻷس ﻣﻊ طردﯾﺎ ﺗﺗﻧﺎﺳب T ﺣﯾث s . ﺳﺗﯾﻔﺎن ﺛﺎﺑت 4 T U وﺟوﻧز راﯾﻠﻲ ﺗﻔﺳﯾر • ال اﻟﻘرن ﻧﮭﺎﯾﺔ ﻓﻲ اﻟﻌﻠﻣﺎء ﺣﺎول ﻟﻘد 19 اﻟﺗوزﯾﻌﺎت ﺑﮭذه ﯾﺗﻧﺑﺄ ﻓﯾزﯾﺎﺋﯾﺎ ﻧﻣوذﺟﺎ ﺗﻘدﯾم ﻟﻛﯾﻔﯾﺔ ﺗﺻورا وﺟوﻧز راﯾﻠﻲ اﻟﻌﺎﻟﻣﺎن ﻓﻘدم اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻧظر وﺟﮭﺔ ﻣن وذﻟك اﻟطﯾﻔﯾﺔ وھذه ذرات ﻣن ﺗﺗﻛون اﻟﺟﺳم ﺟدران أن ﺑﻣﺎ: اﻟﺗﺎﻟﻲ اﻟﻧﺣو ﻋﻠﻰ اﻷﺳود اﻟﺟﺳم اﺷﻌﺎع ﺣ ﺗﺗﺣرك ﺷﺣﻧﺎت ﺑﮭﺎ اﻟذرات ﺗﻧص اﻟﺗﻲ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻧظرﯾﺔ ﻋﻠﻰ ﺑﻧﺎء اھﺗزازﯾﺔ رﻛﺔ اﻹﺷﻌﺎع ﻓﺈن وﺑﺎﻟﺗﺎﻟﻲ ﻛﮭروﻣﻐﻧﺎطﯾﺳﯾﺔ ﻣوﺟﺎت ﻣﻧﮭﺎ ﺗﻧطﻠﻖ اﻟﻣﺗﺳﺎرﻋﺔ اﻟﺷﺣﻧﺎت ﺑﺄن
- 17. 17 ﻋﻠﻰ وﺑﻧﺎء اﻟﺟﺳم ﻣن اﻹﺷﻌﺎع ﯾﻧﺑﻌث اﻟطرﯾﻘﺔ وﺑﮭذه اﻟذرات ھذه ﻣن ﯾﻧطﻠﻖ أن ﯾﻣﻛن :اﻟﺗﺎﻟﻲ اﻟﻘﺎﻧون وﺟوﻧز راﯾﻠﻲ وﺿﻊ ذﻟك 4 8 4 T k c U B ﺣﯾث k و ﺑوﻟﺗزﻣﺎن ﺛﺎﺑت ھو l ﺟﯾدة ﺑﺻورة اﻟﻘﺎﻧون ھذا وﯾﻧطﺑﻖ اﻟﻣﻧﺑﻌث اﻟﺿوء ﻣوﺟﺔ طول ﺣﺎﻟﺔ ﻓﻲ وﻟﻛن (اﻟطﺎﻗﺔ )ﻣﻧﺧﻔﺿﺔ اﻟطوﯾﻠﺔ اﻟﻣوﺟﯾﺔ اﻷطوال ﺣﺎﻟﺔ ﻓﻲ اﻟﻣﻌﻣﻠﯾﺔ اﻟﺗﺟﺎرب ﻣﻊ وﻻ ﻻﻧﮭﺎﺋﯾﺔ اﻟﻣﻧﺑﻌﺛﺔ اﻟطﺎﻗﺔ ﻛﺛﺎﻓﺔ ﺗﺻﺑﺢ اﻟﺻﻔر ﻣن اﻟﻘرﯾﺑﺔ أي اﻟﻘﺻﯾرة اﻟﻣوﺟﯾﺔ اﻷطوال ھذا ﯾﺗﻔﻖ وﻟﮭذا ﺟدا ﻗﺻﯾر ﻣوﺟﻲ طول ﻟﮭﺎ اﻟﺑﻧﻔﺳﺟﯾﺔ ﻓوق اﻷﺷﻌﺔ أن ﻧﻌﻠم ﻓﻧﺣن اﻟﺗﺟرﺑﺔ ﻣﻊ ﺑﻧﻔﺳﺟﯾﺔ ﻓوق اﻷﺷﻌﺔ ﻛﺎرﺛﺔ ﺑﺈﺳم ﺗﻌرف اﻟﻣﺷﻛﻠﺔ ھذه أﺻﺑﺣت اﻟﺳﺑب وﺗوﺻل اﻟﺟزﯾﺋﺎت ﻣن ﻏﺎز ﻋن ﻋﺑﺎرة اﻹﺷﻌﺎع ﺑﺄن اﻓﺗراﺿﮫ ﻓﯾن اﻟﻌﺎﻟم ﻗدم اﻟﺻﯾﺎغ ﻧﻔس وﻓﻲ ب ﯾﻌطﻰ اﻹﺷﻌﺎع ھذا ﺗوزﯾﻊ أن إﻟﻰ T k hc hc c U B exp 8 4 3 ﺗﻔﺳﯾر ﻓﻲ ﻓﺷل وﻟﻛﻧﮫ اﻟﻘﺻﯾرة اﻟﻣوﺟﯾﺔ اﻷطوال ﻓﻲ اﻟﻌﺎﻟﯾﺔ اﻟطﺎﻗﺎت ﻣﻊ اﻟﻘﺎﻧون ھذا وﯾﺗﻔﻖ اﻟطوﯾﻠﺔ ﺑﺎﻷﻣواج اﻟﺧﺎص اﻟﺟزء :اﻷﺳود اﻟﺟﺳم اﺷﻌﺎع ﺗﻔﺳﯾر وﻛﺎﻧت , ﻛﺎﻣﻠﺔ ﺑﺻورة اﻷﺳود اﻟﺟﺳم اﺷﻌﺎع ﺗﻔﺳﯾر ﻓﻲ اﻟﺳﺎﺑﻘﺔ اﻟﻘواﻧﯾن ﺟﻣﯾﻊ ﺗﻔﻠﺢ ﻟم اﻟﻧﺗﺎﺋﺞ ﺗطﺎﺑﻖ ﻓﻲ ﻣﺣدودة ﻋدم أن إﻟﻰ ﺑﻼﻧك ﻣﺎﻛس اﻟﻌﺎﻟم ﺗوﺻل وﻟذﻟك, واﻟﻧظرﯾﺔ اﻟﺗﺟرﯾﺑﯾﺔ : أن واﻓﺗرض اﻟظﺎھرة ھذه ﻟﺗﻔﺳﯾر اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻘواﻧﯾن اﺳﺗﺧدام ﻣن ﺟﺎء اﻟﺳﺎﺑﻖ اﻟﺗطﺎﺑﻖ ) 1 ( ﻣﻊ ﺗﺗﻧﺎﺳب اﻷﺳود اﻟﺟﺳم ﻓﻲ اﻟﻣﺗذﺑذب ﻣن اﻟﻣﻣﺗﺻﺔ أو اﻟﻣﻧﺑﻌﺛﺔ اﻟطﺎﻗﺔ ﻛﻣﯾﺔ ﺗردده E=hn ) 2 ( ﻗﯾم اﻟﻣﺗذﺑذب طﺎﻗﺔ ﺗﺄﺧذ أن أي ()ﻣﻛﻣﻣﺔ ﻣﺣددة E=nhn ﻛﺎﻧت ﻓﺈذا n=0 وﯾﺳﻣﻰ اﻟطﺎﻗﺔ ﻓﻲ ﻟﮫ ﻗﯾﻣﺔ أدﻧﻰ ﻓﻲ اﻟﻣﺗذﺑذب ﯾﻛون Ground Level اﻷﺳود اﻟﺟﺳم ﻓﻲ اﻟﻣﺗذﺑذﺑﺎت ﻋﻠﻰ اﻟﺗﻛﻣﯾم ﻣﺑدأ ادﺧل ﺑﻼﻧك أن ﻧﻼﺣظ ھﻧﺎ وﻣن اﻟﻛﻣﻲ ﺑﺎﻟﻌدد ﻣﺣددة وﺑﻘﯾم ﻣﺣددة طﺎﻗﺎت ﻟﮭﺎ وأﻧﮭﺎ n ﻛﻣﺎ ﻟﻠطﺎﻗﺔ ﻣﺗﺻﻠﺔ ﻟﻘﯾم وﺟود وﻻ اﻓﺗ اﻟﺟﺳم طﺎﻗﺔ ﻛﺛﺎﻓﺔ ﻟﺗوزﯾﻊ اﻟﺗﺎﻟﻲ اﻟﻘﺎﻧون إﻟﻰ ﺑﻼﻧك وﺗوﺻل.ﺟﯾﻧز راﯾﻠﻲ اﻟﻌﺎﻟﻣﺎن رض اﻟﺗﺎﻟﯾﺔ اﻟﺻورة ﻋﻠﻰ وذﻟك اﻷﺳود
- 18. 18 1 exp 1 8 4 ) , ( 5 T k hc hc c T U B ﺑﯾن اﻟطﺎﻗﺔ ﻓرق ﺗﺳﺎوي طﺎﻗﺗﮭﺎ ﻓﺈن اﻷﺳود اﻟﺟﺳم ﻣن اﻧﺑﻌﺎﺛﮭﺎ أو أﺷﻌﺔ اﻣﺗﺻﺎص وﻋﻧد إن ﺑﺣﯾث ﻟﻠﻣﺗذﺑذﺑﺎت اﻟطﺎﻗﺔ ﻣﺳﺗوﯾﺎت E = hn اﻟﻌﺎﻟم ﺗﻣﻛن اﻟﻔرﺿﯾﺎت ھذه أﺳﺎس وﻋﻠﻰ اﻟﻔوﺗون ﯾﺳﻣﻰ ﺟﺳﯾم اﻟطﺎﻗﺔ ﻣن اﻟﻛم ھذا وﯾﺣﻣل أن وﺟد وﻗد , اﻟﻌﻠﻣﯾﺔ اﻟﻧﺗﺎﺋﺞ ﻓﺳر اﻟذي اﻷﺳود اﻟﺟﺳم ﻹﺷﻌﺎع ﺑﻼﻧك ﻗﺎﻧون اﺷﺗﻘﺎق ﻣن ﺑﻼﻧك اﻷﺳود اﻟﺟﺳم ﻹﺷﻌﺎع اﻟﺗﺟرﯾﺑﯾﺔ اﻟﻧﺗﺎﺋﺞ ﻣﻊ ﺗﻣﺎﻣﺎ ﯾﺗﻔﻖ ﺑﻼﻧك ﻗﺎﻧون
- 19. 19 اﻟﺛﺎﻧﻲ اﻟﻔﺻل اﻟﺗﻌرﯾف اﻟﻛﻣوﻣﻲ اﻟﺣﺎﺳب ﺑﻣﺎھﯾﺔ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ھﻮ ﻛﻤﺒﯿﻮﺗﺮ ﯾﺤﺎﻛﻲ ﻣﻨﻈﻮﻣﺔ اﻟﺤﺴﺎﺑﺎت ﻓﻲ اﻟﻔﯿﺰﯾﺎء ،اﻟﻜﻤﻮﻣﯿﺔ ﺑﺤﯿﺚ ﯾﺘﻢ إﻋﺎدة ﺑﻨﺎء دارات وﺑﻮاﺑﺎت اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻼﺳﯿﻜﻲ ًاداﻋﺘﻤﺎ ﻋﻠﻰ وﺧﻮارزﻣﯿﺎت ﻣﺴﺎﺋﻞ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ اﻟﻐﺮﯾﺒﺔ واﻟﻤﺪھﺸﺔ . اﻟﻜﻔﺎءة اﻟﻨﻈﺮﯾﺔ ﻟﻠﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ ﻓﻲ ﺣﻞ اﻟﻜﺜﯿﺮ ﻣﻦ اﻷﻟﻐﺎز اﻟﻔﯿﺰﯾﺎﺋﯿﺔ ﻓﻲ اﻟﻌﺼﺮ ،اﻟﺤﺪﯾﺚ وﺗﻮﻗﻌﺎﺗﮭﺎ اﻟﻤﺒﻜﺮة ﻻﻛﺘﺸﺎف ﺧﻮارزﻣﯿﺔ ﻛﻤﻮﻣﯿﺔ ﺗﻔﯿﺪ ﻏﺮض اﻟﺘﻄﻮر ﻓﻲ اﻟﻜﺒﯿﺮ ﻋﺎﻟﻢ ،اﻟﻜﻤﺒﯿﻮﺗﺮ ﻗﺎدﺗﺎ اﻟﻜﺜﯿﺮ ﻣﻦ اﻟﻌﻠﻤﺎء إﻟﻰ اﻟﻌﻤﻞ اﻟﺘﻄﺒﯿﻘﻲ ﻋﻠﻰ ﻧﻤﺎذج ﻣﺨﺒﺮﯾﺔ ﻟﻠﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ ًﺎﯿﻛﻤﻮﻣ ﺗﺘﺠﺎوز ﺗﻠﻚ اﻟﻤﺼﻤﻤﺔ ًاداﻋﺘﻤﺎ ﻋﻠﻰ أﻧﺼﺎف واﻟﻔﯿﺰﯾﺎء اﻟﻨﻮاﻗﻞ ،اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﺘﻲ ﺑﻘﯿﺖ ﺗﻌﻤﻞ ﺑﻜﻔﺎءة ﻋﺎﻟﯿﺔ ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﺘﻘﻠﯿﺪي ﺣﺘﻰ ﺑﻠﻮغ اﻟﺘﺮاﻧﺰﺳﺘﻮرات ﻓﻲ وﺣﺪة اﻟﻤﺴﺎﺣﺔ ﻓﻲ اﻟﺪارات اﻟﺮﻗﻤﯿﺔ اﻹﻟﻜﺘﺮوﻧﯿﺔ ،اﻟﺬري اﻟﻤﺴﺘﻮى ،وﺗﻘﻊ ،ﺑﺎﻟﻀﺮورة ﻓﻲ ﻣﺠﺎل ﻋﻤﻞ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ ﺑﺘﻔﻮق . ﺑﺎت ﻣﻔﮭﻮم اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ) Quantum Computer, QC ( ﻣﺤﻄﺎﻻھﺘﻤﺎم ،اﻷﻛﺒﺮ ﻓﻲ اﻟﺴﻨﻮات ،اﻷﺧﯿﺮة ﻓﻲ ﻋﺎﻟﻢ اﻟﺘﻘﻨﯿﺔ واﻷﺑﺤﺎث واﻟﺪراﺳﺎﺗﺎﻟﻌﻠﻤﯿﺔ اﻟﺘﻲ أﻋﺎدت اﻟﺒﺤﺚ اﻟﻌﻠﻤﻲ اﻟﻔﯿﺰﯾﺎﺋﻲ واﻟﺘﻘﻨﻲ إﻟﻰ اﻟﺘﺮﻛﯿﺰ ﻋﻠﻰ ﻣﻔﺎھﯿﻤﻮظﻮاھﺮ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ / اﻟﻜﻮاﻧﺘﯿﺔ ) Quantum Physics ( ﺑﻐﯿﺔ اﺳﺘﺨﺪاﻣﮭﺎﻓﻲ ﻋﺎﻟﻢ اﻟﻜﻤﺒﯿ ﻮﺗﺮ ﺑﺨﻮارزﻣﯿﺎﺗﮫ وﺑﻮاﺑﺎﺗﮫ وداراﺗﮫ اﻟﻤﻨﻄﻘﯿﺔ ،واﻟﺮﻗﻤﯿﺔ ﺗﻠﻚ اﻟﺘﯿﯿﻤﻜﻨﮭﺎ ﺣﻞ اﻟﻜﺜﯿﺮ ﻣﻦ اﻟﻤﺸﺎﻛﻞ اﻟﺘﻘﻨﯿﺔ اﻟﺘﻲ ﺑﺪأت ﺗﻈﮭﺮ ﻓﻲ ﻋﺎﻟﻢ اﻟﻜﻤﺒﯿﻮﺗﺮاﻟﻜﻼﺳﯿﻜﻲ . 1 وﺗﺸﯿﺮ اﻟﺪراﺳﺎت اﻟﺤﺪﯾﺜﺔ إﻟﻰ اﻟﺘﻔﻮق اﻟﻜﻤﻲ ﻟﻠﺤﻮاﺳﯿﺐ اﻟﻜﻤﻮﻣﯿﺔاﻟﺘﻲ ﺗﻌﺘﻤﺪ ﻋﻠﻰ ﻣﻌﺎﻟﺞ ﻓﺎﺋﻖ ،اﻟﺘﻮﺻﯿﻞ وﯾﺴﺘﺨﺪم ﺧﻮارزﻣﯿﺔ ﻛﻤﻮﻣﯿﺔ ﻗﺎﺑﻠﺔﻹﻧﺸﺎء ﻣﻌﺎﻟﺞ ﱠﻒ ﻣﺆﻟ ﻣﻦ 53 ﻛﯿﻮﺑﺖ ) Qubits ( ُﺪﻋﻰﯾ ) Sycamore ( ﯾﻨﺠﺰﻣﮭﻤﺘﮫ ﺧﻼل 200 ،ﺛﺎﻧﯿﺔ ﻓﻲ ﺣﯿﻦ ﯾﻨﺠﺰه اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻼﺳﯿﻜﻲ ب 10000 ﻋﺎم ! 2 ﯾﻜﻤﻦ اﻷﺳﺎس اﻟﺘﻘﻨﻲ اﻟﺬي ﻗﺎد اﻟﻌﻠﻤﺎء إﻟﻰ اﻟﺒﺤﺚ ﻓﻲ ﻣﻮﺿﻮع اﻟﻜﻤﺒﯿﻮﺗﺮاﻟﻜﻤﻮﻣﻲ ﻓﻲ ﻛﯿﻔﯿﺔ زﯾﺎدة ﻛﻔﺎءة اﻟﺤﻮاﺳﯿﺐ ًﺎﯿﺗﻘﻨ ﻣﻦ ﺣﯿﺚ ﺳﺮﻋﺔ ﻣﻌﺎﻟﺠﺔ اﻟﺒﯿﺎﻧﺎت وﻧﻘﻠﮭﺎ ،وﺗﺨﺰﯾﻨﮭﺎ واﻟﺘﻲ ﻛﺎﻧﺖ ً ﻧﺘﯿﺠﺔ ﻟﺰﯾﺎدة أﺳﯿﺔ ﻓﻲ اﻟﺘﺮاﻧﺰﺳﺘﻮرات ﻋﺪد ﻓﻲ وﺣﺪة اﻟﻤﺴﺎﺣﺔ ﻓﻲ اﻟﺪارات واﻟﺒﻮاﺑﺎت اﻟﺮﻗﻤﯿﺔ إﻟﻰ واﻟﻤﻌﺎﻟﺠﺎت ﺣﺪ ﻻ ﯾﻤﻜﻦ ﺗﺠﺎوزه ًﺎﯿﺗﻘﻨ وھﻮ ﺣﺪ اﻟﺒﻌﺪ ،اﻟﺬري ﺣﯿﺚ ﺗﺼﺒﺢ اﻟﻈﻮاھﺮ اﻟﻜﻤﻮﻣﯿﺔ اﻟﻐﺮﯾﺒﺔ ھﻲ اﻷﻛﺜﺮ ھﯿﻤﻨﺔ ﻣﻦ اﻟﻈﻮاھﺮ اﻟﻔﯿﺰﯾﺎﺋﯿﺔ اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﻤﻌﺮوﻓﺔ واﻟﻤﺄﻟﻮﻓﺔ . 3 ا ًﻣﺒﻜﺮ وﻓﻲ ﻋﺎم 1965 ، ﺗﻨﺒﺄ Gordon Moore ، ﻣﻦ ﺷﺮﻛﺔ )- Fair child Semiconductor Corporation ، ﺑﺄن ﻋﺪد وﺣﺪات اﻟﺘﺮاﻧﺰﺳﺘﻮر Transistor واﻷﺟﺰاء اﻹﻟﻜﺘﺮوﻧﯿﺔ اﻷﺧﺮى ﻓﻲ اﻟﺸﺮاﺋﺢ واﻟﺪارات اﻹﻟﻜﺘﺮوﻧﯿﺔ اﻟﻤﺘﻜﺎﻣﻠﺔ ( Integrated Circuits, IC ( ﺳﯿﺘﻀﺎﻋﻒ ﻛﻞ ﻋﺎم 4 وذﻟﻚ ﺣﺘﻰ ﺗﻜﻮن ﻗﺎدرة ﻋﻠﻰ ﻣﻮاﻛﺒﺔ ﻣﺘﻄﻠﺒﺎت اﻟﺘﻜﻨﻮﻟﻮﺟﯿﺎ اﻟﺤﺪﯾﺜﺔ
- 20. 20 ﺣﯿﺚ ﻣﻦ اﻟﺴﺮﻋﺔ وﻗﻮة ﻣﻌﺎﻟﺠﺔ ،اﻟﺒﯿﺎﻧﺎت وﺑﻌﺪ ذﻟﻚ ﯾﻌﺪل ﻣﻮر ﺗﻮﻗﻌﺎﺗﮫ ،إﻟﯨﻌﺎﻣﯿﻦ ﺛﻢ إﻟﻰ 18 ،ا ًﺷﮭﺮ وھﻮ ﻣﺎ ﺑﺎت ﯾﻌﺮف ﺑﻘﺎﻧﻮن ﻣﻮر ﻛﻤﺎ ھﻮ ﻣﻮﺿﺢ ) اﻟﺸﻜﻞ ﻓﻲ 1 ( أدى اﻟﺘﻄﻮر اﻟﺘﻘﻨﻲ ،اﻟﻤﺘﺰاﯾﺪ ﺑﺪءًا ﻣﻦ اﻟﺘﺮاﻧﺰﺳﺘﻮر ﺛﻢ اﻟﺪارات اﻟﻤﺘﻜﺎﻣﻠﺔﺛﻢ اﻟﻤﺘﺤﻜﻤﺎت اﻟﺼﻐﺮﯾﺔ Microprocessor إﻟﻰ ﺛﻮرة ھﺎﺋﻠﺔ ﻓﻲ اﻟﺘﻜﻨﻮﻟﻮﺟﯿﺎ ﻋﺎﻟﻢ ،واﻟﺤﻮاﺳﯿﺐ وﺻﻠﺖ إﻟﻰ ﻣﺮﺣﻠﺔ ﯾﺼﻌﺐ ﺗﺠﺎوزھﺎ ﻋﻠﻰ ﺳﺮﻋﺔ ﻣﺴﺘﻮﯾﻲ ﻧﻘﻞ اﻟﺒﯿﺎﻧﺎت وﻣﻌﺎﻟﺠﺘﮭﺎ وﺗﺨﺰﯾﻨﮭﺎ ﻓﻲ اﻟﺒﻨﺎء اﻹﻟﻜﺘﺮوﻧﻲ ،ذاﺗﮫ ﺑﺒﻮاﺑﺎﺗﮭﻮداراﺗ ﮫ اﻹﻟﻜﺘﺮوﻧﯿﺔ ﻓﻲ اﻟﺤﻮاﺳﯿﺐ اﻟﻜﻼﺳﯿﻜﯿﺔ؛ ذﻟﻚ أن زﯾﺎدة ﻋﺪد ﻓﻲ اﻟﺘﺮاﻧﺰﺳﺘﻮرات وﺣﺪة ،اﻟﻤﺴﺎﺣﺔ ﺑﺤﺴﺐ ،ﻣﻮر ﺳﯿﺼﻞ إﻟﻰ ﺣﺪ اﻟﺒﻌﺪ ،اﻟﺬري ﻣﺎ ﯾﺠﻌﻞ اﻟﺤﺴﺎﺑﺎت اﻟﻜﻤﻮﻣﯿﺔ ًةﺿﺮور ً ﻣﻨﻄﻘﯿﺔ ﻓﻲ ٍﺔﻣﺤﺎوﻟ ﻧﻈﺮﯾﺔ ،ًﺎﯿأوﻟ وذﻟﻚ ﻣﺮﺣﻠﺔ ﻟﺘﺠﺎوز أﻧﺼﺎف اﻟﻨﻮاﻗﻞ واﻟﻌﻤﻞ ﻋﻠﻰ اﻟﻤﺴﺘﻮى اﻟﺬري وﻗﻮاﻧﯿﻨﮭﺎ اﻟﻜﻤﻮﻣﯿﺔ ﺑﺎت ﻓﯿﻤﺎ ﯾﻌﺮف ﺑﺎﺳﻢ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ) 6.)QC وﺑﺎﻟﻨﺴﺒﺔ إﻟﻰ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ﻓﮭﻮ ﻛﻤﺒﯿﻮﺗﺮ ﯾﺤﺎﻛﻲ ﻣﻨﻈﻮﻣﺔ ﻓﻲ اﻟﺤﺴﺎﺑﺎت اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ اﻟﻐﺮﯾﺒﺔ واﻟﻤﺪھﺸﺔ ﻓﻲ ﻋﺎﻟﻢ اﻟﺠﺴﯿﻤﺎت ودراﺳﺔ ،ﺳﻠﻮﻛﮭﺎ ﻓﮭﻮ ،ﯾﺠﻤﻊ ﻣﻦ ﺣﯿﺚ اﻷﺳﺎس ،اﻟﻌﻠﻤﻲ ﺑﯿﻦ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ وﺑﯿﻦ دارات وﺑﻮاﺑﺎت اﻟﻤﻨﻄﻖ اﻟﺘﻲ ُﻨﻲﺑ ﻋﻠﻰ أﺳﺎﺳﮭﺎ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻼﺳﯿﻜﻲ اﻟﻤﻌﺮوف اﻟﯿﻮم . ﻓﺎﻟﻜﻔﺎءة اﻟﻨﻈﺮﯾﺔ ﻟﻠﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ ﻓﻲ ﺣﻞ اﻟﻜﺜﯿﺮ ﻣﻦ اﻷﻟﻐﺎز ،اﻟﻔﯿﺰﯾﺎﺋﯿﺔ وﺗﻮﻗﻌﺎﺗﮭﺎ اﻟﻤﺒﻜﺮة ﻻﻛﺘﺸﺎف ﺧﻮارزﻣﯿﺔ ﻛﻤﻮﻣﯿﺔ ﺗﻔﯿﺪ ﻏﺮض اﻟﺘﻄﻮر اﻟﻜﺒﯿﺮ ﻋﺎﻟﻢ ﻓﻲ ،اﻟﻜﻤﺒﯿﻮﺗﺮ ﻗﺎدﺗﺎ اﻟﻜﺜﯿﺮ ﻣﻦ اﻟﻌﻠﻤﺎء إﻟﻰ اﻟﻌﻤﻞ اﻟﺘﻄﺒﯿﻘﻲ ﻋﻠﻰ ﻣﺨﺒﺮﯾﺔ ﻧﻤﺎذج أوﻟﯿﺔ ﻟﺘﺼﻤﯿﻢ وﺗﺼﻨﯿﻊ اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ ))- Quantum Log ical Gates, QLG ( ، ﻓﻲ ﻣﺤﺎوﻟﺔ ﻟﺘﺠﺎوز ﺗﻠﻚ اﻟﻤﺼﻤﻤﺔ ًاداﻋﺘﻤﺎ ﻋﻠﻰ اﻟﻨﻮاﻗﻞ أﻧﺼﺎف واﻟﻔﯿﺰﯾﺎء اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﺘﻲ ﺑﻘﯿﺖ ﺗﻌﻤﻞ ﺑﻜﻔﺎءة ﻋﺎﻟﯿﺔ ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮاﻟﺘﻘﻠﯿﺪي ﺣﺘﻰ ﺑﻠﻮﻏﮭﺎ اﻟﻤﺴﺘ ﻮى اﻟﺠﺰﯾﺌﻲ واﻟﺬري ﻣﻦ ﺣﯿﺚ اﻟﻌﺪد ﻓﻲ وﺣﺪة
- 21. 21 ،اﻟﻤﺴﺎﺣﺔ ﻓﺒﺎت ﻣﻦ اﻟﺼﻌﺐ ﺗﺼﻤﯿﻢ اﻟﺘﺮاﻧﺰﺳﺘﻮر وأﺳﻼك اﻟﻨﻘﻞ ﺑﺄﺑﻌﺎد ذرﯾﺔ . وﻣﻦ اﻟﻤﻔﯿﺪ ًﺎﯿﻋﻠﻤ اﻹﺷﺎرة ھﻨﺎ إﻟﻰ أن اﻟﻌﻤﻞ وﻓﻖ اﻟﺨﻮارزﻣﯿﺎت اﻟﻜﻤﻮﻣﯿﺔ ،ﻻﯾﻌﻨﻲ ،ﺑﺎﻟﻀﺮورة اﺳﺘﺒﺪال ﻛﺎﻓﺔ ﻣﻜﻮﻧﺎت اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻼﺳﯿﻜﻲ ﺑﻘﺪر اﻻﺳﺘﻔﺎدة ﻣﻦ اﻟﻈﻮاھﺮ اﻟﻜﻤﻮﻣﯿﺔ اﻟﻔﯿﺰﯾﺎﺋﯿﺔ ﻓﻲ ﻋﻼج اﻟﻤﺴﺎﺋﻞ اﻟﺘﻲ ﻻ ﯾﻤﻜﻦ اﻟﻜﻼﺳﯿﻜﯿﺔ ﻟﻠﻔﯿﺰﯾﺎء ﻋﻼﺟﮭﺎ ﻋﺒﺮ ﺑﻨﺎء اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ اﻟﺘﻲ ﺗﺴﮭﻢ ﻓﻲ ﺳﺮﻋﺔ زﯾﺎدة ﻣﻌﺎﻟﺠﺔ اﻟﺒﯿﺎﻧﺎت ،ًﺎﯿﻛﻤ 7 وﺑﺎﻟﻀﺮورة ،ًﺎﻀأﯾ إﻣﻜﺎﻧﯿﺔ اﺳﺘﺨﺪام اﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ ) Quantum Computation ( ﻓﻲ ﻣﻌﺎﻟﺠﺔ اﻟﻌﺪﯾﺪ ﻣﻦ اﻟﻌﻠﻤﯿﺔ اﻟﻘﻀﺎﯾﺎ ذات اﻷوﺟﮫ اﻻﺣﺘﻤﺎﻟﯿﺔ اﻟﻤﻌﻘﺪة اﻟﺘﻲ ﺗﺤﺘﺎج إﻟﻰ ﺣﺴﺎﺑﺎت ﺗﺄﺧﺬ ﻛﻼﺳﯿﻜﯿﺔ ًﺎﻧأزﻣﺎ ﻛﺒﯿﺮة ﻓﻲ ﺣﻠﮭﺎ ،ًﺎﯿﻛﻼﺳﯿﻜ ﻣﺎ ﺟﻌﻞ أﻓﻀﻠﯿﺔ اﻟﻌﻤﻞ ﻋﻠﻰ اﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ ﺗﺄﺧﺬ ﻣﺠﺎ ًل ًﺎواﺳﻌ ﻓﻲ اﻟﺪراﺳﺎت اﻟﻌﺸﻮاﺋﯿﺔ اﻟﻜﻤﯿﺔ ﻓﺎﺋﻘﺔ ،اﻻﺣﺘﻤﺎﻻت )Quantum Walks( ﻛﻤﺎ ﻓﻲ اﻟﺘﻄﺒﯿﻘﺎت اﻟﺤﺪﯾﺜﺔ ﻟﻠﻜﯿﻤﯿﺎء اﻟﻜﻤﻮﻣﯿﺔ Quantum Chemistry واﻟﺠﺰﯾﺌﯿﺔ ،واﻟﺒﯿﻮﻟﻮﺟﯿﺔ إذ ﺗﻘﺪﻣﺖ اﻟﺘﺠﺎرب اﻟﻌﻤﻠﯿﺔ ﻓﻲ ﺗﺤﺪﯾﺪ وﺗﺼﻨﯿﻒ اﻟﺘﺸﺎﺑﻚ اﻟﻜﻤﻮﻣﻲ اﻟﺠﺰﯾﺌﻲ ،ًﺎ ﺣﺪﯾﺜ ﻛﺘﻠﻚ اﻟﺘﻲ ًاداﻋﺘﻤﺎ اﻋﺘﻤﺪت ًﺎﺴرﺋﯿ ﻋﻠﻰ ﺗﺠﺎرب اﻟﺘﺒﻌﺜﺮ ﻟﻠﻤﺮﻛﺐ اﻟﺠﺰﯾﺌﻲ ﻟﻨﻈﯿﺮ اﻟﮭﯿﺪروﺟﯿﻦ ﱠﮫﺟاﻟﻤﻮ اﻟﺜﻨﺎﺋﻲ ) H2H( )Oriented hydrogen deuteride ( واﻟﻤﻌﺮوف ب ) ، )HD واﻟﮭﯿﺪروﺟﯿﻦ ،اﻟﺠﺰﯾﺌﻲ 9 وﯾﻤﻜﻦ إﻓﺮاد دراﺳﺎت أﺧﺮى ﺗﻔﻲ ﺑﻐﺮﺿﮭﺎ ﺑﺘﻘﻨﯿﺎﺗﮭﺎ؛ وﺗﻠﻢ ذﻟﻚ أن اﻟﻤﺠﺎل ﻟﻤﻨﺎﻗﺸﺘﮭﺎ ﻻ ﯾﺘﺴﻊ ﻓﻲ ھﺬه اﻟﺪراﺳﺔ
- 22. 22 اﻟﺜﺎﻟﺚ اﻟﻔﺼﻞ اﻟﺤﺎﺳﻮب اﺟﻠﮭﺎ ﻣﻦ ﺻﻤﻢ اﻟﺘﻲ واﻟﻐﺎﯾﺎت اﻻھﺪاف اﻟﻜﻤﻮﻣﻲ ﻓﻲ إطﺎر ﺗﻠﻚ اﻟﻔﺮﺿﯿﺎت واﻟﺘﺠﺎرب اﻟﻌﻠﻤﯿﺔ اﻟﻤﺨﺒﺮﯾﺔ اﻟﻜﺜﯿﺮة اﻟﺘﻲ ّمﺪُﻗ ﺧﻼﻟﮭﺎ ﻣﻦ اﻟﻜﺜﯿﺮ ﻣﻦ اﻷوراق واﻟﺪراﺳﺎت اﻟﻌﻠﻤﯿﺔ ﺑﻐﯿﺔ ﺟﻌﻞ اﻟﻜﻤﺒﯿﻮﺗﺮ ﯾﻌﻤﻞ اﻟﺘﻘﻠﯿﺪي ﻋﻠﻰ أﺳﺎس اﻟﺤﺴﺎﺑﺎت ﻧﺘﺘﺒﻊ،اﻟﻜﻤﻮﻣﯿﺔ ﻓﻲ دراﺳﺘﻨﺎ ھﺬه اﻟﻤﺤﺎوﻻت اﻟﺘﻘﻨﯿﺔ اﻷﻛﺜﺮ ﺷﮭﺮة ﻟﺒﻨﺎء اﻟﺒﻮاﺑﺎت واﻟﺪارات اﻟﻤﻨﻄﻘﯿﺔ ﻓﻲ اﻟﺤﻮﺳﺒﺔ ،اﻟﻤﻘﺘﺮﺣﺔ اﻟﻜﻤﻮﻣﯿﺔ ً ﻣﺘﻀﻤﻨﺔ ﺗﻘﺪﯾﻢ ﻋﺮض ﻣﺮﻛّﺰ ﻋﻦ أھﻢ ﻣﺒﺎدﺋﮭﺎ اﻟﻜﻤﻮﻣﯿﺔ ،ًﺎﯿوﺗﻘﻨ ًﺎﯿﻓﯿﺰﯾﺎﺋ ﺑﺤﯿﺚ ﺗﺸﻜّﻞ ًﺎﺳأﺳﺎ ًﺎﯿﻋﻠﻤ ًﺎﻔﻣﻜﺜ ﻟﻠﻄﻼب اﻟﻌﺮب اﻟﻤﮭﺘﻤﯿﻦ ﺑﮭﺬا اﻟﻤﺠﺎل ،ًﺎﯾﻧﻈﺮ وﻣﻦ ﺛﻢ إﻣﻜﺎﻧﯿﺔ ﺗﻄﺒﯿﻘﮫ ًﺎﯿﻋﻤﻠ . وﻹﻓﺮاد ﻣﺴﺎﺣﺔ اﻟﻌﻤﻞ واﻟﺘﻔﻜﯿﺮ ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻤﻮﻣﻲ ﻓﺈن اﻷھﻤﯿﺔ اﻟﻌﻠﻤﯿﺔ ﺗﻜﻤﻦ ًﺎﺳأﺳﺎ ﻓﻲ اﻟﻔﯿﺰﯾﺎء ،اﻟﻜﻤﻮﻣﯿﺔ وﯾﺼﺒﺢ اﻟﺘﻄﻠﻊ اﻟﺘﻘﻨﻲ ًﺎﺒﻗﺮﯾ اﻟﻤﺴﺘﻘﺒﻠﻲ ،ًﺎﻨوﻣﻤﻜ وھﺬا إن ﺗﺤﻘﻖ ﻓﺈﻧﮫ ﻟﻦ ﯾﺸﻜّﻞ ﺛﻮرة ﻓﻲ ﻋﺎﻟﻢ واﻟﺘﻜﻨﻮﻟﻮﺟﯿﺎ اﻟﺤﻮاﺳﯿﺐ ،ﻓﺤﺴﺐ ﺑﻞ ﺳﯿﻤﺜﻞ ﻧﻘﻠﺔ ﻧﻮﻋﯿﺔ ًﺎﻀأﯾ ﻓﻲ اﻟﺘﻔﻜﯿﺮ اﻟﻌﻠﻤﻲ ﻋﺎﻣﺔ؛وذﻟﻚ ﻋﻨﺪﻣﺎ ﺗﺠﺪ ﻗﻮاﻧﯿﻦ اﻟﻤﯿﻜﺎﻧﯿﻚ اﻟﻜﻤﻮﻣﻲ اﻟﻤﻮﺻﻮﻓﺔ ﺑﺎﻟﻐﺮاﺑﺔ اﻟﯿﻮم إﻟﻰ طﺮﯾﻘﮭﺎ اﻟﺘﻤﻮﺿﻊ اﻟﻌﻠﻤﻲ واﻟﺘﻘﻨﻲ ﻋﻠﻰ ﻧﺤﻮ ﻣﻠﻤﻮس ﻟﻜﺎﻓﺔ ﺷﺮاﺋﺢ اﻟﺒﺸﺮ . إن ﻋﻠﻢ اﻟﻤﯿﻜﺎﻧﯿﻚ اﻟﻜﻤﻮﻣﻲ اﻟﺬي ﺑﻘﻲ اًﺣﻜﺮ ًﺎﯾﻧﻈﺮ ﻋﻠﻰ ﻣﺆﺳﺴﯿﮫ ﻋﻠﻤﺎء ﻣﻦ اﻟﻔﯿﺰﯾﺎء واﻟﻌﺎﻣﻠﯿﻦ اﻟﻤﺨﺘﺼﯿﻦ ﻣﻦ ،ﺑﻌﺪھﻢ ،ﺳﯿﺼﺒﺢ ﻣﻊ ﻋﺎﻟﻢ ،اﻟﻜﻤﻮﻣﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ ﻋﻠﻤًﺎ ذا ﻗﺎﺑﻠﯿﺔ ﻟﻠﻔﮭﻢ اﻷﻛﺜﺮ ،ًﺎﻋﺷﯿﻮ وذﻟﻚ ﻋﻨﺪﻣﺎ ﯾﻨﺘﻘﻞ ﻣﻦ ﻣﺮﺣﻠﺔ اﻟﺘﺠﺮﯾﺪ اﻟﻜﻤﻲ اﻟﻨﻈﺮي إﻟﻰ ﻣﺮﺣﻠﺔ اﻟﻤﺤﺴﻮس واﻟﻤﻠﻤﻮس واﻟﻤﻔﯿﺪ ﻟﻜﻞ ﯾﺴﺘﺨﺪم ﻣﻦ َﺟﮭﺎز ﻛﻤﺒﯿﻮﺗﺮ أو ًﺎﻔھﺎﺗ ًﺎﯿذﻛ ًﺎﯿﻛﻤﻮﻣ . اﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ 1-3 اﻟﻜﻤﺒﯿﻮﺗﺮ : ﻟﻤﺤﺔ ﺗﺎرﯾﺨﯿﺔ ﻋﻠﻰ اﻟﺮﻏﻢ ﻣﻦ اﻟﺘﻄﻮر اﻟﻜﺒﯿﺮ ﻟﻌﻠﻮم اﻟﺮﯾﺎﺿﯿﺎت واﻟﻤﺤﺎوﻻت اﻟﻜﺜﯿﺮة اﻟﺘﻲ ّﻣﮭﺎﺪﻗ ﺑﻌﺾ اﻟﻌﻠﻤﺎء ﻓﻲ اﻟﺴﺎﺑﻖ ﻹﯾﺠﺎد آﻟﺔ ﻋﻤﻞ ﺣﺴﺎﺑﯿﺔ ﺗﻌﻤﻞ ،ًﺎﯿآﻟ ﻓﺈن ﻋﻠﻮم اﻟﻜﻤﺒﯿﻮﺗﺮ ﻟﻢ ﺗﺄﺧﺬ ﺣﯿﺰ ﺗﻄﻮرھﺎ اﻟﻤﺘﺴﺎرع ﻛﻤﺎ ﻧﺸﮭﺪه اﻟﯿﻮم إﻻ ﻣﻊ اﻟﺘﻄﻮر اﻟﻜﺒﯿﺮ ﻓﻲ ﻓﯿﺰﯾﺎء أﻧﺼﺎف اﻟﻨﻮاﻗﻞ وﻋﺎﻟﻢ اﻟﺪارات اﻟﻤﺘﻜﺎﻣﻠﺔ . ،ًﺎﯿﺗﺎرﯾﺨ ﻛﺎﻧﺖ ھﻨﺎك ﻋﺪة ﻣﺤﺎوﻻت ﻟﺘﺼﻨﯿﻊ ﻛﻤﺒﯿﻮﺗﺮ ﯾﻌﻤﻞ ﺑﺼﻮرة ،أوﺗﻮﻣﺎﺗﯿﻜﯿﺔ ﺑﺤﯿﺚ ﯾﺮﺑﻂ ﺑﯿﻦ ﻋﻤﻞ اﻵﻟﺔ واﻟﺬﻛﺎء اﻟﺮﯾﺎﺿﻲ ،اﻟﻤﻨﻄﻘﻲ ﻛﺎﻧﺖ أوﻟﮭﺎ ﻣﺤﺎوﻟﺔ ﺗﺸﺎرﻟﺰ ﺑﺎﺑﺎج ) Charles Babbage ( ﻓﻲ ﻋﺎم 1822 ، ﻟﺘﻄﻮﯾﺮ ﻣﺤﺮك ﯾﻌﻤﻞ ﻋﻠﻰ ﺣﺴﺎب ﻋﺪة ﻣﺠﻤﻮﻋﺎت ﻣﻦ اﻷرﻗﺎم وطﺒﺎﻋﺔ وﻧﺴﺦ ،اﻟﻨﺘﺎﺋﺞ 11 ﻟﻜﻨﮫ
- 23. 23 ﻟﻢ ﯾﺘﻤﻜّﻦ ﻣﻦ إﻛﻤﺎل ﺗﺼﻨﯿﻊ ﺣﺎﺳﺒﮫ ﻟﻌﺪم ﻛﻔﺎﯾﺔ ،اﻟﺘﻤﻮﯾﻞ ﺣﺘﻰ ﻗﺎم ﻣﺘﺤﻒ ﻟﻨﺪن ﻟﻠﻌﻠﻮم ﻓﻲ ﻋﺎم 2000 ﺑﺈﻛﻤﺎل ﻣﺸﺮوﻋﮫ ﻓﻲ ﻣﺌﻮﯾﺔ ﻣﯿﻼده اﻟﺜﺎﻧﯿﺔ . ،ًﺎوﻻﺣﻘ اﻋﺘﻤﺪ ﻋﺎﻟﻢ اﻟﺮﯾﺎﺿﯿﺎت اﻟﺸﮭﯿﺮ آﻻن ﺗﻮرﯾﻨﻎ ) Alan Turing ( ، ﻓﻲ ﻋﺎم 1936 ، ﻋﻠﻰ ﻣﺤﺎﻛﺎة ﺳﻠﺴﻠﺔ ﻣﻦ اﻟﺘﻌﻠﯿﻤﺎت اﻟﻤﻨﻄﻘﯿﺔ ًﺎﺴﺗﺄﺳﯿ ﻟﻨﻈﺮﯾﺎت أﺳﺎﺳﯿﺔ ﻟﻌﻤﻞ اﻟﺤﻮاﺳﯿﺐ وأﺟﮭﺰة ،اﻟﻜﻤﺒﯿﻮﺗﺮ ﺗﻌﺘﺒﺮ اﻟﯿﻮم ﻣﻦ اﻷﺳﺲ اﻟﻨﻈﺮﯾﺔ اﻷوﻟﻰ ﻟﻌﻤﻞ أﺟﮭﺰة اﻟﻜﻤﺒﯿﻮﺗﺮ . 12 وﺑﻌﺪ ،ذﻟﻚ وﻓﻲ ﻋﺎم 1937 ، ﺑﺪأت اﻟﻮﻻﯾﺎت اﻟﻤﺘﺤﺪة اﻷﻣﯿﺮﻛﯿﺔ اﻟﻌﻤﻞ ﻋﻠﻰ ﺗﻄﻮﯾﺮ أﺟﮭﺰة اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﺮﻗﻤﯿﺔ أدى ذﻟﻚ إﻟﻰ ﺗﺼﻨﯿﻊ ﺟﮭﺎز « إﯾﻨﯿﺎك Electronic Numerical Integrator Analyzer and( » Computer, ENIAC ﻓﻲ ﻋﺎم 1946 ، اﻟﺬي ﺷﻐﻞ ً ﻣﺴﺎﺣﺔ ّرﺪﺗﻘ ب 1800 ﻗﺪم ،ﻣﺮﺑﻊ واﺳﺘﺨﺪم ﻣﺎ ﯾﻘﺮب ﻣﻦ 18000 أﻧﺒﻮب ﻣﻔﺮغ ﻟﻠﺤﺴﺎﺑﺎت ،اﻟﺮﻗﻤﯿﺔ ھﺬا وﯾﻌﺘﺒﺮ اﻟﺠﮭﺎز أول ﺟﮭﺎز ﻛﻤﺒﯿﻮﺗﺮ رﻗﻤﻲ ﻓﻲ اﻟﻌﺎﻟﻢ . ﻛﺎن اﻟﺘﻄﻮر اﻟﻌﻠﻤﻲ اﻟﻤﺘﻘﺪم ﻓﻲ ﻋﺎﻟﻢ اﻟﻜﻤﺒﯿﻮﺗﺮ ﻣﺘﺘﺎﺑﻌًﺎ ًﺎوﻣﺘﻼﺣﻘ ﻣﻊ اﻟﺘﻘﺪم اﻟﺘﻘﻨﻲ ﻓﻲ ﺛﻮرة اﻟﺘﻜﻨﻮﻟﻮﺟﯿﺎ ،واﻟﻤﻌﻠﻮﻣﺎت إذ ﺗﻢ اﻻﻧﺘﻘﺎل ﻣﻦ ﺟﯿﻞ إﻟﻰ آﺧﺮ ﻓﻲ أﺟﮭﺰة اﻟﺤﻮاﺳﯿﺐ ﻣﻦ ﺣﯿﺚ اﻟﻘﺪرة واﻟﻜﻔﺎءة اﻟﻤﺘﻤﺜﻠﺔ ﺑﺴﺮﻋﺔ اﻟﻤﻌﺎﻟﺠﺔ وﻧﻘﻞ ،اﻟﺒﯿﺎﻧﺎت وذﻟﻚ ﺑﺎﻻﻧﺘﻘﺎل ﻣﻦ اﻟﺘﺮاﻧﺰﺳﺘﻮر إﻟﻰ اﻟﺪارات اﻟﻤﺘﻜﺎﻣﻠﺔ ًﺎوﻻﺣﻘ إﻟﻰ اﻟﻤﺘﺤﻜﻤﺎت ،اﻟﺼﻐﺮﯾﺔ وﻣﻦ ﺛﻢ اﻟﻮﺻﻮل اﻟﯿﻮم إﻟﻰ ﻣﺎ ﺑﺎت ُﻌﺮفﯾ ب « ﻋﺎﻟﻢ اﻟﻨﺎﻧﻮ ﺗﻜﻨﻮﻟﻮﺟﻲ » ، وﻣﺴﺘﻘﺒﻠﮭﺎ ،اﻟﻤﻤﻜﻦ ﻋﻠﻰ ﻣﺴﺘﻮى ،اﻟﺤﻮاﺳﯿﺐ ﻓﻲ اﻟﺤﺎﺳﺐ اﻟﻜﻤﻮﻣﻲ واﻷﺟﮭﺰة اﻟﺬﻛﯿﺔ . َﻖﻓﺗﺮا ھﺬا ﻣﻊ ﺗﻄﻮر ﻓﻲ اﻟﺨﻮارزﻣﯿﺎت واﻟﻠﻐﺎت اﻟﺒﺮﻣﺠﯿﺔ ﺑﺪءًا ﻣﻦ اﻟﻜﻮﺑﻮل ) Cobol ( إﻟﻰ )++ C( وﻣﺎ ﺑﯿﻨﮭﻤﺎ و / أو ﻣﺎ ُﻨﻲﺑ ﻋﻠﯿﮭﺎ ﻣﻦ ﺧﻮارزﻣﯿﺎت وﻟﻐﺎت ﺑﺮﻣﺠﯿﺔ ﺗﺤﺎول ﺣﻞ ﻣﺸﻜﻠﺘﻲ ﺳﺮﻋﺔ اﻟﻤﻌﺎﻟﺠﺔ واﻟﻨﻘﻞ ﻋﻠﻰ ﻧﺤﻮ ٍﻣﺘﺘﺎل وﻣﺘﻘﺪم . 14 اﻟﻜﻤﺒﯿﻮﺗﺮ ،ﻋﻤﻮﻣًﺎ ﺳﻮاء اﻟﻜﻼﺳﯿﻜﻲ أو ،اﻟﻜﻤﻮﻣﻲ ﯾﻤﻜﻦ ،ﺗﻮﺻﯿﻔﮫ ،ﺑﺎﺧﺘﺼﺎر ﺑﺄﻧﮫ ﯾﻘﻮم ﻋﻠﻰ ﺛﻼﺛﺔ أﺳﺲ ﻋﻠﻤﯿﺔ : ﻟﻐﺔ ،ﺑﺮﻣﺠﯿﺔ وﺧﻮارزﻣﯿﺔ ،رﯾﺎﺿﯿﺔ وﻗﺪرة ﺗﻘﻨﯿﺔ إﻟﻜﺘﺮوﻧﯿﺔ ﺗﻤﺜﻠﺖ ﺑﺎﻟﺒﻮاﺑﺎت واﻟﺪارات اﻟﻤﻨﻄﻘﯿﺔ ،واﻟﺮﻗﻤﯿﺔ ﻋﻠﻰ أن ﺗﻜﻮن اﻷﺳﺲ اﻟﺜﻼﺛﺔ ھﺬه ﻣﺘﻮاﻓﻘﺔ ﻣﻊ ﺑﻌﻀﮭﺎ اﻟﺒﻌﺾ . اﻟﻜﯿﻮﺑﺖ ) Qubit ( واﻟﺤﺴﺎب اﻟﻜﻤﻮﻣﻲ 1-2-3 اﻟﺨﻠﻔﯿﺔ اﻟﻔﯿﺰﯾﺎﺋﯿﺔ ﻟﻠﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ ،ًﺎ ﺣﺪﯾﺜ وﻣﻨﺬ أن وﺿﻊ رﯾﺘﺸﺎرد ﻓﺎﯾﻨﻤﺎن ) R. Feynman ( اﻷﺳﺲ اﻟﻨﻈﺮﯾﺔ ﻹﻣﻜﺎﻧﯿﺔ إﻧﺸﺎء ﺣﻮﺳﺒﺔ ،ﻛﻤﻮﻣﯿﺔ ﺗﻌﺘﻤﺪ ﻋﻠﻰ اﻷﺳﺲ اﻟﻨﻈﺮﯾﺔ واﻟﺘﻄﺒﯿﻘﯿﺔ ﻟﻠﻤﯿﻜﺎﻧﯿﻚ ،اﻟﻜﻤﻮﻣﻲ ﺣﺘﻰ ﺑﺪأت اﻟﺪراﺳﺎت اﻟﻨﻈﺮﯾﺔ ﻓﻲ ﻣﺤﺎوﻟﺔ ﺑﻨﺎء اﻟﺪارات واﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ ﻓﻲ اﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ . اﻗﺘﺮح ﻓﺎﯾﻨﻤﺎن إﻣﻜﺎﻧﯿﺔ اﻻﺳﺘﻔﺎدة ﻣﻦ اﻟﻤﯿﻜﺎﻧﯿﻚ ،اﻟﻜﻤﻮﻣﻲ ًﺎﻣﺘﻮﻗﻌ ًةﻗﻮ ﻓﺎﺋﻘﺔ اﻷداء ﻷﺟﮭﺰة اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻤﻮﻣﯿﺔ إذ إن أي ﻣﺤﺎﻛﺎة ﻛﻼﺳﯿﻜﯿﺔ ﻟﻠﺤﺎﻟﺔ اﻟﻜﻤﻮﻣﯿﺔ ﺳﺘﻨﻄﻮي ﻋﻠﻰ ﺗﺒﺎطﺆ ﻛﺒﯿﺮ ً ﻣﻘﺎرﻧﺔ ﺑﺎﻟﺘﻄﻮر اﻟﻄﺒﯿﻌﻲ ﻟﻠﺤﺪث؛ وذﻟﻚ ﻷن ﻛﻤﯿﺔ اﻟﻤﻌﻠﻮﻣﺎت اﻟﻤﻄﻠﻮﺑﺔ ﻟﻮﺻﻒ اﻟﺤﺎﻟﺔ اﻟﻜﻤﻮﻣﯿﺔ ًﺎﯿﻛﻼﺳﯿﻜ ﺳﺘﻨﻤﻮ ا ً ﻧﻤﻮ ا ًﻛﺒﯿﺮ ﻓﻲ اﻟﻮﻗﺖ ،ذاﺗﮫ 15 وﻗﺪ اﻋﺘﺒﺮ ﻓﺎﯾﻨﻤﺎن ذﻟﻚ ً ﻓﺮﺻﺔ ﻟﻠﻌﻤﻞ ًلﺑﺪ ﻣﻦ اﻋﺘﺒﺎرھﺎ ﻋﻘﺒﺔ؛ ﻓﺎﻟﻤﯿﻜﺎﻧﯿﻚ اﻟﻜﻤﻮﻣﻲ ﯾﻘﺪم رؤﯾﺔ ﻛﻤﻮﻣﯿﺔ
- 24. 24 ،ﻟﻠﺤﺪث ﻣﻦ ﺣﯿﺚ ﻣﺜﻨﻮﯾﺔ اﻟﻤﻈﮭﺮ اﻟﺠﺴﯿﻤﻲ واﻟﻤﻮﺟﻲ اﻟﻤﯿﻜﺮوﯾﺔ وﺣﻮادث اﻟﺘﺮاﻛﺐ واﻟﺘﺮاﺑﻂ واﻟﺘﺪاﺧﻞ اﻟﻜﻤﻮﻣﯿﺔ اﻟﻨﺎﺷﺌﺔ ﻋﻨﮭﺎ . ﺗﻠﻚ اﻟﻘﻮاﻧﯿﻦ واﻟﻤﺒﺎدئ اﻟﻜﻤﻮﻣﯿﺔ اﻟﻤﺨﺘﻠﻔﺔ واﻟﻤﻐﺎﯾﺮة ﻓﻲ طﺮﻗﮭﺎ وﻣﻨﻄﻘﮭﺎ ﻋﻦ اﻟﻘﻮاﻧﯿﻦ اﻟﻔﯿﺰﯾﺎﺋﯿﺔ اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﻤﻌﺮوﻓﺔ ًاﺪﺟﯿ ﺗﺤﻜﻢ وﺗﺤﺪد ﻋﺎﻟﻢ ّﺎتﯿاﻟﺤﺴ اﻟﻤﺮﺋﻲ واﻟﺤﺮﻛﺔ اﻟﻤﺮﺻﻮدة ًﺎﯾﺑﺸﺮ ،ﺑﺈﺣﻜﺎم وذﻟﻚ ﺑﺤﻜﻢ طﺒﯿﻌﺔ اﻟﺤﻮاس اﻟﺒﺸﺮﯾﺔ وﻗﻮاﻧﯿﻨﮭﺎ اﻟﺤﺎﻛﻤﺔ . ﻣﻜﻨﺖ ﻧﻈﺮﯾﺎت وأﻓﻜﺎر اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ ﻣﻦ اﻟﻐﻮص ًﺎﻋﻤﯿﻘ ﻓﻲ ﻣﺎھﯿﺔ اﻟﻤﻮاد ُﻨﺎھﺎﺑو ﻋﻠﻰ اﻟﻤﺴﺘﻮى اﻟﺬري وﻣﺎ ،دوﻧﮫ ﺳﻮاء ﺑﻈﻮاھﺮه اﻟﺠﺴﯿﻤﯿﺔ دون اﻟﺬرﯾﺔ أو ،اﻟﻤﻮﺟﯿﺔ ﻟﺘﺸﻜّﻞ ٌ ﺟﻤﻠﺔ ﻣﻦ اﻟﻤﻔﺎھﯿﻢ واﻟﻘﻮاﻧﯿﻦ ﻓﻲ اﻟﻔﯿﺰﯾﺎء اﻟﺤﺪﯾﺜﺔ ﻓﻲ ﺑﺪاﯾﺎت اﻟﻘﺮن ،اﻟﻌﺸﺮﯾﻦ وﺑﺎﻷﺧﺺ اﻟﻜﻤﻮﻣﯿﺔ ﻣﻨﮭﺎ ) اﻟﺘﻲ ﻣﻦ اﻟﻤﻤﻜﻦ اﻟﻌﻮدة إﻟﯿﮭﺎ ًﻞﺗﻔﺼﯿ ( ، 16 َ اﻷﺳﺎس اﻟﻌﻠﻤﻲ ﻟﺜﻮرة اﻟﺘﻘﻨﯿﺔ اﻟﯿﻮم؛ وذﻟﻚ ﺑﺪءًا ﻣﻦ اﻟﺠﺴﻢ اﻷﺳﻮد وإﺷﻌﺎ ﻋﮫ ﻟﺪى ﻣﺎﻛﺲ ﺑﻼﻧﻚ ) Max Planck’s Black Body Radiation وﻣﺒﺪأ ﻣﺜﻨﻮﯾﺔ اﻟﻤﻮﺟﺔ - اﻟﺠﺴﯿﻢ ﻟﺪﯾﺒﺮوﻟﻲ ) Louis De Broglie’s Wave-Particle Dualityy ، ﺛﻢ ﻣﺒﺪأ اﻟﺸﻚ أو اﻟﻼﯾﻘﯿﻦ ﻟﻔﯿﺮﻧﺮ ھﺎﯾﺰﻧﺒﺮغ )- Wer ، )ner Heisenberg’s Uncertainty Principle ا ًﻣﺮور ﺑﺘﻔﺎﻋﻼت اﻟﻔﻮﺗﻮن ﻣﻊ اﻟﻤﺎدة ) Photon Interactions with Matter ( وﻣﻨﮭﺎ اﻟﻤﻔﻌﻮل اﻟﻜﮭﺮوﺿﻮﺋﻲ ﻟﺪى أﯾﻨﺸﺘﺎﯾﻦ ) 18 ) Albert Einstein Photoelectric Effect ، واﻟﺒﻨﯿﺔ اﻟﺬرﯾﺔ وطﯿﻒ ذرة ،اﻟﮭﯿﺪروﺟﯿﻦ واﻹﺛﺎرة واﻟﺴﻮﯾﺎت ،اﻟﻄﺎﻗﯿﺔ ﻟﺪى ﻧﯿﻠﺰ ﺑﻮھﺮ ) Niels H. Bohr’s Atomic Structure ( ، ﻛﻤﺎ اﻟﺒﻨﯿﺔ اﻟﺪﻗﯿﻘﺔ وﻓﻮق اﻟﺪﻗﯿﻘﺔ ) Fine and Hyperfine Structure ، واﻟﺴﺒﯿﻦ اﻟﻨﻮوي واﻹﻟﻜﺘﺮوﻧﻲ ) Nuclear and electron spin ًلوﺻﻮ إﻟﻰ اﻟﺘﺮاﺑﻂ واﻟﺘﺸﺎﺑﻚ اﻟﻜﻤﻮﻣﻲ Entanglemen( واﻟﺘﺮاﻛﺐ اﻟﻜﻤﻮﻣﻲ ) Quantum Superposition ( ﻛﻤﺎ ) Quantum ﺿﻤﻨﮭﺎ ﺑﯿﺘﺮ ﺷﻮر ) Peter Shor ( ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ وﺣﺴﺎﺑﺎﺗﮫ اﻟﻤﻌﻘﺪة . 2-2-3 اﻟﺒﺖ واﻟﻜﯿﻮﺑﺖ ) )Bit & Qubit ﻛﺎﻧﺖ اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ واﻟﺪارات اﻹﻟﻜﺘﺮوﻧﯿﺔ ،اﻟﻤﺘﻜﺎﻣﻠﺔ وﻻ ،ﺗﺰال ﺗﻌﺘﻤﺪ ًﺎﺳأﺳﺎ ﻓﻲ ﺑﻨﺎﺋﮭﺎ ﻋﻠﻰ اﻟﺨﻮارزﻣﯿﺎت اﻟﺮﯾﺎﺿﯿﺔ واﻟﺠﺒﺮ اﻟﻤﻨﻄﻘﻲ ،اﻟﺒﻮﻟﯿﺎﻧﻲ ﻧﺴﺒﺔ إﻟﻰ اﻟﻌﺎﻟﻢ اﻹﯾﺮﻟﻨﺪي ﺟﻮرج ﺑﻮل ) 21 ، )George Boole اﻟﺬي ﯾﻤﺜﻞ اﻷﺳﺎس اﻟﻨﻈﺮي واﻵﻟﯿﺔ اﻟﻤﺴﺘﻘﺮة ﻟﻌﻤﻞ أﺟﮭﺰة اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﯿﻮم . ﻓﻌﻠﻰ اﻟﺮﻏﻢ ﻣﻦ اﻟﺘﻄﻮﯾﺮ اﻟﻤﺘﺰاﯾﺪ ﻓﻲ ﻋﺎﻟﻢ اﻟﻜﻤﺒﯿﻮﺗﺮ ﻛﻤﺎ ﺗﻮﻗﻌﮫ ،ﻣﻮر ﻓﺈن اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ ھﺬه ﺑﻘﯿﺖ ﺗﻌﺘﻤﺪ ﻋﻠﻰ اﻟﺨﻮارزﻣﯿﺎت ذاﺗﮭﺎ وأﻧﻈﻤﺔ اﻟﻌﺪ اﻟﺜﻨﺎﺋﻲ واﻟﺜﻤﺎﻧﻲ اﻟﻤﺤﻤﻠﺔ واﻟﻤﺒﺮﻣﺠﺔ ﻓﻲ اﻟﺪارات اﻹﻟﻜﺘﺮوﻧﯿﺔ اﻟﻤﺘﻜﺎﻣﻠﺔ وﺑﻮاﺑﺎﺗﮭﺎ اﻟﻤﻨﻄﻘﯿﺔ اﻟﻤﺒﯿﻨﺔ ﻓﻲ اﻟﺸﻜﻞ 2.
- 25. 25 ﻛﻤﺎ ھﻮ ﻣﻌﺮوف ،ًاﺪﺟﯿ ﺗﺸﻤﻞ اﻟﺪارات واﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ ھﺬه اﻟﻌﺪﯾﺪ ﻣﻦ اﻟﺒﻮاﺑﺎت ،اﻟﻤﻨﻄﻘﯿﺔ ﻣﻨﮭﺎ ﻋﻠﻰ ﻧﺤﻮ رﺋﯿﺲ : ) )NOT, AND, OR, COPY وإﻣﻜﺎﻧﯿﺔ ﺟﻤﻊ ﻋﺪد ﻣﻨﮭﺎ ﻓﻲ ﺑﻮاﺑﺎت أﺧﺮى ﻣﻦ ﻗﺒﯿﻞ ) ، )NOR, NAND, XOR ﺑﺤﯿﺚ ﺗﺆدي ﻛﺎﻓﺔ ﻣﺘﻄﻠﺒﺎت اﻟﻌﻤﻞ ﻓﻲ اﻟﺤﻮاﺳﯿﺐ اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﻤﻌﺮوﻓﺔ اﻟﯿﻮم ﻋﻠﻰ ﻧﺤﻮ ﻣﺴﺘﻘﺮ . 22 ﻛﻤﺎ ﯾﻤﺜﻞ اﻟﺒﺖ ) Bit ( اﻷﺳﺎس اﻟﺮﻗﻤﻲ ﻟﺒﻨﺎء ھﺬه ،اﻟﺒﻮاﺑﺎت وﯾﺄﺧﺬ إﺣﺪى ﻗﯿﻤﺘﯿﻦ ) 0=False أو 1=True ( وﯾﻌﺮف ھﺬا ﺑﻨﻈﺎم اﻟﻌﺪ اﻟﺜﻨﺎﺋﻲ 23 ، )Binary Code System( إذ ﯾﻤﺜﻞ ) 1( ﺗﻨﻔﯿﺬ اﻷ ﻣﺮ وھﻮ ﯾﻌﻨﻲ ﻣﺮور ﻓﻮﻟﺘﯿﺔ ّرﺪﺗﻘ ب 5 ،ﻓﻮﻟﺘﺎت أو اﻷﻣﺮ ) 0( ﻋﻨﺪ ﻋﺪم ﻣﺮور ،ﻓﻮﻟﺘﯿﺔ ﺑﺤﯿﺚ ﯾﻜﻮن ﺗﻨﻔﯿﺬ اﻷﻣﺮ ﻓﻲ اﻟﺤﺎﺳﺐ اﻟﻜﻼﺳﯿﻜﻲ ﺑﺒﻮاﺑﺎﺗﮫ اﻟﻤﻨﻄﻘﯿﺔ ﺑﺈﺟﺮاء أﺣﺪ اﻷﻣﺮﯾﻦ ﻓﻘﻂ . ﯾﺘﻤﺜﻞ اﻟﺴﺆال اﻷﺳﺎﺳﻲ ﻓﻲ اﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ ﻓﻲ : ﻣﺎ ھﻮ اﻟﺘﺎﺑﻊ اﻟﻘﺎﺑﻞ ﻟﻠﺤﺴﺎب ًﺎﯿﻛﻤﻮﻣ وﯾﻌﻄﻲ اﻻﺗﺴﺎق ذاﺗﮫ ﻓﻲ ﺣﺴﺎﺑﺎت اﻟﺠﺒﺮ اﻟﺒﻮﻟﯿﺎﻧﻲ واﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﺘﻲ ﺑﻨﺘﮭﺎ أﻧﺼﺎف اﻟﻨﻮاﻗﻞ؟ ﻓﺎﻟﺘﻮاﺑﻊ اﻟﮭﺎﻣﻠﺘﻮﻧﯿﺔ Hamiltonian( ( ﻗﺪﻣﺖ ًلﺣﻠﻮ ﻛﻤﻮﻣﯿﺔ ﻣﮭﻤﺔ ﻓﻲ ﻋﺎﻟﻢ ﻣﺎ دون ،اﻟﺬرﯾﺔ إذ إن إﻣﻜﺎﻧﯿﺔ ﺣﻞ ﺟﻤﻠﺔ ﻣﻦ اﻟﻤﺪﺧﻼت ﻋﻠﻰ ﻣﺴﺘﻮى اﻟﻜﯿﻮﺑﺖ ) Qubit ( ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻤﻮﻣﻲ 24 ﯾﻤﻜﻨﮭﺎ أن ﺗﻘﺪم ﻣﺨﺮﺟﺎت ﻋﻠﻰ اﻟﻘﺪرة ذاﺗﮭﺎ ﻣﻦ اﻟﺨﺮج ﻓﻲ اﻟﻜﯿﻮﺑﺖ واﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ . اﻟﻜﯿﻮﺑﺖ ﻋﺒﺎرة ﻋﻦ ﻧﻈﺎم ﻛﻤﻮﻣﻲ ﯾﺘﻢ ﻓﯿﮫ اﺳﺘﺮﺟﺎع اﻟﺤﺎﻟﺘﯿﻦ اﻟﺒﻮﻟﯿﺎﻧﯿﺘﯿﻦ ) 0 و 1( ﺑﻮاﺳﻄﺔ زوج ﻣﺤﺪد ﻓﻲ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ ﯾﺮﻣﺰ إﻟﯿﮭﻤﺎ ب )< 0> Or |1 |( ، ﺑﺤﯿﺚ ﯾﻤﺜﻞ اﻟﻜﯿﻮﺑﺖ ﺣﺎﻟﺘﯿﻦ ﻛﻤﻮﻣﯿﺘﯿﻦ ﯾﻤﻜﻦ ﻣﺤﺎﻛﺎﺗﮭﻤﺎ ﺑﺴﻮﯾﺘﯿﻦ ﻛﻤﻮﻣﯿﺘﯿﻦ ﺧﺎﺻﺘﯿﻦ ) Eigenstates (. ﻓﺈذا ﻛﺎن اﻟﻜﯿﻮﺑﺖ ﯾﻤﺜﻞ إﺣﺪى اﻟﺤﺎﻟﺘﯿﻦ اﻟﻜﻤﻮﻣﯿﺘﯿﻦ )< 0> Or |1 |( ، ﻓﺈﻧﮫ ﺳﯿﺨﻀﻊ ﻟﺤﺎﻟﺔ اﻟﺘﺮاﻛﺐ واﻟﺘﺪاﺧﻞ اﻟﻜﻤﻮﻣﻲ ،ًﺎﻀأﯾ وھﺬا ﯾﻤﺜﻞ ًادﻋﺪ ﻣﻦ اﻟﺤﺎﻻت ﻻ ﺣﺼﺮ ﻟﮭﺎ ًﺎ؛ﯿﻛﻤﻮﻣ ﻣﺎ ﯾﺠﻌﻞ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ﯾﺘﻔﻮق ًﺎﯿأﺳ ﻋﻠﻰ ﻗﺮﯾﻨﮫ اﻟﻜﻼﺳﯿﻜﻲ اﻟﺬي ﻻ ﯾﺤﯿﻞ ﺳﻮى ﻋﻠﻰ إﺣﺪى اﻟﻘﯿﻤﺘﯿﻦ ﻟﻠﺒﺖ ) Bit ( وﻓﻖ اﻟﺒﻮاﺑﺔ اﻟﻤﻨﻄﻘﯿﺔ؛ وﻣﻦ ﺛﻢ ﯾﻤﻜﻦ ﻛﺘﺎﺑﺔ أي ﺣﺎﻟﺔ ﻧﻘﯿﺔ أﺧﺮى ﻣﻦ اﻟﻜﯿﻮﺑﺘﺎت ) ﺟﻤﻊ ﻛﯿﻮﺑﺖ Qubits ( ﻓﻲ ﺻﻮرة ﺗﺮاﻛﺐ ﻛﻤﻮﻣﻲ ﻓﻲ اﻟﻨﻈﺎم ،اﻟﻤﺠﮭﺮي ﻛﺎﻟﺴﺒﯿﻦ اﻹﻟﻜﺘﺮوﻧﻲ أو اﻟﻨﻮوي ذي اﻟﺘﻮﺟﮭﯿﻦ
- 26. 26 اﻷﻋﻠﻰ واﻷدﻧﻰ ،ًﺎﯿﻣﻐﻨﺎطﯿﺴ أو ﻧﻤﻮذج اﻟﺬرة ًﻞﻛﺎﻣ ﻋﻨﺪ إﺛﺎرﺗﮭﺎ ﻣﻦ ﺳﻮﯾﺘﮭﺎ اﻟﻄﺎﻗﯿﺔ اﻷﺳﺎﺳﯿﺔ اﻟﺬرﯾﺔ إﻟﻰ ﺳﻮﯾﺎت ،أﻋﻠﻰ أو اﻟﻔﻮﺗﻮن اﻟﻤﺴﺘﻘﻄﺐ ،ًﺎﯾﻟﯿﺰر ﺣﯿﺚ ﺗﺴﻤﻰ ﻣﺠﻤﻮﻋﺔ ﻣﻦ اﻟﻜﯿﻮﺑﺘﺎت ) n( اﻟﺴﺠﻞ اﻟﻜﻤﻮﻣﻲ ﻓﻲ اﻟﺤﺠﻢ ) 25.)n اﻟﺤﺴﺎﺑﺎت اﻟﻜﻤﻮﻣﯿﺔ ﻗﺎﺑﻠﺔ ﻟﻠﻌﻜﺲ اﻟﻤﻨﻄﻘﻲ ،واﻟﻔﯿﺰﯾﺎﺋﻲ وﺑﻤﺎ أن أي ﻣﺴﺄﻟﺔ ﯾﻤﻜﻦ ﺣﻠﮭﺎ ًﺎﯿﻛﻼﺳﯿﻜ ﯾﻤﻜﻦ ﻣﺤﺎﻛﺎﺗﮭﺎ ،ًﺎﯿﻛﻤﻮﻣ ﻓﺈن ﻣﻦ اﻟﻤﻤﻜﻦ ﺗﺼﻨﯿﻊ ﺣﺎﻻت ﻣﺘﻌﺪدة ﻣﻦ اﻟﻜﯿﻮﺑﺖ ﺗﺴﺘﻄﯿﻊ ﺣﻞ ﻣﺸﻜﻼت اﻟﺤﻮاﺳﯿﺐ اﻟﻜﻼﺳﯿﻜﯿﺔ . ﻓﺎﻟﻤﯿﺰات اﻟﺤﺪﯾﺜﺔ ﻟﻠﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ﻣﻦ ﺣﯿﺚ اﻟﺘﺮاﻛﺐ ) )Superposition واﻟﺘﺪاﺧﻞ ﺑﯿﻦ اﻟﻜﯿﻮﺑﺘﺎت ) Qubit’s Interferences ( واﻟﺘﺸﺎﺑﻚ أو اﻟﺘﺮاﺑﻂ اﻟﻜﻤﻮﻣﻲ ) Entanglement ( ﺳﺘﺴﻤﺢ ﻷﺟﮭﺰة اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﯿﺔ ﺑﺤﻞ ﻛﺜﯿﺮ ﻣﻦ اﻟﻤﺸﺎﻛﻞ ،اﻟﺤﺴﺎﺑﯿﺔ ﻣﻦ أھﻤﮭﺎ اﻟﺒﺤﺚ ﻓﻲ ﻗﻮاﻋﺪ اﻟﺒﯿﺎﻧﺎت واﻟﻤﻌﺎﻣﻼت اﻟﻌﺎﺋﻤﺔ ﻋﻠﻰ ﻧﺤﻮ أﺳﺮع ًﺎﯿأﺳ ﻣﻤﺎ ﯾﻤﻜﻦ أن ﯾﻘﻮم ﺑﮫ أي ﻛﻤﺒﯿﻮﺗﺮ ﺗﻘﻠﯿﺪي؛ إذ ﺑﺴﺒﺐ اﻟﺘﺮاﺑﻂ واﻟﺘﺪاﺧﻞ ﱠﯿﻦﯿاﻟﻜﻤﻮﻣ ﻟﻠﺠﺰﯾﺌﺎت ﻓﺈن اﻟﺸﺒﻜﺎت اﻟﻜﻤﻮﻣﯿﺔ ﺳﺘﻜﻮن أﻛﺜﺮ ﻓﺎﻋﻠﯿﺔ ﻣﻦ أي ﻧﻈﺮﯾﺔ إﺣﺼﺎﺋﯿﺔ ﻛﻼﺳﯿﻜﯿﺔ أﺧﺮى . 26 ﻟﻘﺪ ﺗﻤﺖ اﻻﺳﺘﻔﺎدة ﻣﻦ اﻟﺘﺪاﺧﻞ اﻟﻜﻤﻮﻣﻲ ﻛﻈﺎھﺮة ﻓﯿﺰﯾﺎﺋﯿﺔ ﻣﺪھﺸﺔ ﺗﺠﻌﻞ ﻧﻈﺮﯾﺔ اﻟﻜﻢ ﺑﻄﺒﯿﻌﺘﮭﺎ ﻣﺨﺘﻠﻔﺔ ًﺎﯾﺟﺬر ﻋﻦ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻼﺳﯿﻜﯿﺔ وإﺣﺼﺎﺋﮭﺎ ﻓﻲ اﻻﻧﺘﻘﺎل ﻣﻦ اﻟﺤﺴﺎﺑﺎت اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﺮﻗﻤﯿﺔ اﻟﻤﺘﻌﻠﻘﺔ ﺑﺎﻟﻨﻈﺎم اﻟﺜﻨﺎﺋﻲ إﻟﻰ اﻟﺤﺴﺎﺑﺎت اﻟﻜﻤﯿﺔ اﻟﻤﺘﻌﻠﻘﺔ ﺑﺎﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ . ﻓﺎﻟﺘﺪاﺧﻞ ،ًﺎﯿﻛﻤﻮﻣ ﻻ ﯾﻘﺘﺼﺮ ﻋﻠﻰ اﻟﻔﻮﺗﻮﻧﺎت ،اﻟﻀﻮﺋﯿﺔ ﺑﻞ ﻋﻠﻰ اﻟﺠﺴﯿﻤﺎت ،ًﺎﻀأﯾ ﻛﺎﻹﻟﻜﺘﺮوﻧﺎت واﻟﻨﯿﻮﺗﺮوﻧﺎت واﻟﺬرات أو ﺣﺘﻰ ،اﻟﺠﺰﯾﺌﺎت وﺑﺎﻟﻀﺮورة ﯾﻤﻜﻦ اﺳﺘﺨﺪام درﺟﺎت ﺣﺮﯾﺔ ﻛﻤﻮﻣﯿﺔ أﻛﺜﺮ ﺧﺎرﺟﯿﺔ وداﺧﻠﯿﺔ . وﺑﻨﺎء ،ﻋﻠﯿﮫ ﻓﺈن ﻧﻈﺎﻣًﺎ ًﺎﯿﻛﻤﻮﻣ ﻻ ﯾﺘﺠﺎوز ﺑﻀﻊ ﻣﺌﺎت ﻣﻦ ،اﻟﻜﯿﻮﺑﺘﺎت ًادﻣﻮﺟﻮ ﻓﻲ ﻓﺮاغ ھﯿﻠﺒﺮت اﻟﻜﻤﻮﻣﻲ ) Hilbert ( ، ﯾﺘﻄﻠﺐ ﻧﻤﻮذﺟًﺎ ﻣﻦ اﻟﻤﺤﺎﻛﺎة ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻼﺳﯿﻜﻲ اﻟﺘﻲ ﺗﻌﺘﻤﺪ اﻟﻌﻤﻞ ﻋﻠﻰ ﻣﺼﻔﻮﻓﺎت ﻛﺒﯿﺮة اﻷﺑﻌﺎد ﺑﺸﻜﻞ ﻛﺒﯿﺮ ﻣﻦ ﺣﯿﺚ إﺟﺮاء اﻟﺤﺴﺎﺑﺎت ﻋﻠﻰ ﻛﻞ ﺣﺎﻟﺔ ﻓﺮدﯾﺔ ﯾﺘﻢ ﺗﻤﺜﯿﻠﮭﺎ ،ًﺎﯿﻣﺼﻔﻮﻓ ﻣﺎ ﯾﻌﻨﻲ ًﺎﺘوﻗ أطﻮل ًﺎﯿأﺳ ً ﻣﻘﺎرﻧﺔ ﺑﺎﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ اﻷوﻟﻲ . 27 اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ ﻓﻲ ھﺬا اﻟﺠﺰء ﻣﻦ اﻟﺪراﺳﺔ ﺳﻨﺤﺎول إﻟﻘﺎء اﻟﻀﻮء ﻋﻠﻰ اﻟﺨﻮارزﻣﯿﺎت واﻟﺘﻄﺒﯿﻘﺎت اﻟﻜﻤﻮﻣﯿﺔ اﻷﻛﺜﺮ ًﺎﻋﺷﯿﻮ ﻓﻲ ﺗﺼﻤﯿﻢ اﻟﺪارات واﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ ،اﻟﻜﻤﻮﻣﯿﺔ اﻟﺘﻲ ﻻ زاﻟﺖ ﺗﻌﺘﺒﺮ إﻟﻰ اﻟﯿﻮم ﻣﺨﺒﺮﯾﺔ ﻗﯿﺪ اﻟﺪراﺳﺔ واﻟﺘﻄﻮﯾﺮ . 1-3-3 ﺧﻮارزﻣﯿﺔ دوﯾﺘﺶ ﺑﺤﺴﺐ دوﯾﺘﺶ ، ﻓﺈن اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ ) QLG ( ھﻲ ﺟﮭﺎز ﯾﻘﻮم ﺑﺈﺟﺮاء ﻋﻤﻠﯿﺔ أﺣﺎدﯾﺔ ﺛﺎﺑﺘﺔ ﻋﻠﻰ وﺣﺪات اﻟﻜﯿﻮﺑﺖ اﻟﻤﺤﺪدة ﻓﻲ ﻓﺘﺮة زﻣﻨﯿﺔ ،ﻣﺤﺪدة واﻟﺸﺒﻜﺔ اﻟﻜﻤﻮﻣﯿﺔ ﻋﺒﺎرة ﻋﻦ ﺟﮭﺎز ﯾﺘﻜﻮن ﻣﻦ ﺑﻮاﺑﺎت ﻣﻨﻄﻘﯿﺔ ﻛﻤﻮﻣﯿﺔ
- 27. 27 ﺗﺘﻢ ﻣﺰاﻣﻨﺔ ﺧﻄﻮاﺗﮭﺎ ،اﻟﺤﺎﺳﻮﺑﯿﺔ وﯾﺘﻢ ﺗﻮﺻﯿﻞ ﻣﺨﺮﺟﺎت اﻟﺒﻮاﺑﺎت ﻋﻦ طﺮﯾﻖ اﻷﺳﻼك ،ﺑﻤﺪﺧﻼﺗﮭﺎ وﺣﺠﻢ اﻟﺸﺒﻜﺔ ھﻮ ﻋﺪد اﻟﺒﻮاﺑﺎت اﻟﺘﻲ ﺗﺤﺘﻮﯾﮭﺎ . 28 ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻼﺳﯿﻜﻲ ﯾﺒﻘﻰ اﻟﺒﺖ ًادﻣﺤﺪ ﺑﻘﯿﻤﺔ ﻣﻌﯿﻨﺔ ﻣﻌﺮوﻓﺔ وﻗﺎﺑﻠﺔ ،ﻟﻠﻤﻼﺣﻈﺔ ﺑﯿﻨﻤﺎ ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ﻓﺈن اﻟﻜﯿﻮﺑﺖ ﯾﺤﺘﺎج داﺋﻤًﺎ إﻟﻰ دراﺳﺔ اﺣﺘﻤﺎﻟﯿﺘﮫ اﻟﺘﺸﺎﺑﻜﯿﺔ واﻟﺘﺪاﺧﻠﯿﺔ ،اﻟﻜﻤﻮﻣﯿﺔ وإﺟﺮاء ﺗﺼﺤﯿﺤﺎت ﻛﻤﻮﻣﯿﺔ ،ﻋﻠﯿﮫ ﺧﺎﺻﺔ ﻓﯿﻤﺎ ﯾﺘﻌﻠﻖ ﺑﺎﻟﺒﻮاﺑﺎت اﻟﺘﻲ ﺗﻄﻠﺐ اﻟﻌﻤﻞ ﻋﻠﻰ أﻛﺜﺮ ﻣﻦ ﻛﯿﻮﺑﺖ واﺣﺪ؛ ﻓﻘﺪ أظﮭﺮت اﻟﺨﻮارزﻣﯿﺎت اﻟﻜﻤﻮﻣﯿﺔ اﻷوﻟﻰ ﻣﺰاﯾﺎ ﺣﺴﺎﺑﯿﺔ ﻛﻤﻮﻣﯿﺔ ﻣﻦ دون اﻟﺘﻌﻘﯿﺪ اﻟﺤﺴﺎﺑﻲ اﻟﻤُﻘﺎس ﺑﺨﺼﺎﺋﺺ اﻟﻘﯿﺎس ﻷﺣﺠﺎم اﻟﺸﺒﻜﺔ . وﻗﺪ ﺗﻢ اﻛﺘﺸﺎف اﻟﻘﺪرة اﻟﺤﺴﺎﺑﯿﺔ ﻟﻠﺘﺪاﺧﻞ اﻟﻜﻤﻮﻣﻲ ﻋﻦ طﺮﯾﻖ ﺣﺴﺎب ﻋﺪد اﻟﻤﺮات اﻟﺘﻲ ﯾﺠﺐ ﻓﯿﮭﺎ ﺗﻘﯿﯿﻢ ﺑﻌﺾ اﻟﻮظﺎﺋﻒ اﻟﻤﻨﻄﻘﯿﺔ ﻣﻦ أﺟﻞ اﻟﻌﺜﻮر ﻋﻠﻰ إﺟﺎﺑﺔ ﻟﻤﺸﻜﻠﺔ ﻣﻌﯿﻨﺔ . اﻓﺘﺮﺿﺖ ﺧﻮارزﻣﯿﺔ ،دوﯾﺘﺶ اﻟﻤﻌﺮوﻓﺔ ﺑﺎﻟﺼﻨﺪوق اﻷﺳﻮد ) Black Box ، أﻧﮫ ﺑﺎﻟﻨﺴﺒﺔ إﻟﻰ إﺣﺪى ھﺬه اﻟﻮظﺎﺋﻒ ،اﻟﻜﻤﻮﻣﯿﺔ اﻟﺘﻲ ﺗﻌﺪ ﺛﺎﺑﺘﺔ أو ﻣﺘﻮازﻧﺔ ) ﺑﻤﻌﻨﻰ أﻧﮫ ﯾﺤﺘﻮي ﻋﻠﻰ ﻋﺪد ٍﻣﺘﺴﺎو ﻣﻦ اﻟﻤﺨﺮﺟﺎت : 0 ﻣﺜﻞ 1( ، وذﻟﻚ ﺑﮭﺪف ﺗﺤﺪﯾﺪ أي ﻣﻦ اﻟﺨﻮاص اﻟﻤﻤﯿﺰة ﻟﻠﻮظﯿﻔﺔ ﺑﺎﻟﻔﻌﻞ ًﺎ؛ﯿﻛﻤﻮﻣ إذ ﺗﺘﻄﻠﺐ أي ﺧﻮارزﻣﯿﺔ ﻛﻼﺳﯿﻜﯿﺔ ﻟﺤﻞ ھﺬه اﻟﻤﺸﻜﻠﺔ اﻟﻘﯿﺎم ب ) 1 + 2n−1 ( ﻣﻦ اﻟﻌﻤﻠﯿﺎت ﻗﺒﻞ ﺗﺤﺪﯾﺪ اﻹﺟﺎﺑﺔ ﺑﻜﻞ ﺗﺄﻛﯿﺪ . وﺑﺤﺴﺐ ﺧﻮارزﻣﯿﺔ دوﯾﺘﺶ ،اﻟﻜﻤﻮﻣﯿﺔ اﻟﻤﻮﺿﺤﺔ ﻓﻲ اﻟﺸﻜﻞ 3 ، ﺗﺤﻞ ھﺬه اﻟﻤﺸﻜﻠﺔ ﻣﻊ ﺗﻘﯿﯿﻢ ﻛﻤﻮﻣﻲ ،واﺣﺪ ﻟﺬﻟﻚ وﺑﺤﺴﺐ ،دوﯾﺘﺶ ﻣﻦ ﺧﻼل ﻗﯿﺎس اﻟﺒﺘﺎت اﻷوﻟﻰ ) n( ، واﻟﻤﻤﻜﻦ ﺗﺤﺪﯾﺪھﺎ ﻋﻠﻰ وﺟﮫ اﻟﯿﻘﯿﻦ ﺑﺄﻧﮭﺎ ،ﻣﺘﻮازﻧﺔ ﯾﻤﻜﻦ ﺑﻨﺎء ﺑﻮاﺑﺔ ﻣﻨﻄﻘﯿﺔ ﻣﻦ ﺛﻼﺛﺔ ﻛﯿﻮﺑﺘﺎت ﺑﻤﺘﺎﺑﻌﺔ ﺗﺤﻮﯾﻼت ﺧﻮارزﻣﯿﺔ ھﺎدﻣﺎرد Hadamard( ( ، وذﻟﻚ ﺑﺈﺟﺮاء ﺗﻘﯿﯿﻢ ﻟﻠﻮظﯿﻔﺔ ،اﻟﻜﻤﻮﻣﯿﺔ وﻣﺘﺎﺑﻌﺔ اﻟﺘﺤﻮﯾﻼت اﻟﺘﺴﻠﺴﻠﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ وﻓﻖ اﻟﺘﻮاﺑﻊ واﻟﺤﻠﻮل اﻟﮭﺎﻣﻠﺘﻮﻧﯿﺔ؛ وھﻮ ﻣﺎ ﯾﺴﻤﻰ اﻟﺘﺪاﺧﻞ اﻟﻜﻤﻮﻣﻲ ﻛﺤﺎﻟﺔ ﻧﻤﻄﯿﺔ ﻋﺎﻣﺔ ﺗﺴﺘﻠﺰم ﻣﺘﺎﺑﻌﺔ دراﺳﺘﮭﺎ واﻟﺒﺤﺚ ﻋﻦ إﻣﻜﺎﻧﯿﺔ اﻟﺘﺤﻜﻢ ﻓﯿﮭﺎ وﻓﻲ ﻧﺘﺎﺋﺠﮭﺎ .
- 28. 28 ﺧﻮارزﻣﯿﺘﺎ ﺗﻮﻓﻮﻟﻲ وھﺎدﻣﺎرد اﺗﺠﮭﺖ اﻟﺪراﺳﺎت اﻟﻜﻤﻮﻣﯿﺔ اﻟﺤﺪﯾﺜﺔ ﻧﺤﻮ اﻟﺘﺤﻜﻢ اﻟﺘﻘﻨﻲ ﺑﺎﻟﻜﯿﻮﺑﺖ ﻓﻲ اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ واﺣﺘﻤﺎﻻﺗﮭﺎ اﻟﻤﺘﻌﺪدة اﻟﻨﺎﺗﺠﺔ ﻣﻦ ﻣﻔﮭﻮم اﻟﺘﺮاﺑﻂ واﻟﺘﺸﺎﺑﻚ ،اﻟﻜﻤﻮﻣﻲ ﺧﺎﺻﺔ ﺗﻠﻚ اﻟﻤﺘﻌﻠﻘﺔ ﺑﺎﻟﺒﻮاﺑﺔ اﻟﻤﻨﻄﻘﯿﺔ ﻟﺘﻮﻓﻮﻟﻲ ) Toffoli ( اﻟﻘﺎﺑﻠﺔ ﻟﻠﺘﺤﻜﻢ ﻓﻲ ﺛﻼﺛﺔ ﻛﯿﻮﺑﺘﺎت ، ﺑﺤﯿﺚ ﯾﺘﻢ اﻟﺘﺤﻜﻢ ﻓﻲ دﺧﻞ وﺧﺮج اﻟﻤﻌﻠﻮﻣﺎت ﺑﻮاﺑﺔ ﻣﻨﻄﻘﯿﺔ ﺛﻨﺎﺋﯿﺔ اﻟﻜﯿﻮﺑﺖ ﺗﻤﺜﻞ اﻟﺤﺎﻟﺔ ،اﻷﺳﺎﺳﯿﺔ وﺑﺘﻢ رﺑﻄﮭﺎ ﺑﺒﻮاﺑﺎت ﻣﻨﻄﻘﯿﺔ ﯾﻤﻜﻨﮭﺎ اﻟﺘﺤﻜﻢ ﻓﻲ ﻣﺴﺘﻮﯾﺎت اﻟﻜﯿﻮﺑﺖ اﻷﺧﺮى ﻛﻤﺎ ھﻮ ﻣﻮﺿﺢ ﻓﻲ اﻟﺸﻜﻞ ) 4(. وﺟﺪت اﻟﺪراﺳﺔ ذاﺗﮭﺎ أن ﺑﻨﺎء ھﺬه اﻟﺒﻮاﺑﺔ ﯾﺨﻀﻊ ﻟﻼﻧﺰﯾﺎح اﻟﻄﻮري اﻟﺰاوي ﻓﻘﻂ وﯾﻜﺎﻓﺊ ًﺎﯿﻣﻨﻄﻘ ﺧﻮارزﻣﯿﺔ ﺗﻮﻓﻮﻟﻲ ﺑﻜﯿﻮﺑﺖ واﺣﺪ أو اﺛﻨﯿﻦ . 30 وﺑﺎﺳﺘﺨﺪام ﺧﻮارزﻣﯿﺔ ،ھﺎدﻣﺎرد اﻟﻤﻌﺘﻤﺪة ﻋﻠﻰ اﻟﻜﯿﻮﺑﺖ اﻷﺳﺎﺳﻲ 0> Or |1>( |( ، واﻟﺘﻲ ﺗﻤﺜﻞ ﺣﺎﻟﺔ اﻟﺴﺒﯿﻦ اﻟﻨﻮوي ودوراﻧﮫ اﻟﻤﺤﻮري اﻟﻘﺎﺑﻞ ﻟﻠﻌﻜﺲ ًﺎﯿﻛﻤﻮﻣ ﺑﺎﻟﻤﺼﻔﻮﻓﺔ ،اﻟﻮاﺣﺪﯾﺔ ﺗﻤﺖ دراﺳﺔ اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ اﻟﻘﺎﺑﻠﺔ ﻟﻠﻌﻜﺲ . دراﺳﺔ اﻻﺣﺘﻤﺎﻻت اﻟﻜﻤﻮﻣﯿﺔ ﺗﻢ ﺗﻤﺜﯿﻠﮭﺎ ،ًﺎﯿﻣﺼﻔﻮﻓ ﺑﺤﺴﺐ ﻣﻘﺘﺮﺣﺎت ﺑﺎوﻟﻲ ) Pauli ( ، ﺑﺄﺣﺪ أﺷﻜﺎل اﻟﺪوران ﺣﻮل اﻟﻤﺤﺎور ), X, Y Z ، وﺗﻤﺜﻞ اﻟﺒﻮاﺑﺔ ) NOT ( ﺑﺎﻟﺪوران ﺣﻮل اﻟﻤﺤﻮر ﺑﺰاوﯾﺔ ) π( ، واﻻﺧﺘﻼف ﺑﯿﻨﮭﻢ ﻓﻘﻂ ھﻮ ﻣﺤﻮر اﻟﺪوران . ﻛﻤﺎ أن ﺑﻮاﺑﺔ اﻻﻧﺰﯾﺎح اﻟﻄﻮري ) )Phase shift gates اﻟﺘﻲ ﺗﻌﺘﻤﺪ ﻋﻠﻰ ﻧﻤﻮذج ﻛﺮة ﺑﻠﻮخ ) Bloch Sphere ( ،اﻟﺪوراﻧﻲ وﻓﯿﮭﺎ اﺣﺘﻤﺎل ﻗﯿﺎس اﻟﺤﺎﻻت اﻷﺳﺎﺳﯿﺔ < 0> Or |1 | وﻻ ﯾﺘﻐﯿﺮ ﺑﻌﺪ ﺗﻄﺒﯿﻖ اﻟﺒﻮاﺑﺔ ،اﻟﻜﻤﻮﻣﯿﺔ ﻟﻜﻨﮭﺎ ﻗﺎﺑﻠﺔ ﻟﻠﺘﻌﺪﯾﻞ اﻟﻄﻮري . اﻟﺸﻜﻞ 4. ﻧﻤﻮذج ﺑﻮاﺑﺔ ﻣﻨﻄﻘﯿﺔ ﻗﺎﺑﻠﺔ ﻟﻠﺘﺤﻜﻢ ﻓﻲ ﻣﺴﺘﻮﯾﺎت ﺛﻼﺛﺔ ﻛﯿﻮﺑﺘﺎت . 30 ﻓﻲ ﺣﯿﻦ ﯾﺒﯿﻦ اﻟﺸﻜﻞ 5 ﻣﻌﺎدﻻت اﻟﻨﻤﻮذج اﻟﮭﺎﻣﻠﺘﻮﻧﻲ ﻟﺒﻨﺎء ھﺬه اﻟﺒﻮاﺑﺔ ﻣﻊ ﺷﻜﻞ ﺗﻤﺜﯿﻠﻲ ﻟﻠﺒﻮاﺑﺔ ) NOT ( واﻟﺒﻮاﺑﺔ اﻟﻌﻜﺴﯿﺔ اﻟﻘﺎﺑﻠﺔ ﻟﻠﺘﺤﻜﻢ ) )CCN ﺑﺤﺴﺐ ﺗﻮﻓﻮﻟﻲ . ﺑﯿﻨﻤﺎ ﺑﻮاﺑﺎت اﻟﺘﺤﻜﻢ ) Controlled gates ( ﺗﻌﺘﻤﺪ ﻋﻠﻰ ،ﻛﯿﻮﺑﺘﯿﻦ ﺣﯿﺚ ﯾﻌﻤﻞ ﻛﯿﻮﺑﺖ واﺣﺪ أو أﻛﺜﺮ ﻛﻌﻨﺼﺮ ﺗﺤﻜﻢ ﻓﻲ ﺑﻌﺾ اﻟﻌﻤﻠﯿﺎت . 31 Hadamard gate: H(a0 |0〉 + a1 |1〉) = 1/√2 [ (a0 + a1)|0〉 + (a0 - a1)|0〉
- 29. 29 ﺧﻮارزﻣﯿﺔ ﻏﺮوﻓﺮ واﻟﺴﺒﯿﻦ اﻹﻟﻜﺘﺮوﻧﻲ اﻗﺘﺮح ﻏﺮوﻓﺮ أن ﺧﻮارزﻣﯿﺔ اﻟﺒﺤﺚ اﻟﻜﻤﻮﻣﯿﺔ ﺗﺴﻤﺢ ﺑﺈﺟﺮاء ﺑﺤﺚ ﻓﻌﺎل ﻋﻦ أﺣﺪ اﻟﻌﻨﺎﺻﺮ ) K( ﺿﻤﻦ ﻣﺴﺎﺣﺔ اﻟﺒﺤﺚ ذات اﻟﺤﺠﻢ ) n( ، وﺗﻢ ﺗﻮﺻﯿﻒ ھﺬه اﻟﺨﻮارزﻣﯿﺔ ﺑﻨﻈﺎم ﺛﻨﺎﺋﻲ ﯾﺘﯿﺢ َدﻋﺪ ) n( ﻣﻦ ،اﻟﻤﺪﺧﻼت وﻧﺘﯿﺠﺔ اﻟﺒﺤﺚ ھﺬه ﺗﺤﯿﻞ إﻟﻰ اﻟﻘﯿﻤﺔ ) 1(. وﺑﺤﺴﺐ ،ﻏﺮوﻓﺮ ﻓﺈن أﻓﻀﻞ اﻟﺤﻠﻮل ﻟﺨﻮارزﻣﯿﺔ ﻛﻼﺳﯿﻜﯿﺔ ﺗﻌﻤﻞ ﻋﻠﻰ إﺟﺮاء ﻣﺪﺧﻼت ﺑﻌﺪد ) n( ،ًﺎﯿﻋﺸﻮاﺋ وھﺬا ﻣﺎ ﯾﻜﺎﻓﺊ إﺟﺮاء ) n( ﻋﻤﻠﯿﺔ إﺟﺮاﺋﯿﺔ . ﺑﯿﻨﻤﺎ ﺗﻘﻮم اﻟﺨﻮارزﻣﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ ﺑﺎﻟﺒﺤﺚ ﻋﻦ اﻟﻌﻨﺼﺮ اﻟﻤﺤﺪد ﺑﻌﺪد ﯾﻜﺎﻓﺊ اﻟﺠﺬر اﻟﺘﺮﺑﯿﻌﻲ ﻟﻠﻌﻤﻠﯿﺎت ) n( ﻓﻲ اﻟﺤﺎﻟﺔ ،اﻟﻜﻼﺳﯿﻜﯿﺔ ﻣﺎ ﯾﻌﻨﻲ إﻣﻜﺎﻧﯿﺔ ﺗﻮﻓﯿﺮ اﻟﻮﻗﺖ اﻟﻼزم ﻟﻠﺒﺤﺚ ًﺎﯿﻛﻤﻮﻣ ﻓﻲ إﺟﺮاء اﻟﻌﻤﻠﯿﺎت اﻟﺤﺴﺎﺑﯿﺔ ﻋﻠﻰ ﻧﺤﻮ ﻛﺒﯿﺮ ًاﺪﺟ . 32 أظﮭﺮت اﻟﺪراﺳﺎت اﻟﻜﻤﻮﻣﯿﺔ اﻷوﻟﻰ إﻣﻜﺎﻧﯿﺔ ﺑﻨﺎء ﺑﻮاﺑﺔ ﻣﻨﻄﻘﯿﺔ ﻛﻤﻮﻣﯿﺔ ﻣﺆﻟﻔﺔ ﻣﻦ ﻛﯿﻮﺑﺖ وﺣﯿﺪ ﺳﮭﻠﺔ ،اﻟﺘﻨﻔﯿﺬ إذ ﯾﺘﻢ اﺳﺘﺨﺪام إﺛﺎرة ﻟﯿﺰرﯾﺔ ﻟﺬرة وﺣﯿﺪة ﻣﻦ ﺳﻮﯾﺘﮭﺎ اﻟﻄﺎﻗﯿﺔ ،اﻷﺳﺎﺳﯿﺔ وﺗﻜﻮن ﺳﮭﻠﺔ اﻟﺘﺤﻜﻢ ﻓﯿﮭﺎ ﻣﻦ ﺧﻼل اﻟﺘﺤﻜﻢ ﻓﻲ طﻮل ﻣﻮﺟﺔ اﻟﻠﯿﺰر وﺗﺮدده . وﺑﺤﺴﺐ ﻧﻤﻮذج ذرة اﻟﮭﯿﺪروﺟﯿﻦ ،ﻟﺒﻮر ﻓﺈن اﻟﻔﺮق اﻟﻄﺎﻗﻲ ﺑﯿﻦ اﻟﺴﻮﯾﺔ اﻷﺳﺎﺳﯿﺔ اﻟﻤﺴﺘﻘﺮة ) E1 ( وﺳﻮﯾﺔ اﻟﻄﺎﻗﺔ اﻟﻤﺜﺎرة اﻷوﻟﻰ ) E2 ( ﯾﺘﻨﺎﺳﺐ ًﺎﯿﻛﻤ ﻣﻊ طﻮل ﻣﻮﺟﺔ اﻟﻠﯿﺰر ) اﻣﺘﺼﺎص اﻟﺬرة ﻟﻔﻮﺗﻮن ﺿﻮﺋﻲ ﺑﻄﺎﻗﺔ ﻣﺤﺪدة ﺗﻜﺎﻓﺊ اﻟﻔﺮق اﻟﻄﺎﻗﻲ ﺑﯿﻦ اﻟﺴﻮﯾﺘﯿﻦ (. ﻓﺈذا أﺧﺬت اﻟﺬرة اﻟﻜﯿﻮﺑﺖ )| 0<( ﻟﻠﺤﺎﻟﺔ اﻟﻜﻤﻮﻣﯿﺔ واﻟﺬرة ﺑﺴﻮﯾﺔ طﺎﻗﯿﺔ ،ﻣﺴﺘﻘﺮة ﻓﺈن اﻟﺬرة وھﻲ ﺑﺤﺎﻟﺔ إﺛﺎرة ﺗﻌﻄﻰ ﺑﺎﻟﻜﯿﻮﺑﺖ )| 1<( ، وﺑﻨﺎء ،ﻋﻠﯿﮫ ﻓﺈﻧﮫ ﻣﻦ اﻟﺴﮭﻮﻟﺔ ﺑﻤﻜﺎن ﺑﻨﺎء اﻟﺒﻮاﺑﺔ ) NOT ( ﺑﻤﺠﺮد إﺛﺎرة اﻟﺬرة ﺑﻄﻮل ﻣﻮﺟﻲ ،ﻣﺤﺪد واﻟﻌﻜﺲ ﺻﺤﯿﺢ . ﺑﯿﻨﻤﺎ اﻟﺘﺤﻜﻢ ﻓﻲ ﻛﯿﻮﺑﺘﯿﻦ ﺑﺪا ًﺎﺒﺻﻌ ﻓﻲ ،اﻟﺒﺪاﯾﺔ ﻓﻤﻦ أﺟﻞ ﺗﺼﻤﯿﻢ ﺑﻮاﺑﺔ ﻛﻤﻮﻣﯿﺔ ﻣﻨﻄﻘﯿﺔ ﻣﺆﻟﻔﺔ ﻣﻦ ﻛﯿﻮﺑﺘﯿﻦ ﻣﻦ وﺟﮭﺔ ﻧﻈﺮ ،ﺗﺠﺮﯾﺒﯿﺔ ﯾﻜﻔﻲ اﻟﺒﺤﺚ ﻓﻲ اﻛﺘﻤﺎل اﻟﺸﺮوط اﻟﺪﯾﻨﺎﻣﯿﻜﯿﺔ ،ًﺎﯿﻓﯿﺰﯾﺎﺋ وذﻟﻚ ﻣﻦ ﻗﺒﯿﻞ ﻣﻮاءﻣﺔ اﻟﺸﺮوط اﻟﻜﻤﻮﻣﯿﺔ ﻋﻠﻰ اﻟﺤﺎﻟﺔ اﻟﻜﻼﺳﯿﻜﯿﺔ ﻟﺒﻨﺎء اﻟﺒﺖ ،ًﺎﺳأﺳﺎ وﻣﺜﺎل ذﻟﻚ اﻟﺒﻮاﺑﺔ ) AND ( اﻟﺘﻲ ﺗﻄﻠﺐ وﺟﻮد ﺛﻼث ذرات ) ﺛﻼﺛﺔ ﻛﯿﻮﺑﺘﺎت ( ﻛﻤﺎ ھﻮ ﻣﻮﺿﺢ ﻓﻲ اﻟﺸﻜﻞ 6. 33
- 30. 30 اﻟﻛم ﺗﺳرﯾﻊ ﻗﯾﺎس أن ﻧﻘول أن ﻣﻌﻧﻰ ﻣﺎ اﻟﻛﻼﺳﯾﻛﻲ؟ اﻟﻛﻣﺑﯾوﺗر ﻣن أﻛﺑر ﺑﺳرﻋﺔ اﻟﻣﺷﻛﻠﺔ ﯾﺣل اﻟﻛﻣوﻣﻲ اﻟﻛﻣﺑﯾوﺗر اﻟﻣﻌﻘدة ﻟﻠﻣﻘﺎﯾﯾس اﻟﻣﻘﺎرب اﻟﻘﯾﺎس ﻓﻲ ﻋﻣوﻣًﺎ ﺳﻧﻧظر ، اﻟﺣﺳﺎﺑﻲ اﻟﺗﻌﻘﯾد ﻧظرﯾﺔ ﻓﻲ ﻣﻌﺗﺎد ھو ﻛﻣﺎ ذات اﻟﻔردﯾﺔ اﻟﻣﺷﻛﻼت ﻣن ًﺑدﻻ ، اﻟﻣﺷﻛﻠﺔ ﺣﺟم ﻣﻊ اﻟﻔﺿﺎء اﺳﺗﺧدام أو اﻟﺗﺷﻐﯾل وﻗت ﻣﺛل ﻣن ﻛل ﻓﻲ .اﻟﺛﺎﺑت اﻟﺣﺟم اﻟﻌﻣﻠﯾﺎت ﺑﻌدد اﻟﺗﺷﻐﯾل وﻗت ﻧﻘﯾس ، واﻟﻛﻣﯾﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻹﻋدادات ﻧﻣوذج ﺑﺎﺳﺗﺧدام ذﻟك ﻗﯾﺎس ﯾﻣﻛن ، اﻟﻛم ﺣﺳﺎب ﺣﺎﻟﺔ ﻓﻲ .اﻟﺧوارزﻣﯾﺔ ﺗﺳﺗﺧدﻣﮭﺎ اﻟﺗﻲ اﻷوﻟﯾﺔ ﺗﺳﻣﻰ اﻷوﻟﯾﺔ اﻟﻛﻣﯾﺔ اﻟﻌﻣﻠﯾﺎت ﻣن ﺳﻠﺳﻠﺔ اﻟﻛﻣوﻣﯾﺔ اﻟداﺋرة ﺗﻣﺛل ﺣﯾث ، اﻟﻛﻣوﻣﯾﺔ اﻟداﺋرة ﻛل ﯾطﺑﻖ ، اﻟﻛﻣوﻣﯾﺔ اﻟﺑواﺑﺎت أداء ﻟﻣﻘﺎرﻧﺔ .(اﻟﻛﻣوﻣﯾﺔ )اﻟﺑﺗﺎت اﻟﺑﺗﺎت ﻣن ﺻﻐﯾر ﻋدد ﻋﻠﻰ ﻣﻧﮭﺎ اﻟﻛﻣﺑﯾوﺗر ﻋﻠوم ﻧﻣط ﺗدوﯾن ﻧﺳﺗﺧدم ، اﻟﺧوارزﻣﯾﺎت O ( f ( n )) ﻋﻠﻰ ﯾﻔﺳر أن ﯾﺟب واﻟذي ، ﺑواﺳطﺔ ﻣﺗﻧﺎظرة ﺣدود "ذو أﻧﮫ f ( n )". اﻟﺣﺳﺎﺑﻲ اﻟﺗﻌﻘﯾد ﻧظرﯾﺔ ﻣن اﻷﺳﺎﺳﯾﺔ اﻷﻓﻛﺎر ًﺎﻧأﺣﯾﺎ ﻧﺳﺗﺧدم ) 10 ( وﺑﺻﻔﺔ ، ﻓﺋﺎت ﻣﻔﮭوم ﺧﺎﺻﺔ اﻟﺟدول اﻧظر .ﺑﺻﻌوﺑﺔ اﻟﻣﺷﻛﻼت ﻣن ﻣﺟﻣوﻋﺎت ھﻲ واﻟﺗﻲ ، اﻟﺗﻌﻘﯾد 1 وﺻف ﻋﻠﻰ ﻟﻠﺣﺻول ﻓﺈن ، اﻟﺗﻌﻘﯾد ﻟﻔﺋﺔ ﺑﺎﻟﻧﺳﺑﺔ ﻣﻛﺗﻣﻠﺔ اﻟﻣﺷﻛﻠﺔ أن ﻗﯾل إذا .اﻟﮭﺎﻣﺔ اﻟﺗﻌﻘﯾد ﻓﺋﺎت ﻟﺑﻌض رﺳﻣﻲ ﻏﯾر اﻟﻔﺋﺔ ﺗﻠك ﻓﻲ ﻣﺿﻣﻧﺔ ﻓﮭﻲ :اﻟﻔﺋﺔ ﺗﻠك داﺧل اﻟﻣﺷﻛﻼت أﺻﻌب ﻣن واﺣدة أﻧﮭﺎ ﯾﻌﻧﻲ ھذا وﻛل ، إﻟﯾﮭﺎ ﺗﻘﻠل اﻟﻔﺋﺔ ﺗﻠك داﺧل أﺧرى ﻣﺷﻛﻠﺔ . اﻟﺗﺷﻔﯾر وﺗطﺑﯾﻘﺎت اﻟﻣﺧﻔﯾﺔ اﻟﻔرﻋﯾﺔ اﻟﻣﺟﻣوﻋﺔ ﻣﺷﻛﻠﺔ ﺧوارزﻣﯾﺔ ﻛﺎﻧت اﻟﻣﻛﺗﺷﻔﺔ اﻟﻛﻣوﻣﯾﺔ اﻟﻛﻣﺑﯾوﺗر ﻷﺟﮭزة اﻷوﻟﻰ اﻟﺗطﺑﯾﻘﺎت أﺣد Shor ﻋدد ﻟﻌﺎﻣل ﺻﺣﯾﺢ 11 . ﺻﺣﯾﺢ ﻋدد إﻋطﺎء ﻋﻧد ، اﻟﻌواﻣل ﻣﺷﻛﻠﺔ ﻓﻲ N = p × q اﻷوﻟﯾﺔ اﻷﻋداد ﻟﺑﻌض p و q ﺗﺣدﯾد ھﻲ ﻣﮭﻣﺗﻧﺎ ، p و q . اﻟرﻗم ﺣﻘل )ﻏرﺑﺎل ﻣﻌروﻓﺔ ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ أﻓﺿل اﻟﻣﻧﺎﺳب اﻟوﻗت ﻓﻲ ﺗﻌﻣل (اﻟﻌﺎم ( 12 )) 2/3 (log log N ) 1/3 ( O (log N ) ، اﻟواﻗﻊ ﻓﻲ ﺷور ﺧوارزﻣﯾﺔ أن ﺣﯾن ﻓﻲ ، (ﻣﺎ ﺣد إﻟﻰ أﻋﻠﻰ ﺻﺎرم ارﺗﺑﺎط أﻓﺿل ؛ ارﺷﺎدي ﺣد ھو ھذا
- 31. 31 اﻟ ھذه ﺗﺣل اﻟﻛﻣوﻣﯾﺔ اﻟوﻗت ﻓﻲ ، ﺑﻛﺛﯾر أﺳرع ﺑﺷﻛل ﻣﺷﻛﻠﺔ ( O ﺳﺟل ). 3 N ) ھذه ﺗظﮭر ﻗد اﻟﻌﻣوﻣﯾﺔ ﺑﺎﻟﻣﻔﺎﺗﯾﺢ اﻟﺗﺷﻔﯾر ﻧظﺎم أن ﺣﻘﯾﻘﺔ ﻟوﻻ ، اﻟرﯾﺎﺿﯾﺔ اﻷھﻣﯾﺔ ﺣﯾث ﻣن ﻓﻘط اﻟﻧﺗﯾﺟﺔ 13 RSA ﻛﻔﺎءة ﻣﻌﺎﻣل ﺧوارزﻣﯾﺔ ﺗﺗﺿﻣن .ﺻﺣﯾﺢ ﻋدد ﺻﻼﺑﺔ ﻋﻠﻰ ﯾﻌﺗﻣد واﺳﻊ ﻧطﺎق ﻋﻠﻰ Shor ﻏﯾر ھذا اﻟﺗﺷﻔﯾر ﻧظﺎم أن اﻟﻔﻌﺎﻟﺔ ﻛﺑﯾر ﻛم ﻛﻣﺑﯾوﺗر ﺑواﺳطﺔ اﻟﮭﺟوم ﺿد آﻣن . ﻋﺎم ﻓﻲ ، أﻋﻼه اﻟﺗﻘرﯾﺑﯾﺔ اﻟﺗﺷﻐﯾل أوﻗﺎت ﻋن ًادﺗﺣدﯾ أﻛﺛر ﻛﻣﻘﺎرﻧﺔ 2010 Kleinjung et . al ذﻛرت 14 ﻟﻌدد ﻛﻼﺳﯾﻛﯾﺎ ﻋﺎﻣﻼ 768 اﻟﻛﻣﺑﯾوﺗر أﺟﮭزة ﻣن اﻟﻣﺋﺎت ﺑﺎﺳﺗﺧدام وذﻟك ، ﺑت ~ ﻟل اﻟﻛﻠﻲ اﻟﺣﺳﺎﺑﻲ اﻟﺟﮭد ﻣﻊ ، ﻋﺎﻣﯾن ﻓﺗرة ﻣدى ﻋﻠﻰ اﻟﺣدﯾﺛﺔ 10 20 ﺗﺣﻠﯾل ﯾﺷﯾر .ﻋﻣﻠﯾﺎت اﻷﻋطﺎل ﻣﻊ ﺗﺗﺳﺎﻣﺢ واﺣدة ﻛﻣوﻣﯾﺔ ﺣوﺳﺑﺔ ﻟﺑﻧﯾﺔ ﻣﻔﺻل ) 7 ( ﺣول ﻣﻌﻘوﻟﺔ اﻓﺗراﺿﺎت ﻣﻊ ، رﻗم ﻣﻌﺎﻟﺟﺔ ﯾﻣﻛن أﻧﮫ إﻟﻰ ، اﻷﺳﺎﺳﯾﺔ اﻷﺟﮭزة 2000 ~ ﺑﺎﺳﺗﺧدام ﻛﻣﻲ ﻛﻣﺑﯾوﺗر ﺑواﺳطﺔ ﺑت 3 × 10 11 ﻓﻘط واﺣد ﯾوم ﻣن ﻷﻛﺛر ﯾﻌﻣل ، ﺑﺎﯾت ﻣﻠﯾﺎر وﺣواﻟﻲ ، ﻛﻣوﻣﯾﺔ ﺑواﺑﺔ ﺑﻣﻌدل 10 ﻛﮭدف واﻗﻌﻲ ﻏﯾر ﯾﺑدو ﻻ ﻟﻛﻧﮫ ، اﻟﺣﺎﻟﯾﺔ اﻟﺗﻛﻧوﻟوﺟﯾﺎ ﯾﺗﺟﺎوز ھذا أن اﻟواﺿﺢ ﻣن .ﻣﯾﻐﺎھﯾرﺗز اﻷﺟل طوﯾل . طرﯾﻘﺔ ﺗﻌﺗﻣد Shor ﺧﺎﺻﺔ ﺣﺎﻟﺔ إﻟﻰ اﻟﻣﮭﻣﺔ ﺗﻘﻠﯾص ﻋﻠﻰ اﻟﺻﺣﯾﺣﺔ اﻷﻋداد ﻣﻌﺎﻣل ﻋﻠﻰ اﻟﻣﺧﻔﯾﺔ اﻟﻔرﻋﯾﺔ اﻟﻣﺟﻣوﻋﺔ ﻣﺷﻛﻠﺔ ﺑﺎﺳم ﺗﻌرف رﯾﺎﺿﯾﺔ ﻟﻣﺷﻛﻠﺔ ) HSP ( ، 15 ، 16 إﻋط ﺛم ﺎء ﺗﺣدﯾد ﯾﺗم .اﻟﻣﺷﻛﻠﺔ ﻟﮭذه ﻓﻌﺎﻟﺔ ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ HSP ﻣﺟﻣوﻋﺔ ﺑواﺳطﺔ G وﺗﻘوم ، ﺧوارزﻣﯾﺔ Shor اﻟﺣﺎﻟﺔ ﺑﺣل G = ℤ. ﻟﻧظﺎم اﻟﻔﻌﺎﻟﺔ اﻟﺣﻠول ﺗﺗﺣول HSP ﻟﻠﻣﺟﻣوﻋﺎت اﻷﺧرى G اﻟﺣﺎﻻت ﺑﻌض ﻧﻠﺧص ؛ اﻷﺧرى اﻟﺗﺷﻔﯾر أﻧظﻣﺔ ﻟﻛﺳر ﻓﻌﺎﻟﺔ ﺧوارزﻣﯾﺎت إﻟﻰ ﻟـ اﻟﻣﮭﻣﺔ HSP اﻟﻣﺷﻔرة اﻷﻧظﻣﺔ وﺑﻌض اﻟﺟدول ﻓﻲ ﻟﮭﺎ اﻟﻣﻘﺎﺑﻠﺔ 2 ﻣﺛﯾرﺗﺎن ﺣﺎﻟﺗﺎن وھﻧﺎك . ﻓﻲ ﺧﺎص ﺑﺷﻛل ﻟﻼھﺗﻣﺎم HSP اﻟوﻗت ﻓﻲ اﻟﺣدود ﻛﺛﯾر ﻓﻲ اﻟﻛم ﺧوارزﻣﯾﺎت ًﺎﯾﺣﺎﻟ ﺗﻌرﻓﮭﻣﺎ ﻟم اﻟﺣدود ﻣﺗﻌددة ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ﺷﺄن ﻣن .واﻟﺗﻣﺎﺛﻠﯾﺔ اﻟﺳطﺣﯾﺔ اﻟﺛﻧﺎﺋﯾﺔ اﻟﻣﺟﻣوﻋﺎت وھﻣﺎ اﻟﺣﺎﻟﻲ ﺧوارزﻣﯾﺔ ﺗﻌطﻲ أن اﻟﺳﺎﺑﻘﺔ ﻟﻠﺣﺎﻟﺔ اﻟزﻣﻧﯾﺔ اﻟﺷﺑﻛﺎت ﻓﻲ ﻧﺎﻗﻼت أﻗﺻر ﻹﯾﺟﺎد ﻓﻌﺎﻟﺔ ؛ 17 اﻟرﺳوم ﻣن ﻟﻠﺗﻣﺎﺛل ﻓﻌﺎﻻ اﺧﺗﺑﺎرا ﯾﻌطﻲ أن ﺷﺄﻧﮫ ﻣن اﻷﺧﯾرة ﻟﻠﺣﺎﻟﺔ ﻓﻌﺎﻟﺔ اﻟﻛم ﺧوارزﻣﯾﺔ (اﻟرؤوس ﺗﺳﻣﯾﺔ إﻋﺎدة ﺗﺣت )اﻟﺗﻛﺎﻓؤ اﻟﺑﯾﺎﻧﯾﺔ . واﻟﺗﺣﺳﯾن اﻟﺑﺣث ﯾﻣﻛن .اﻟﻣﻧظم ﻏﯾر اﻟﺑﺣث ھﻲ اﻟﻛﻣﺑﯾوﺗر ﻋﻠوم ﻓﻲ اﻷﺳﺎﺳﯾﺔ اﻟﻣﺷﺎﻛل أﻛﺛر ﻣن واﺣدة إﺿﻔﺎء اﻟﺗﺎﻟﻲ اﻟﻧﺣو ﻋﻠﻰ اﻟﻣﺷﻛﻠﺔ ھذه ﻋﻠﻰ اﻟرﺳﻣﻲ اﻟطﺎﺑﻊ : داﻟﺔ ﺗﻘﯾﯾم ﻋﻠﻰ اﻟﻘدرة إﻟﻰ ﺑﺎﻟﻧظر f : {0 ، 1 → {0 n } ، 1 } ﻋن اﺑﺣث ، x ﺑﺣﯾث f ( x ) = 1 ﻣﺛل ﻛﺎن إذا ، x ﻣوﺟود "ﻏﯾر اﻹﺧراج ، ذﻟك ﺧﻼف ؛ ًادﻣوﺟو ". ﻋن ﻣﺳﺑﻘﺔ ﻣﻌﻠوﻣﺎت وﺟود ﻋدم ﻣﻊ أﻧﮫ ﻧرى أن اﻟﺳﮭل ﻣن f ﯾﺟب ، ﺧوارزﻣﯾﺔ أي ّمﯾﺗﻘ أن ، ﻣؤﻛد ﺑﺷﻛل اﻟﻣﮭﯾﻛﻠﺔ ﻏﯾر اﻟﺑﺣث ﻣﺷﻛﻠﺔ ﺗﺣل واﻟﺗﻲ ، ﻛﻼﺳﯾﻛﯾﺔ f n = 2 أﺳوأ ﻓﻲ ﻣرات
- 32. 32 اﺣﺗﻣﺎل ﻣﻊ ، اﻟﻣﺛﺎل ﺳﺑﯾل ﻋﻠﻰ ، ﺗﻧﺟﺢ ﻋﺷواﺋﯾﺔ ﺧوارزﻣﯾﺔ ﻋن ﺑﺣﺛﻧﺎ إذا ﺣﺗﻰ .اﻟﺣﺎﻻت 1 / 2 ﺑﺎﻟﺗرﺗﯾب ھو اﻟﻣطﻠوﺑﺔ اﻟﺗﻘﯾﯾﻣﺎت ﻋدد ﻓﺈن ، اﻟﺣﺎﻻت أﺳوأ ﻓﻲ N. ﺑﺷﻛل ، ذﻟك وﻣﻊ ، ﻣﻠﺣوظ ﺑﺳﺑب ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ھﻧﺎك Grover ، 18 ﺑﺎﺳﺗﺧدام اﻟﻣﺷﻛﻠﺔ ھذه ﺗﺣل واﻟﺗﻲ O (N) ﺗﻘﯾﯾﻣﺎت f ﻟـ اﻷﺻﻠﯾﺔ )اﻟﺧوارزﻣﯾﺔ اﻟﺣﺎﻻت أﺳوأ ﻓﻲ Grover ﯾﻛون اﻟﺗﻲ اﻟﺧﺎﺻﺔ اﻟﺣﺎﻟﺔ ّت ﺣﻠ ﻗﻠﯾﻼ ﻻﺣﻖ وﻗت ﻓﻲ ﻣﺗﻌددة ﺣﻠول إﻟﻰ اﻹﺿﺎﻓﺔ ﺟﺎءت ؛ ًادﻓرﯾ اﻟﺣل ﻓﯾﮭﺎ ). 19 اﻟﺧوارزﻣﯾﺔ ﯾﺣدھﺎ اﻻﺣﺗﻣﺎل ﻣﻊ ﯾﻔﺷل أﻧﮫ ، ﯾﻌﻧﻲ وھذا ﺧطﺄ؛ small (اﻟﺛﺎﺑت )ﻟﻛن اﻟﺗﻌﺳﻔﻲ ﻟﻠﺻﻐﯾر ، 0 > 0. أن ﻣن اﻟرﻏم ﻋﻠﻰ f ﺧوارزﻣﯾﺔ ﻓﺈن ، اﻟداﺧﻠﯾﺔ اﻟﺑﻧﯾﺔ ﻣن ﻧوع ﻟﮫ ﯾﻛون ﻗد Grover ﻻ أن ﻧﻘول ؛ اﻹطﻼق ﻋﻠﻰ ھذا ﺗﺳﺗﺧدم f ﻓﻲ أﺳود ﺻﻧدوق أو أوراﻛل ﻛﺻورة ﯾﺳﺗﺧدم اﻟﺧوارزﻣﯾﺔ . اﻟﻔور ﻋﻠﻰ ﯾﻣﻛن ﺧوارزﻣﯾﺔ ﺗطﺑﯾﻖ Grover اﻟﺗﻌﻘﯾد ﻓﺋﺔ ﻓﻲ ﻣﺷﻛﻠﺔ أي ﻋﻠﻰ NP. ھذا ﯾﺷﻣل ﺧوارزﻣﯾﺔ ﺗوﺟد :اﻟﺗﺎﻟﻲ ﺑﺎﻟﻣﻌﻧﻰ ، ﺑﻛﻔﺎءة ﺣﻠوﻟﮭﺎ ﻣن اﻟﺗﺣﻘﻖ ﯾﻣﻛن اﻟﺗﻲ اﻟﻘرار ﻣﺷﻛﻼت اﻟﻔﺻل ﻓﻌﺎﻟﺔ ﻛﻼﺳﯾﻛﯾﺔ ﺗﺣﻘﻖ A ، ""ﻧﻌم اﻹﺟﺎﺑﺔ ﺗﻛون أن ﯾﺟب ﺣﯾث اﻟﺣﺎﻻت ﻣن ﺣﺎﻟﺔ أي ﻓﻲ ﺑﺣﯾث ، ﺗﻛون أن ﯾﻣﻛن ﺷﮭﺎدة ھﻧﺎك إﻟﻰ إدﺧﺎل A دﻟﯾل ھﻲ اﻟﺷﮭﺎدة ، آﺧر ﺑﻣﻌﻧﻰ .اﻟﺷﮭﺎدة ﯾﻘﺑل ﺑﺣﯾث ﺑواﺳطﺔ ﻣﻧﮭﺎ اﻟﺗﺣﻘﻖ ﯾﻣﻛن واﻟﺗﻲ ، ""ﻧﻌم ھﻲ اﻹﺟﺎﺑﺔ أن ﻋﻠﻰ A. أي ﻋﻠﻰ ، أﺧرى ﻧﺎﺣﯾﺔ ﻣن .ﺗﻘﺑﻠﮭﺎ "أ " ﺗﺟﻌل أن ﯾﻣﻛن ﺷﮭﺎدة ھﻧﺎك ﺗﻛون أﻻ ﯾﺟب ، ""ﻻ اﻹﺟﺎﺑﺔ ﺗﻛون أن ﯾﺟب ﺣﯾث ﺣﺎل اﻟﻔﺻل ﯾﺷﻣل NP اﻟﻣﺷﻛﻼ ﻣن اﻟﻌدﯾد اﻟﻘﯾد ورﺿﺎ اﻟﺗﺣﺳﯾن ﺗﺗﺿﻣن اﻟﺗﻲ اﻟﮭﺎﻣﺔ ت . ﻓﻲ ﻣﺷﻛﻠﺔ ﻟوﺟود ا ًﻧظر NP طول ﺷﮭﺎدة ﻋﻠﻰ ﺗﺣﺗوي m ﺧوارزﻣﯾﺔ ﺗطﺑﯾﻖ ﺧﻼل ﻣن ، Grover ﻋﻠﻰ A ﺗﺳﺗﺧدم ﺧوارزﻣﯾﺔ ﻋﻠﻰ ﻧﺣﺻل ، اﻟﻣﻣﻛﻧﺔ اﻟﺷﮭﺎدات ﺟﻣﯾﻊ ﻓﻲ واﻟﺑﺣث اﻟوﻗت poly ( m )) m / 2 O (2 ﻣن ًﺑدﻻ ، O ( 2 م ﻣن اﻟﻣﺳﺗﺧدﻣﺔ (( م ) ﺑوﻟﻲ اﻟﺑﺣث ﻗﺑل ﻣن وﺿوﺣًﺎ أﻗل (ًﺎﺑ)ﺗﻘرﯾ اﻟﺗرﺑﯾﻌﻲ اﻟﺗﺳرﯾﻊ ھذا .اﻟﺷﮭﺎدات ﺟﻣﯾﻊ ﻋﻠﻰ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺷﺎﻣل ﺧوارزﻣﯾﺔ ﺣﻘﻘﺗﮫ اﻟذي اﻟﻔﺎﺋﻖ اﻟﺣدود ﻣﺗﻌدد اﻟﺗﺳرﯾﻊ Shor أن اﻟﻣﻣﻛن ﻣن ﯾزال ﻻ وﻟﻛن ، اﻟﺳﺎﻋﺔ ﺳرﻋﺔ ﺑﻧﻔس ﯾﻌﻣل اﻟﻛﻣوﻣﻲ اﻟﻛﻣﺑﯾوﺗر ﻛﺎن إذا ، اﻟواﻗﻊ ﻓﻲ .ﻣﺎ ﺣد إﻟﻰ ا ًﻛﺑﯾر ﯾﻛون ًﺎﺑﺗﻘرﯾ اﻟﺣﺟم ﺿﻌف ﺗﺑﻠﻎ اﻟﺗﻲ اﻟﻣﺷﻛﻠﺔ ﻣﺛﯾﻼت أن ﯾﻌﻧﻲ ﻓﮭذا ، اﻟﻛﻼﺳﯾﻛﻲ اﻟﻛﻣﺑﯾوﺗر ﻣﺛل ًﺎﺑﺗﻘرﯾ ﻣﻣﺎﺛﻠﺔ زﻣﻧﯾﺔ ﻓﺗرة ﻓﻲ ﺣﻠﮭﺎ ﯾﻣﻛن . ﻛﺎﻣﻠﺔ اﻟدارة ﺛﺑﺎت ﻣﺷﻛﻠﺔ اﻻﻋﺗﺑﺎر ﺑﻌﯾن ﺧذ ، ذﻟك ﻋﻠﻰ ﻧﻣوذﺟﻲ ﻛﻣﺛﺎل NP (Circuit SAT) اﻟﺷﻛل ﻓﻲ اﻟﻣوﺿﺣﺔ ، 1 ﻟداﺋ وﺻف اﻟﻣﺷﻛﻠﺔ ھذه ﻋﻠﻰ وﻣﺛﺎل . ﺗﺿم إﻟﻛﺗروﻧﯾﺔ رة ﺑواﺑﺎت AND و OR و NOT ﺗﺄﺧذ اﻟﺗﻲ n وﺗﻧﺗﺞ ﻛﻣدﺧﻼت ﺑت 1 ﺗﺗﻣﺛل .اﻹﺧراج ﻣن ﺑت اﻟﻧﺎﺗﺞ ﯾﻛون ﺑﺣﯾث ﻟﻠداﺋرة إدﺧﺎل ھﻧﺎك ﻛﺎن إذا ﻣﺎ ﺗﺣدﯾد ﻓﻲ اﻟﻣﮭﻣﺔ 1 اﺳﺗﺧدام ﯾﻣﻛن . ﺧوارزﻣﯾﺎت Circuit SAT ؛ اﻹﻟﻛﺗروﻧﯾﺔ ﺑﺎﻟدواﺋر اﻟﻣﺗﻌﻠﻘﺔ اﻟﻣﺷﻛﻼت ﻣن ﻛﺑﯾر ﻋدد ﻟﺣل اﻷ وﻣن اﻟﻧﻣﺎذج وﻓﺣص اﻟدواﺋر وﻣﻌﺎدﻟﺔ اﻟﺗﺻﻣﯾم أﺗﻣﺗﺔ ذﻟك ﻋﻠﻰ ﻣﺛﻠﺔ 20 . أﻓﺿل ﺗﻌﻣل ﺑﺎﺳم اﻟﻣﻌروﻓﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت Circuit SAT اﻟﺗرﺗﯾب ﻓﻲ وﻗت أﺳوأ ﻓﻲ 2 ن إدﺧﺎل ﻟﻣﺗﻐﯾرات n اﻟﺷﺎﻣل اﻟﺑﺣث ﻣن ﺑﻛﺛﯾر أﺳرع ﻟﯾس أي ، 21 . ﻣن ﺗطﺑﯾﻖ ﺧﻼل
- 33. 33 ﺧوارزﻣﯾﺔ Grover اﻟداﻟﺔ ﻋﻠﻰ f ( x ) اﻟﺗﻲ اﻟﻣدﺧﻼت ﻋﻠﻰ اﻟداﺋرة ﺗﻘﯾم {0 ∈ x ، 1 n } ، ﺗﺷﻐﯾل وﻗت ﻋﻠﻰ اﻟﻔور ﻋﻠﻰ ﻧﺣﺻل poly ( n )) n / 2 O (2 ﺣﯾث ، ) poly ( n) ﻣن ﯾﺄﺗﻲ ﻣﻌﯾن ﻣدﺧل ﻋﻠﻰ اﻟداﺋرة ﻟﺗﻘﯾﯾم اﻟﻣﺳﺗﻐرق اﻟوﻗت . اﻟﺳﻌﺔ ﺗﺿﺧﯾم ﺧوارزﻣﯾﺔ ﺗﻘوم Grover ﯾﻣﻛ .اﻟﻣﻧظم ﻏﯾر ﻟﻠﺑﺣث اﻟﺳﺎذﺟﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺔ ﺑﺗﺳرﯾﻊ ن ًادﺗﻌﻘﯾ اﻷﻛﺛر اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت ﺗﺳرﯾﻊ ًﺎﺿأﯾ اﻟﻛﻣوﻣﯾﺔ ﻟﻠﺧوارزﻣﯾﺎت . اﺣﺗﻣﺎﻟﯾﺔ ""ﺗﺧﻣﯾن ﺧوارزﻣﯾﺔ ﺗﻧﻔﯾذ ﻋﻠﻰ اﻟﻘدرة إﻟﻰ ﺑﺎﻟﻧظر Α داﻟﺔ ""ﻓﺣص و ، f ﻣﺛل ، Pr [ Α ﻣﺧرﺟﺎت w ﺑﺣﯾث f ( w ) = 1] = ε ﺧرج ، w ﺑﺣﯾث f ( w ) = 1 . اﻟﺗﺟرﯾﺑﻲ اﻟﺑﺣث ﻣﺷﻛﻠﺔ ﻟﺣل اﻟطرق إﺣدى ﺗﺷﻐﯾل ﺑﺑﺳﺎطﺔ ھﻲ ﻛﻼﺳﯾﻛﻲ ﺑﺷﻛل A ﻣﺗﻛرر ﺑﺷﻛل ﺑﺎﺳﺗﺧدام ﻣرة ﻛل ﻓﻲ اﻹﺧراج ﻣن واﻟﺗﺣﻘﻖ f ﺗﻘﯾﯾﻣﺎت ﻋﻧﮫ ﯾﻧﺗﺞ ﻗد ﻣﻣﺎ ، O (1 / ϵ ) ﻓﻲ ﻋن ﻧﺎﺗﺟﺔ ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ﺗﺟد أن ﯾﻣﻛن ، ذﻟك وﻣﻊ .اﻟﻣﺗوﺳط Brassard و Høyer و Mosca و 22 Tapp ھذه ﻣﺛل f ( w ) = 1 اﺳﺗﺧداﻣﺎت ﻣﻊ ε) O (1 / ﻓﻘ ﻟـ ط f واﺣﺗﻣﺎل ، ﻣن ًﺎﯾﺗﻌﺳﻔ ﻗرﯾب اﻟﻔﺷل 0 ﺑﺎﺳم اﻟﺧوارزﻣﯾﺔ ھذه ُﻌرفﺗ .اﺳرع ﺗرﺑﯾﻌﻲ ﺗﺣﻘﯾﻖ وﺑﺎﻟﺗﺎﻟﻲ ، اﻟﻛﻼﺳﯾﻛﻲ اﻻﺣﺗﻣﺎل ﺗﺿﺧﯾم ﻣﻊ اﻟﻘﯾﺎس طرﯾﻖ ﻋن ، اﻟﺳﻌﺔ ﺗﺿﺧﯾم . ﺑﺑﺳﺎطﺔ وذﻟك ، اﻹطﺎر ھذا ﻓﻲ أﻋﻼه ﻣﻧﺎﻗﺷﺗﮭﺎ ﺗﻣت اﻟﺗﻲ اﻟﻣﮭﯾﻛﻠﺔ ﻏﯾر اﻟﺑﺣث ﻣﺷﻛﻠﺔ ﺗﺗواﻓﻖ أﺧذ ﺧﻼل ﻣن A ﻟﺗﻛ ﺳﻠﺳﻠﺔ ُﻧﺗﺞﺗ واﻟﺗﻲ ، اﻟﺧوارزﻣﯾﺔ ون n -bit ﻋﻼوة .ﻣوﺣد ﺑﺷﻛل ﻋﺷواﺋﯾﺔ ﻣدﺧﻼت ھﻧﺎك ﻛﺎن إذا ، ذﻟك ﻋﻠﻰ {0 ∈ k w ، 1 n } ﺑﺣﯾث f ( w ) = 1 ﺛم ، Pr [Aoutputswsuchthatf (w) = 1] = kN إﯾﺟﺎد ﯾﻣﻛﻧﻧﺎ ﻟذﻟك ، w ھذه ﻣﺛل f ( w ) = 1 ﺑﺎﺳﺗﻌﻼﻣﺎت O (N / k) إﻟﻰ f . ﯾﻣﻛﻧ ، ذﻟك وﻣﻊ أو ًادﺗﻌﻘﯾ أﻛﺛر اﻟﺧوارزﻣﯾﺔ أن ﻧﺗﺧﯾل أن ﻧﺎ ﻣن واﺣدة ، اﻟﻣﺛﺎل ﺳﺑﯾل ﻋﻠﻰ .ﺣﻠﮭﺎ ﻧود ﻣﻌﯾﻧﺔ ﻣﺷﻛﻠﺔ وﺗﺳﺗﮭدف اﻷﻣور ﻣﺟرﯾﺎت اﻟﻘﯾد اﻟرﺿﺎ ﺑﻣﺷﻛﻠﺔ اﻟﻣﻌروﻓﺔ ﻛﻔﺎءة اﻷﻛﺛر اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت NP- اﻷﺳﺎﺳﯾﺔ ﻛﺎﻣﻠﺔ 3 - SAT اﻟوﻗت ﻓﻲ وﯾﻌﻣل اﻟﻌﺷواﺋﯾﺔ O ((4/3) ن ( ن ) ﺑوﻟﻲ 23 ). اﻟﺳﻌﺔ ﺗﺿﺧﯾم ﺗطﺑﯾﻖ ﯾﻣﻛن اﻟﺗﺷﻐﯾل وﻗت ﻣﻊ ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ﻋﻠﻰ ﻟﻠﺣﺻول اﻟﺧوارزﻣﯾﺔ ھذه ﻋﻠﻰ n / O ((4/3) ) poly ( n ) 2 اﻟﺧوارزﻣﯾﺎت ﺗﺳرﯾﻊ ﯾﻣﻛﻧﮭﺎ اﻟﻛﻣوﻣﯾﺔ اﻟﻛﻣﺑﯾوﺗر أﺟﮭزة أن ﯾوﺿﺢ ﻣﻣﺎ ، إﻛﻣﺎل ﻟﻣﺷﻛﻼت اﻟﺗﺎﻓﮭﺔ ﻏﯾر اﻟﻛﻼﺳﯾﻛﯾﺔ NP. ﻟﻠﺧوارزﻣ ﻟﻼھﺗﻣﺎم ﻣﺛﯾر ﻣﺳﺗﻘﺑﻠﻲ اﺗﺟﺎه ﯾﺗﻣﺛل دﻗﯾﻘﺔ ﺗﻘرﯾﺑﯾﺔ ﺣﻠول إﯾﺟﺎد ﻓﻲ اﻟﻛﻣوﻣﯾﺔ ﯾﺎت ﻟـ اﻷﺧﯾر اﻟﻌﻣل أﻋطﻰ .اﻟﺗﺣﺳﯾن ﻟﻣﺷﺎﻛل Farhi و Goldstone و 24 Gutmann أول ﻟﺷﻛل اﻟﺧطﯾﺔ اﻟﻣﻌﺎدﻻت ﻣن ﺑﺎﻟﻌدﯾد واﺣد وﻗت ﻓﻲ )ﺗﻔﻲ اﻧدﻣﺎﺟﯾﺔ ﻟﻣﮭﻣﺔ ﻛﻣوﻣﯾﺔ ﺧوارزﻣﯾﺔ ﺣ ﻣن ﻣﻌروﻓﺔ ﻓﻌﺎﻟﺔ ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ أﻓﺿل ﻋﻠﻰ ﺗﻔوﻗت واﻟﺗﻲ (ﻣﻌﯾن ھذه ﻓﻲ ؛ اﻟدﻗﺔ ﯾث ﻟﻧﻔس ﻓﺎﻋﻠﯾﺔ أﻛﺛر ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ ھذا أﻟﮭم .ﺑﺎﻻرﺗﯾﺎح اﻟﻣﻌﺎدﻻت ﻣن ﺟزء ﯾﻘﺎس ، اﻟﺣﺎﻟﺔ
- 34. 34 اﻟﺗﺣﺳﯾن ﻟﻣﺷﺎﻛل اﻟﻛﻣوﻣﯾﺔ اﻟﺧوارزﻣﯾﺎت ﻛﺎﻧت إذا ﻣﺎ ﺣول ﻣﻔﺗوﺣًﺎ اﻟﺳؤال ﯾﺗرك ﻣﻣﺎ ، اﻟﻣﺷﻛﻠﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ ﻧظراﺋﮭم دﻗﺔ ﻋﻠﻰ ﻛﺑﯾر ﺑﺷﻛل ﺗﺗﻔوق أن ﯾﻣﻛن . ﺧوارزﻣ ﺗطﺑﯾﻘﺎت اﻟﺳﻌﺔ وﺗﺿﺧﯾم ﻏروﻓر ﯾﺔ ﺧﻮارزﻣﯿﺔ ﺗﻌﺪ Grover ﻣﻦ ﻛﺠﺰء اﺳﺘﺨﺪاﻣﮫ ﯾﻤﻜﻦ واﻟﺬي ، ًﺎﯾﻗﻮ ًﺎﯿﻓﺮﻋ ًﺎﻨروﺗﯿ اﻟﺴﻌﺔ وﺗﻀﺨﯿﻢ اﻟﻤﺸﻜﻼت ﻣﻦ ﻟﻠﻌﺪﯾﺪ اﻟﻜﻢ ﺗﺴﺮﯾﻊ ﻋﻠﻰ ﺑﺎﻟﺤﺼﻮل ﯾﺴﻤﺢ ﻣﻤﺎ ، ًاﺪﺗﻌﻘﯿ اﻷﻛﺜﺮ اﻟﻜﻢ ﺧﻮارزﻣﯿﺎت ھﺬه ﻣﻦ ﻗﻠﯿﻞ ﻋﺪد ﻓﻘﻂ ﺳﺮد ﻧﺤﻦ .اﻷﺧﺮى speedups ھﻨﺎ . 1 . اﻟﺣد ﻋﻠﻰ اﻟﻌﺛور ﺻﺣﯾﺣﺔ أﻋداد ﻣن ﻓرزھﺎ ﯾﺗم ﻟم ﻟﻘﺎﺋﻣﺔ اﻷدﻧﻰ N ( اﻟﻌﺛور ، ﻣﻛﺎﻓﺋﺔ اﻟﺑداﯾﺔ ﻓﻲ ﻣﻌروﻓﺔ وﻏﯾر ﺗﻌﺳﻔﯾﺔ داﻟﺔ ﻣن اﻷدﻧﻰ اﻟﺣد ﻋﻠﻰ f : {0 ، ). ℤ → n } 1 ﺗﻌﻣل ﻋن اﻟﻧﺎﺗﺟﺔ اﻟﻛﻣﯾﺔ اﻟﺧوارزﻣﯾﺔ Dürr و 26 Høyer ﻋﻠﻰ ﺗﻘﯾﯾﻣﺎت ﺧﻼل ﻣن اﻟﻣﺷﻛﻠﺔ ھذه ﺣل O (N) ﻟـ f ًﺎﯾﺗرﺑﯾﻌ ًﺎﺗﺳرﯾﻌ ﯾﻌطﻲ ﻣﻣﺎ ، اﻟﺧوارزﻣﯾﺔ ﺗﻌﺗﻣد .اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت ﻓوق ﺧوارزﻣﯾﺔ ﺗطﺑﯾﻖ ﻋﻠﻰ ﺑﮭم اﻟﺧﺎﺻﺔ Grover داﻟﺔ ﻋﻠﻰ g : {0 ، 1 → {0 n } ، 1 } ﻓﺔ ّاﻟﻣﻌر ﻗﺑل ﻣن g ( x ) = 1 ﻛﺎن إذا وﻓﻘط إذا ، ( x ) < T اﻟﻌﺗﺑﺔ ﻟﺑﻌض T. ﻋﺷواﺋﯾﺔ اﻟﻌﺗﺑﺔ ھذه ﻛﻣدﺧﻼت ﺗﺣدﯾﺛﮭﺎ ﯾﺗم ﺛم ، ًﺎﯾﻣﺑدﺋ x ﺗﻛون ﺑﺣﯾث ﻣوﺟودة f ( x ) اﻟﻌﺗﺑﺔ ﻣن أدﻧﻰ . 2 . 3 . رؤوس ﻋﻠﻰ اﻟﺑﯾﺎﻧﻲ اﻟرﺳم ﻛﺎن إذا ﻣﺎ ﻟﺗﺣدﯾد .اﻟﺑﯾﺎﻧﻲ اﻟرﺳم اﺗﺻﺎل ﺗﺣدﯾد N ًﻣﺗﺻﻼ اﻟﺗرﺗﯾب وﻗت ﯾﺗطﻠب 2 N ﺑﺷﻛل ﻣن ﻛل ﯾﻘدم .اﻟﺣﺎﻻت أﺳوأ ﻓﻲ ﻛﻼﺳﯾﻛﻲ Dürr و Heiligman و Høyer و 27 Mhalla اﻟﻣﺷﻛﻠﺔ ھذه ﺣل ﻋﻠﻰ ﺗﻌﻣل ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ اﻟوﻗت ﻓﻲ ) 3/2 O ( N إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ ، اﻟﻠوﻏﺎرﯾﺗﻣﯾﺔ اﻟﻌواﻣل إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ ، اﻟﺣد ، ﻗوي )اﺗﺻﺎل اﻟﺑﯾﺎﻧﻲ اﻟرﺳم ﻓﻲ اﻟﻧظرﯾﺔ اﻟﻣﺷﻛﻼت ﻟﺑﻌض ﻓﻌﺎﻟﺔ ﺧوارزﻣﯾﺎت اﻟطرق أﻗﺻر ، اﻻﻣﺗداد ﻟﺷﺟرة اﻷدﻧﻰ ). 4 . ﺗﺗﻣﺛل .اﻟﺣﯾوﯾﺔ واﻟﻣﻌﻠوﻣﺎﺗﯾﺔ اﻟﻧﺻوص ﻣﻌﺎﻟﺟﺔ ﻓﻲ أﺳﺎﺳﯾﺔ ﻣﺷﻛﻠﺔ ، اﻷﻧﻣﺎط ﻣطﺎﺑﻘﺔ ﻓﻲ ھﻧﺎ اﻟﻣﮭﻣﺔ ﻣﻌﯾن ﻧﻣط ﻋﻠﻰ اﻟﻌﺛور P اﻟطول ﻣن M ﻧص داﺧل T ﺑطول N ﺣﯾث ، وﻓﯾﻧﺎي راﻣﯾش أﻋطﻰ ﻟﻘد .اﻷﺑﺟدﯾﺔ اﻟﺣروف ﺑﻌض ﻋﻠﻰ ﺳﻼﺳل واﻟﻧص اﻟﻧﻣط ﯾﻛون ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ 28 اﻟوﻗت ﻓﻲ اﻟﻣﺷﻛﻠﺔ ھذه ﺗﺣل واﻟﺗﻲ O (N + M) اﻟﻌواﻣل ﺣﺗﻰ ، ﻣﻣﻛن ﻛﻼﺳﯾﻛﻲ ﺗﻌﻘﯾد أﻓﺿل ﻣﻊ ﺑﺎﻟﻣﻘﺎرﻧﺔ ، اﻟﻠوﻏﺎرﯾﺗﻣﯾﺔ O ( N + M ). ﻛﻼھﻣﺎ ﯾﻌد ﻣﺗوﺳط ﺣﺎﻟﺔ إﻋداد ﻓﻲ ﯾﻔﻛر أن ًﺎﺿأﯾ ﻟﻠﻣرء ﯾﻣﻛن ﻟﻛن ، اﻷﺳوأ اﻟزﻣﻧﯾﺔ اﻟﺣدود ﻣن :وﺿوﺣًﺎ أﻛﺛر اﻟﻛم ﺗﺳرﯾﻊ ﯾﻛون ھﻧﺎ .ﻋﺷواﺋﻲ ﺑﺷﻛل واﻟﻧﻣط اﻟﻧص اﺧﺗﯾﺎر ﯾﺗم ﺣﯾث اﻟﻣﺟﻣوﻋﺔ ﻣﺷﻛﻠﺔ ﻣن واﻷﻓﻛﺎر اﻟﺳﻌﺔ ﺗﺿﺧﯾم ﺑﯾن ﺗﺟﻣﻊ ﻛواﻧﺗﯾﺔ ﺧوارزﻣﯾﺔ ﺗوﺟد اﻟ اﻟﻔرﻋﯾﺔ اﻟوﻗت ﻓﻲ وﺗﻌﻣل اﻟﺳطوح ﺛﻧﺎﺋﯾﺔ ﻣﺧﻔﯾﺔ O (N / M2O (logM)) ﺣﺗﻰ اﻟﺗﺷﻐﯾل وﻗت اﻟﻣﻣﻛﻧﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻌواﻣل ﺑﺄﻓﺿل ً ﻣﻘﺎرﻧﺔ ، اﻟﻠوﻏﺎرﯾﺗﻣﯾﺔ اﻟﻌواﻣل O 29 (N / M + N). ﺗﻛون ﻋﻧدﻣﺎ اﻟﺣدود ﻣﺗﻌدد ﺗﺳرﯾﻊ ھو ھذا M ﻛﺑﯾرة .
- 35. 35 اﻷدا اﻟﺗﺣﺳﯾن ﺋ ﻲ اﻟﻛﻣﻲ اﻟﺗواﻓﻘﻲ ﻟﻠﺗﺣﺳﯾن ﺑدﯾل ﻧﮭﺞ ﺗوﻓﯾر ﯾﺗم ﺧوارزﻣﯾﺔ ﺧﻼل ﻣن adiabatic اﻟﻛم 30 . ﯾﻣﻛن ﺧوارزﻣﯾﺔ ﺗطﺑﯾﻖ adiabatic اﻟﻘﯾد ﺑرﺿﺎ ﺗﺗﻌﻠﻖ ﻣﺷﻛﻠﺔ أي ﻋﻠﻰ (CSP) ﻣﻧﺣﻧﺎ ﯾﺗم ﺣﯾث إﺧراج ﻣﻧﺎ ُطﻠبﯾو ، اﻹدﺧﺎل ﺑت وﺣدات ﺑﻌض ﻋﻠﻰ اﻟﻣطﺑﻘﺔ اﻟﻘﯾود ﻣن ﻣﺗﺗﺎﻟﯾﺔ ﺳﻠﺳﻠﺔ ھذه ﻣن اﻟﻌدﯾد .اﻟرﺿﺎ ﻗﯾود ﻋدد ﻣن ﯾزﯾد ﻣﻣﺎ ، اﻟﻣدﺧﻼت ﻟﺑﺗﺎت ﺗﺧﺻﯾص ھﻲ اﻟﻣﺷﺎﻛل NP وﺗﺳﺗﻧد ، ﺟﺳدﯾﺔ دواﻓﻊ ﻟﮭﺎ اﻟﺧوارزﻣﯾﺔ وراء اﻷﺳﺎﺳﯾﺔ اﻟﻔﻛرة .ﻛﺑﯾرة ﻋﻣﻠﯾﺔ ﻓﺎﺋدة وذات ﻛﺎﻣﻠﺔ ﺑﯾن اﻟﻣراﺳﻼت إﻟﻰ CSPs ﻋﻠﻰ ﻣوﺣد ﺗراﻛب ھﻲ اﻟﺗﻲ اﻟﻛم ﺣﺎﻟﺔ ﻣﻊ ﻧﺑدأ .اﻟﻣﺎدﯾﺔ واﻷﻧظﻣﺔ ل اﻟﻣﻣﻛﻧﺔ اﻟﺣﻠول ﺟﻣﯾﻊ CSP. ﯾ ھﺎﻣﯾﻠﺗون ﻟرﺟل (طﺎﻗﺔ )أدﻧﻰ اﻷرض ﺣﺎﻟﺔ ھﻲ ھذه ﻣﻛن ﺣﺎﻟﺗﮫ ﺗرﻣز اﻟذي ﺟدﯾد ھﺎﻣﯾﻠﺗون ﻹﻋطﺎء ًﺗدرﯾﺟﯾﺎ ھﺎﻣﯾﻠﺗون ھذا ﺗﻌدﯾل ﯾﺗم ﺛم .ﺑﺳﮭوﻟﺔ إﻋداده اﻟﻛﻣﻲ اﻷدﯾﺎﺑﯾﺔ اﻟﻧظرﯾﺎت ﻧظرﯾﺔ ﺗﺿﻣن .اﻟﻣﻘﻧﻌﺔ اﻟﻘﯾود ﻋدد ﻣن ﯾزﯾد اﻟذي اﻟﺣل إﻟﻰ اﻷﺳﺎﺳﯾﺔ ا طوال اﻟطﺑﯾﻌﯾﺔ ﺣﺎﻟﺗﮫ ﻓﻲ اﻟﻧظﺎم ﻓﺳﯾظل ، ٍﻛﺎف ﺑﺑطء اﻟﻌﻣﻠﯾﺔ ھذه ﺗﻧﻔﯾذ ﺗم إذا أﻧﮫ ﻋﻠﻰ ؛ ﻟوﻗت ﻟـ ًﺎﯾﻣﺛﺎﻟ ًﺣﻼ اﻟﻧﮭﺎﺋﯾﺔ اﻟﺣﺎﻟﺔ ﺗﻌطﻲ ، اﻟﺧﺻوص وﺟﮫ CSP. "ﺑﺑطء ھﻲ ھﻧﺎ اﻟرﺋﯾﺳﯾﺔ اﻟﻌﺑﺎرة ﻣﺛﯾﻼت ﺑﻌض إﻟﻰ ﺑﺎﻟﻧﺳﺑﺔ ؛ "ﻛﺎف CSP ﻋﻠﻰ n bits اﻟﺗطور ﻟﮭذا اﻟﻼزم اﻟوﻗت ﯾﻛون ﻗد ، ﻓﻲ أﺳﻲ n . اﻟﺧوارزﻣﯾﺔ ﺗﻔﺗﻘر ، اﻻﺳﺗﻘﺻﺎء ھذا ﺑﻘﯾﺔ ﻓﻲ اﻟﻣوﺻوﻓﺔ اﻟﺧوارزﻣﯾﺎت ﻋﻛس ﻋﻠﻰ إﻟﻰ اﻷدﯾﺎﺑﯾﺔ ﯾﻣﻛن أﻧﮫ ﻣن اﻟرﻏم ﻋﻠﻰ .اﻟﺗﺷﻐﯾل وﻗت ﻓﻲ اﻟﺣﺎﻻت أﺳوأ ﻓﻲ واﻟﺻﻌﺑﺔ اﻟﻌﺎﻣﺔ اﻟﻌﻠﯾﺎ اﻟﺣدود ﺻﻐﯾرة ﺣﺎﻻت ﻓﻲ أداﺋﮭﺎ ﻟﺗﻘﯾﯾم ﻋددﯾﺔ ﺗﺟﺎرب إﺟراء ) 31 ( ﺑﺳﺑب ًﺎﺳرﯾﻌ اﻷﻣر ھذا ﯾﺻﺑﺢ ، ﺧوارزﻣﯾﺔ ﺗﺳﺗﻐرﻗﮭﺎ اﻟﺗﻲ اﻟﻣﺷﻛﻠﺔ ﺣﺎﻻت ﺑﻧﺎء ﻟﻠﻣرء ﯾﻣﻛن .اﻟﻛﺑﯾرة اﻟﻣﺷﺎﻛل adiabatic ؛ ًﺎﯾأﺳ ًﺎﺗوﻗ اﻟﻘﯾﺎﺳﯾﺔ 32 ، 33 ھذه ﺑﻌض ﻣن اﻟﺗﮭرب اﻟﺧوارزﻣﯾﺔ ﺗﻐﯾﯾر ﯾﻣﻛن ، ذﻟك وﻣﻊ اﻟﺣﺟﺞ 34 . ، 35 ﺧوارزﻣﯾﺔ ﺗﻧﻔﯾذ ﯾﻣﻛن adiabatic ﯾﻔﺳﺢ ﻓﺈﻧﮫ ، ذﻟك وﻣﻊ .ﻋﺎﻟﻣﻲ ﻛم ﻛﻣﺑﯾوﺗر ﺟﮭﺎز ﻋﻠﻰ ﺑﯾن ﺑﺳﻼﺳﺔ ھﺎﻣﯾﻠﺗون ﯾﺗﻧوع أن ﯾﻣﻛن ﻣﺎدي ﻧظﺎم ﻋﻠﻰ اﻟﻣﺑﺎﺷر ﻟﻠﺗﻧﻔﯾذ ًﺎﺿأﯾ اﻟﻣﺟﺎل ھﺎﻣﯾﻠﺗون ﺷرﻛﺔ ھﻲ اﻟﻧﮭﺞ ﻟﮭذا اﻷﺳس وأﺑرز .اﻟﻣطﻠوﺑﯾن واﻟﻧﮭﺎﺋﻲ اﻷوﻟﻲ D-Wave Systems ، ، اﻟﺧوارزﻣﯾﺔ ھذه ﻟﺗﻧﻔﯾذ ﻣﺻﻣﻣﺔ ﻛﺑﯾرة آﻻت ﺑﻧت اﻟﺗﻲ 36 اﻵﻟﺔ ھذه ﻣﺛل أﺣدث ﻣﻊ - D (' Wave 2X') إﻟﻰ ﺗﺻل أﻧﮭﺎ أﻋﻠﻧت اﻟﺗﻲ 1،152 ﻣﺛﯾﻼت ﻟﺑﻌض ﺑﺎﻟﻧﺳﺑﺔ .ﺑت CSP ﻓﻘد ، أ اﻷﺟﮭزة ھذه أﺛﺑﺗت ﻗﯾﺎﺳﻲ ﻛﻣﺑﯾوﺗر ﺟﮭﺎز ﻋﻠﻰ ﺗﻌﻣل اﻟﺗﻲ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻣذﯾﺑﺎت ﻋﻠﻰ ﺗﺗﻔوق ﻧﮭﺎ ، 37 ، 38 ﻣﺛﯾل ﻋﻠﻰ ﻣﺎ ﺣد إﻟﻰ ﺧﻔﻲ اﻋﺗﻣﺎده أن ﯾﺑدو (ذﻟك ﺧﻼف )أو ﺗﺳرﯾﻊ أن ﻣن اﻟرﻏم ﻋﻠﻰ ﻣﻘﺎرﻧﺔ وﻗﯾﺎس ، ﻣﻘﺎرﻧﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ ﺣﻼﻻ ، اﻟﻣﺷﻛﻠﺔ 38 . ، 39 ﻟﺧوارزﻣﯾﺔ اﻟﻧظرﯾﺔ اﻟﺗﺣدﯾﺎت إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ adiabatic ﺑﻌض ًﺎﺿأﯾ ھﻧﺎك ، أﻋﻼه اﻟﻣذﻛورة ﻧظﺎم ﯾواﺟﮭﮭﺎ اﻟﺗﻲ اﻟﮭﺎﻣﺔ اﻟﻌﻣﻠﯾﺔ اﻟﺗﺣدﯾﺎت D-Wave. ھذه ﺗظل ﻻ ، اﻟﺧﺻوص وﺟﮫ ﻋﻠﻰ وﺑﺳﺑب .اﻟﻣطﻠﻖ اﻟﺻﻔر ﻣن أﻋﻠﻰ ﺣرارﯾﺔ ﺣﺎﻟﺔ ﻓﻲ وﻟﻛﻧﮭﺎ ، ﺑﺎﻟﻛﺎﻣل اﻷرض ﺣﺎﻟﺔ ﻓﻲ اﻵﻻت اﻟﺻﻠب ﻣﻊ اﻟﺗﺷﺎﺑﮫ أوﺟﮫ ﺑﻌض ﻟﮭﺎ ﺑﺎﻟﻔﻌل اﻟﻣﻧﺟزة اﻟﺧوارزﻣﯾﺔ ﻓﺈن ، ھذا ، اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻣﺣﺎﻛﺎة
- 36. 36 ﺗﺳرﯾﻊ ﻛﺎن إذا ﻣﺎ اﻟﺣﺎﻟﻲ اﻟوﻗت ﻓﻲ اﻟواﺿﺢ ﻣن ﻟﯾس ."اﻟﻛﻣﻲ "اﻟﺗﻠدﯾن ﺑﺎﺳم ﺗﻌرف ﺛم وﻣن ﻟﻠﺧوارزﻣﯾﺔ اﻟﻣﺗوﻗﻊ اﻟﻛم adiabatic اﻹﻋداد ھذا ﻓﻲ ﺳﯾﺳﺗﻣر . اﻟﻛم ﻣﺣﺎﻛﺎة ﻟﺗﻛﻧوﻟوﺟﯾﺎ اﻟرﺋﯾﺳﯾﺔ اﻟﺗطﺑﯾﻘﺎت أﺣد ﻛﺎن ، اﻟﻛﻼﺳﯾﻛﯾﺔ ﻟﻠﺣوﺳﺑﺔ اﻷوﻟﻰ اﻷﯾﺎم ﻓﻲ ھو اﻟﻛﻣﺑﯾوﺗر آﻧﺗﯾﻛﯾﺛﯾرا آﻟﯾﺔ ﻋن ﯾﻘل ﻻ ﻣﺎ إﻟﻰ ﺗﻌود اﻟﺗطﺑﯾﻘﺎت ھذه إن اﻟﻘول )ﯾﻣﻛن اﻟﻔﯾزﯾﺎﺋﯾﺔ اﻟﻧظم ﻣﺣﺎﻛﺎة اﻟﻛﻣﺑﯾوﺗر ﻷﺟﮭزة أھﻣﯾﺔ اﻷﻛﺛر اﻟﻣﺑﻛر اﻟﺗطﺑﯾﻖ ﻓﺈن ، وﺑﺎﻟﻣﺛل .(اﻟﻣﯾﻼد ﻗﺑل اﻟﺛﺎﻧﻲ اﻟﻘرن ﻣن اﻟﻛﻣوﻣﯾﺔ ﻟﻸﻧظﻣﺔ ﻣﺣﺎﻛﺎة ﯾﻛون أن اﻟﻣرﺟﺢ ﻣن اﻟﻛﻣوﻣﯾﺔ 40 . ، 41 ، 2 4 ﺗﺷﻣل اﻟﻣﺣﺎﻛﺎة ﺗطﺑﯾﻘﺎت ﻗد ، اﻟواﻗﻊ ﻓﻲ .اﻟطﺎﻗﺔ ﻋﺎﻟﯾﺔ واﻟﻔﯾزﯾﺎء اﻷوﻟﯾﺔ اﻟﻣواد ، اﻟﻔﺎﺋﻘﺔ اﻟﻣوﺻﻠﯾﺔ ، اﻟﻛم ﻛﯾﻣﯾﺎء اﻟﻛﻣوﻣﯾﺔ ﻓﯾﮫ دور اﻟﻛم ﻟﻣﯾﻛﺎﻧﯾﻛﺎ ﯾﻛون ﻧظﺎم أي ﻓﮭم ﻋﻠﻰ ﺳﺗﺳﺎﻋدﻧﺎ اﻟﻛم ﻣﺣﺎﻛﺎة أن اﻟﻣرء ﯾﺗوﻗﻊ . وﻟﻛ ، اﻟﻣﺷﻛﻼت ﻣن ﻋدد ﻟوﺻف ""اﻟﻣﺣﺎﻛﺎة ﻛﻠﻣﺔ اﺳﺗﺧدام ﯾﻣﻛن ﻣﺎ ًﺎﺑﻏﺎﻟ اﻟﻛﻣﯾﺔ اﻟﺣوﺳﺑﺔ ﻓﻲ ن ًﺗﺣدﯾدا أﻛﺛر ﺑﺷﻛل ذﻟك ذﻛر ﯾﻣﻛن .ﻟﻠﻧظﺎم اﻟدﯾﻧﺎﻣﯾﻛﯾﺔ اﻟﺧواص ﺣﺳﺎب ﻣﺷﻛﻠﺔ ﻟﺗﻌﻧﻲ ﺗﺳﺗﺧدم ھﺎﻣﯾﻠﺗون إﻋطﺎء ﻋﻧد :اﻟﺗﺎﻟﻲ اﻟﻧﺣو ﻋﻠﻰ H اﻷوﻟﯾﺔ ﻟﻠﺣﺎﻟﺔ ًﺎﻔووﺻ ﻣﺎدي ﻧظﺎم وﺻف | ψ〉 اﻟﺣﺎﻟﺔ ﺧﺻﺎﺋص ﺑﻌض ﺑﺈﺧراج ﻗم ، اﻟﻧظﺎم ﻟﮭذا | ψt〉 = e − iHt | ψ〉 اﻟ ﻟﻠﺗطور ﻣﻘﺎﺑﻠﺔ ، ﺷرودﻧﺟر ﻣﻌﺎدﻟﺔ ﺗطﯾﻊ اﻟﻛﻣوﻣﯾﺔ اﻷﻧظﻣﺔ ﺟﻣﯾﻊ أن ﺑﻣﺎ . ر ﻟوﻗت ھﺎﻣﻠﺗوﻧﯾﺎن ﻟذﻟك وﻓﻘﺎ اﻟﻧظﺎم ﺗﻣﺎﻣًﺎ اﻟﻌﺎﻣﺔ اﻟﻛم ﺣﺎﻻت ﻟوﺻف اﻷﺳﻲ اﻟﺗﻌﻘﯾد ﻓﺈن ، ذﻟك وﻣﻊ ؛ ﻟﻠﻐﺎﯾﺔ ﻣﮭﻣﺔ ﻣﮭﻣﺔ ھذه ﻓﺈن اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﻛﻔﺎءة ﺗﺣﻘﯾﻖ اﻟﻣﺳﺗﺣﯾل ﻣن ﯾﻛون أن ﯾﺟب ﺑﺄﻧﮫ ﯾوﺣﻲ ﻻ اﻟواﻗﻊ وﻓﻲ ، ﻓﺎﯾﻧﻣﺎن اﻷﺻل ﻓﻲ اﻟﻣﺷﻛﻠﺔ ھذه ﺣﻔزت .اﻟﻛم ﻟﻣﺣﺎﻛﺎة ﻓﻌﺎﻟﺔ ﻋﺎﻣﺔ ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ ﺗوﺟد ﺑﻛﻔﺎءة اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻣﺣﺎﻛﺎة ﯾﻣﻛﻧﮫ اﻟﻛﻣوﻣﻲ اﻟﻛﻣﺑﯾوﺗر ﻛﺎن إذا ﻋﻣﺎ اﻟﺗﺳﺎؤل ﻋﻠﻰ 43 . ﺑﮭذا ﺑﻛﻔﺎءة اﻟﻛم ﻣﯾﻛﺎﻧﯾﻛﺎ ﻣﺣﺎﻛﺎة ﺑﺎﻟﻔﻌل اﻟﻌﺎﻣﺔ ﻟﻸﻏراض اﻟﻛﻣوﻣﻲ ﻟﻠﻛﻣﺑﯾوﺗر ﯾﻣﻛن اﻟﻣﻌﻧﻰ ﺗﻔﺎﻋﻼﺗﮭﺎ ﻋﻠﻰ اﻟﻣﺣﻠﯾﺔ اﻟﻘﯾود ذات اﻷﻧظﻣﺔ ﻣﺛل ، اﻟواﻗﻌﯾﺔ اﻟﺣﺎﻻت ﻣن ﻟﻠﻌدﯾد 44 . ﻋﻧد إﻋطﺎء اﻟﻛم ﻟﺣﺎﻟﺔ وﺻف | ψ〉 ﻟـ ووﺻف H واﻟوﻗت t ﻟﻠﺣﺎﻟﺔ ًﺎﺑﺗﻘرﯾ اﻟﻛم ﻣﺣﺎﻛﺎة ﺧوارزﻣﯾﺔ ُﻧﺗﺞﺗ ، | ψt〉. .ﺑﮭﺎ اﻻھﺗﻣﺎم ﻛﻣﯾﺎت ﻟﺗﺣدﯾد اﻟﺣﺎﻟﺔ ھذه ﻓﻲ اﻟﻘﯾﺎﺳﺎت إﺟراء ذﻟك ﺑﻌد ﯾﻣﻛن ﺗﻌﻣل وزﻣن (اﻟﺑﺗﺎت )ﻋدد ﻣﺣﺎﻛﺎﺗﮫ ﯾﺗم اﻟذي اﻟﻧظﺎم ﺣﺟم ﻓﻲ اﻟزﻣﻧﯾﺔ اﻟﺣدود ﻣن ﻛﺛﯾر ﻓﻲ اﻟﺧوارزﻣﯾﺔ اﻟﻌﺎﻣﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت أﻓﺿل ﻋﻠﻰ ًﺎﯾأﺳ ًﺎﺗﺳرﯾﻌ ﯾﻌطﻲ ﻣﻣﺎ ، اﻟﻣرﻏوب اﻟﺗطور .ﻧﺷط ﺑﺣث ﻣوﺿوع اﻟﻛم ﻣﺣﺎﻛﺎة وﯾظل ﻟﻠﺗﺣﺳﯾن ﻣﺟﺎل ھﻧﺎك ﯾزال ﻻ ، ذﻟك وﻣﻊ .اﻟﻣﻌروﻓﺔ اﻷ ﺗﺷﻣل ﺳرﯾﻊ ﺗﺷﻐﯾل ﺑوﻗت اﻻﺣﺗﻔﺎظ ﻣﻊ اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺣﺎﻛﺎة دﻗﺔ زﯾﺎدة ﻋﻠﻰ اﻟﻌﻣل ﻣﺛﻠﺔ ؛ 45 ؛ اﻟﻛم ﻛﯾﻣﯾﺎء ﻣﺛل ﻣﻌﯾﻧﺔ ﻟﺗطﺑﯾﻘﺎت اﻟﺧوارزﻣﯾﺔ ﺗﺣﺳﯾن 46 إﻟﻰ اﻟﺗطﺑﯾﻘﺎت واﺳﺗﻛﺷﺎف اﻟﻛم ﻣﺟﺎل ﻧظرﯾﺔ ﻣﺛل ﺟدﯾدة ﻣﺟﺎﻻت 47 . ا اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺣﺎﻛﺎة ، أﻋﻼه اﻟﻣذﻛور اﻟﻧﮭﺞ ﻋﻠﻰ ﯾطﻠﻖ ، اﻷﺣﯾﺎن ﺑﻌض ﻓﻲ أن ﻧﻔﺗرض :ﻟرﻗﻣﯾﺔ .ﻋﻠﯾﮫ اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺣﺎﻛﺎة ﺧوارزﻣﯾﺔ وﻧدﯾر اﻷﻏراض ﻣﺗﻌدد اﻟﻧطﺎق واﺳﻊ ﻛﻣوم ﻛﻣﺑﯾوﺗر ﻟدﯾﻧﺎ
- 37. 37 ﻧظﺎم ﺑﺎﺳﺗﺧدام ا ًﻣﺑﺎﺷر ًﺎﯾﻣﺎد ﻧظﺎﻣًﺎ ﻧﺣﺎﻛﻲ اﻟﺗﻣﺎﺛﻠﯾﺔ اﻟﻛم ﻣﺣﺎﻛﺎة ﻓﻲ ، ذﻟك ﻣن اﻟﻧﻘﯾض ﻋﻠﻰ ھﺎﻣﯾﻠﺗون ﺑﻌض ﻣﻊ ﻧظﺎم ﻣﺣﺎﻛﺎة ﻓﻲ ﻧرﻏب ﻛﻧﺎ إذا ، ھو وھذا .آﺧر H ﻧﻘ ﺛم ، ﻧظﺎم ﺑﺑﻧﺎء وم ﺗﻘرﯾب ھﺎﻣﯾﻠﺗون ﻗﺑل ﻣن وﺻﻔﮫ ﯾﻣﻛن آﺧر H. ﻛﺎن إذا ﺑذﻟك اﻟﻘﯾﺎم طرﯾﻖ ﻋن ًﺎﺋﺷﯾ اﻛﺗﺳﺑﻧﺎ ﻟﻘد اﻷﻧظﻣﺔ ﻟﺑﻌض ﺑﺎﻟﻧﺳﺑﺔ .ﻣﻧﮭﺎ اﺳﺗﺧراﺟﮭﺎ أو ﺗﺷﻐﯾﻠﮭﺎ أو اﻟﻣﻌﻠوﻣﺎت إﻧﺷﺎء ﻓﻲ أﺳﮭل اﻟﺛﺎﻧﻲ اﻟﻧظﺎم اﻟرﻗﻣ اﻟﻛم ﻣﺣﺎﻛﺎة ﻣن ﺑﻛﺛﯾر أﺳﮭل اﻟﺗﻣﺎﺛﻠﻲ اﻟﻛم ﻣﺣﺎﻛﺎة ﺗﻧﻔﯾذ ﯾﻛون ﻗد ، ﻛوﻧﮭﺎ ﺣﺳﺎب ﻋﻠﻰ ، ﯾﺔ ﻧظﯾراﺗﮭﺎ ﻋﻠﻰ ﺗﺗﻔوق اﻟﺗﻲ اﻟﺗﻣﺎﺛﻠﯾﺔ اﻟﻣﺣﺎﻛﺎة ﺗطﺑﯾﻖ ﯾﺗم أن اﻟﻣﺗوﻗﻊ ﻣن ﻟذﻟك .ﻣروﻧﺔ أﻗل ًأوﻻ اﻟﻛﻼﺳﯾﻛﯾﺔ 40 . ﺣﺳﺎﺑﯾﺔ أداة ﻣﺎرﻛوف ﺳﻠﺳﻠﺔ أو اﻟﻌﺷواﺋﻲ اﻟﻣﺷﻲ ﻣﻔﮭوم ﯾﻌد ، اﻟﻛﻼﺳﯾﻛﻲ اﻟﺣﺎﺳوب ﻋﻠم ﻓﻲ وأﺧذ اﻟﺑﺣث ﻣﺷﻛﻼت ﻋﻠﻰ ﺗطﺑﯾﻘﮫ ﯾﺗم ﻣﺎ ًﺎﺑوﻏﺎﻟ ، ﻗوﯾﺔ اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺳﯾرات ﺗوﻓر .اﻟﻌﯾﻧﺎت اﻟﻣﺷﻲ ﺧوارزﻣﯾﺔ ﺗﻌﺗﻣد ﻣﺛﻠﻣﺎ .ﺳرﯾﻌﺔ ﻛﻣوﻣﯾﺔ ﺧوارزﻣﯾﺎت ﻟﺗﺻﻣﯾم ً ﻣﻣﺎﺛﻼ ًﺎﯾوﻗو ﻋﺎﻣًﺎ ا ًإطﺎر اﻟﺳﯾر ﻓﺈن ، أﺳﺎﺳﯾﺔ ﺑﯾﺎﻧﯾﺔ ﺑﻧﯾﺔ داﺧل ًﺎﯾﻋﺷواﺋ ﯾﺗﺣرك ﻟﺟﺳﯾم اﻟﻣﺣﺎﻛﺎة اﻟﺣرﻛﺔ ﻋﻠﻰ اﻟﻌﺷواﺋﻲ ﯾﺗﺣرك ﻟﺟﺳﯾم اﻟﻣﺗراﺑط اﻟﻛﻣوﻣﻲ اﻟﺗطور ﻋﻠﻰ ﯾﻌﺗﻣد اﻟﻛﻣﻲ ﺑﯾﺎﻧﻲ رﺳم ﻓﻲ . اﻟﺳﯾر ﻋﻠﻰ اﻟﻛم ﻓﯾﮭﻣﺎ ﯾﺗﻔوق طرﯾﻘﺗﯾن إﺣدى ﻣن ﻋﺎم ﺑﺷﻛل اﻟﻛﻣوﻣﻲ اﻟﻣﺷﻲ ﺧوارزﻣﯾﺎت ﺗﺳﺗﻔﯾد ، (اﻟﻣﺻدر رأس ﻣن ﻣﺳﺗﮭدﻓﺔ ﻗﻣﺔ ﻹﯾﺟﺎد اﻟﻣﺳﺗﻐرق )اﻟوﻗت اﻷﺳرع اﻟﺿرب :اﻟﻌﺷواﺋﻲ ﻣﺻدر ﻗﻣﺔ ﻣن ﺑدءا ﺑﻌد اﻟرؤوس ﻛل ﻋﻠﻰ اﻻﻧﺗﺷﺎر ﻓﻲ اﻟﻣﺳﺗﻐرق )اﻟوﻗت اﻷﺳرع واﻟﺧﻠط .(واﺣد أﻗل اﻟﻛم ﻓﻲ اﻟﻣﺷﻲ زﻣن ﺿرب ﯾﻛون أن ﯾﻣﻛن ، اﻟﺑﯾﺎﻧﯾﺔ اﻟرﺳوم ﺑﻌض إﻟﻰ ﺑﺎﻟﻧﺳﺑﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ ﻧظﯾراﺗﮭﺎ ﻣن ﻛﺑﯾر ﺑﺷﻛل 48 . ، 49 اﻟﻛﻣﻲ اﻟﺧﻠط وﻗت ﺑﯾن اﻟﻔﺻل ﯾﻛون أن ﯾﻣﻛن ھذا ﻣن أﻛﺛر ﻟﯾس وﻟﻛن ، اﻟﺛﺎﻧﯾﺔ اﻟدرﺟﺔ ﻣن واﻟﻛﻼﺳﯾﻛﻲ ( 50 أﺛﺑت ﻓﻘد ، ذﻟك وﻣﻊ .(ًﺎﺑﺗﻘرﯾ أﻧﮫ اﻟﺳرﯾﻊ اﻻﺧﺗﻼط اﻟﺧوارزﻣﯾﺎت ﻋﺑر ﻋﺎﻣﺔ ﺳرﻋﺎت ﻋﻠﻰ ﻟﻠﺣﺻول ﻟﻠﻐﺎﯾﺔ ﻣﻔﯾدة أداة اﻟﻛﻼﺳﯾﻛﯾﺔ . اﻟﺷﻛل ﯾوﺿﺢ 2 ﻣﺳﺎرات ﺗﻌرض اﻟﺗﻲ اﻟﺑﯾﺎﻧﯾﺔ اﻟرﺳوم ﻣن ﻣﺟﻣوﻋﺎت ﻟﺛﻼث ﺧﺎﺻﺔ ﺣﺎﻻت "اﻷﺷﺟﺎر اﻟﺑﯾﺎﻧﻲ اﻟرﺳم ، اﻟزاﺋد اﻟﻣﻛﻌب :اﻟﻌﺷواﺋﻲ اﻟﺳﯾر ﻣن أﺳرع ًﺎﺑﺿر اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺷﻲ "اﻷ اﻟﺑﯾﺎﻧﻲ واﻟرﺳم ، "اﻟﻣﻠﺻﻘﺔ ھذا .اﻟﻣﻧﺗﺻف ﻓﻲ ﻋﺷواﺋﯾﺔ دورة إﺿﺎﻓﺔ ﻣﻊ "اﻟﻣﻠﺻﻘﺔ ﺷﺟﺎر أي ﻋﻠﻰ ﺗﺗﻔوق اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺳﯾرات أن إظﮭﺎر ﯾﻣﻛن ﻷﻧﮫ ﺧﺎﺻﺔ أھﻣﯾﺔ ﻟﮫ اﻟﺛﺎﻟث اﻟﻣﺛﺎل .اﻟﻌﺷواﺋﻲ اﻟﺳﯾر إﻟﻰ ﺗﺳﺗﻧد ﻻ ﻛﺎﻧت وإن ﺣﺗﻰ ، اﻟﺑﯾﺎﻧﻲ اﻟرﺳم ﻓﻲ ﻟﻠﺗﻧﻘل ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ ﻋﻧد ﯾﺑدأ اﻟذي اﻟوﻗت اﻟﻣﺳﺗﻣر اﻟﻛﻣﻲ اﻟﻣﺷﻲ ﻟﻠوﻗت وﯾﻣﺗد (اﻷﯾﺳر اﻟﺟﺎﻧب )ﻋﻠﻰ اﻟﻣدﺧل O (log N ) اﺣﺗﻣﺎل ﻣﻊ (اﻷﯾﻣن اﻟﺟﺎﻧب )ﻋﻠﻰ اﻟﻣﺧرج ﯾﺟد 1 / poly اﻷﻗل ﻋﻠﻰ (log N ) . اﻟﺗرﺗﯾب وﻗت ﺗﺗطﻠب ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺔ أي ﻓﺈن ، ذﻟك وﻣﻊ 1/6 N ﻋﻠﻰ ﻟﻠﻌﺛور اﻟﺧروج 51 . ﻓﻲ ﺑﺳرﻋﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺔ ﺗﺗطور أن ﯾﻣﻛن ، ًﺎﯾﺣدﺳ ﺑﻌد وﻟﻛن ، اﻟﺑداﯾﺔ اﻟﻛﻣﻲ اﻟﻣﺷﻲ وﺗﻧﺎﻏم ﺗﻣﺎﺳك إن .اﻟﺑﯾﺎﻧﻲ اﻟرﺳم ﻣﻧﺗﺻف ﻓﻲ اﻟﻌﺷواﺋﻲ اﻟﺟزء ﻓﻲ ﺗﺗﻌطل ذﻟك اﻟﯾﻣﯾن إﻟﻰ اﻟﯾﺳﺎر ﻣن ﺑﻛﻔﺎءة وﯾﺗﻘدم ، اﻟﻌﺷواﺋﯾﺔ ﻟﮭذه أﺳﺎﺳﻲ ﺑﺷﻛل أﻋﻣﻰ ﯾﺟﻌﻠﮫ .
- 38. 38 رؤوس ﻋﻠﻰ اﻟطﺑﯾﻌﯾﺔ ﻟﺗﻌﻣﯾﻣﺎﺗﮭﺎ ﺑﯾﺎﻧﯾﺔ رﺳوم ﺛﻼﺛﺔ N و اﻟﻛﻼﺳﯾﻛﻲ اﻟﻌﺷواﺋﻲ اﻟﺳﯾر ﺗﺗطﻠب ًﺎﺗﻗ اﻟﻣﺧرج إﻟﻰ ﻟﻠوﺻول اﻟﻛﻣﻲ اﻟﻣﺷﻲ ﻣن ﺑﻛﺛﯾر أﻛﺑر (B) اﻟﻣدﺧل ﻣن (A). ﻓﻲ ﺗوﺟد ، ذﻟك وﻣﻊ اﻟﻣﺷﻲ ﻋﻠﻰ ﯾﻌﺗﻣد ﻻ اﻟذي اﻟﻣﺧرج ﻋﻠﻰ ﻟﻠﻌﺛور ﻓﻌﺎﻟﺔ ﻛﻼﺳﯾﻛﯾﺔ ﺧوارزﻣﯾﺎت ﺑﯾﺎﻧﻲ رﺳم أول اﻟﻌﺷواﺋﻲ . ﻋﻠ ﻣﻧطﻘﯾﺔ ﺻﯾﻐﺔ .اﻟﻣﻧطﻘﯾﺔ ﻟﻠﺻﯾﻎ ﺳرﯾﻊ ﺗﻘﯾﯾم ھو اﻟﻛم ﻟﻠﻣﺷﻲ اﻟﻣﻔﺎﺟﺊ اﻟﺗطﺑﯾﻖ ﯾﻛون ﻗد ﻰ ﺛﻧﺎﺋﯾﺔ ﺛﻧﺎﺋﯾﺔ ﻣدﺧﻼت 1 × ، . ، N x ﺑواﺑﺎت اﻟداﺧﻠﯾﺔ رؤوﺳﮭﺎ ﺗﻣﺛل ﺷﺟرة ھﻲ ) ∧ ( AND أو OR (or) أو NOT ) applied ( أوراﻗﮭﺎ ُﺳﻣﻰوﺗ ، اﻟﻔرﻋﯾﺔ رؤوﺳﮭﺎ ﻋﻠﻰ ﻣطﺑﻘﺔ N ﺑﺎﻟﺑت 1 x ، . س ، ن . اﻟﺷﻛل ﻓﻲ اﻟﻘﺑﯾل ھذا ﻣن ﺻﯾﻐﺗﯾن ﺗوﺿﯾﺢ ﺗم 3 ﺑﺗﻘﯾﯾم ﺗﺳﻣﺢ ﻛﻣﯾﺔ ﺧوارزﻣﯾﺔ ﺗوﺟد . ﺻﯾﻐﺔ أي ﻋﻣﻠﯾﺎت ﻣن أﻛﺛر ﻓﻲ اﻟﻘﺑﯾل ھذا ﻣن ) 1/2 O ( N ، ﺑﻘﻠﯾل 52 أﻧﮫ اﻟﻣﻌروف ﻣن ﺑﯾﻧﻣﺎ وﻗت اﻟﻌﺷواﺋﯾﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺔ ﺗﺗطﻠب أي ، اﻟﻣﻧطﻘﯾﺔ اﻟﺻﯾﻎ ﻣن واﺳﻌﺔ ﻟﻔﺋﺔ ﺑﺎﻟﻧﺳﺑﺔ اﻟﺗرﺗﯾب 0.753 N . اﻟﺣﺎﻻت أﺳوأ ﻓﻲ 53 . اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺳﯾرة وﺗﺣﻠﯾل اﺳﺗﺧدام ﺣول اﻟﻛم ﺧوارزﻣﯾﺔ ﺗﺳﺗﻧد ﻋﻠﻰ ﺧﺎص ﺑﺷﻛل ﻟﻼھﺗﻣﺎم وﻣﺛﯾرة ﺧﺎﺻﺔ ﺣﺎﻟﺔ ھﻧﺎك .اﻟﺻﯾﻐﺔ ﻟﺑﻧﯾﺔ اﻟﻣواﻓﻖ اﻟﺷﺟري اﻟﺑﯾﺎﻧﻲ اﻟرﺳم اﻷﺷﺟﺎر ﺗﻘﯾﯾم وھﻲ ًﺎﯾﻛﻣ ًﺎﺗﺳرﯾﻌ ﺗﻌرض واﻟﺗﻲ اﻟﺻﯾﻐﺔ ﺗﻘﯾﯾم ﻟﻣﺷﻛﻠﺔ AND – OR واﻟﺗﻲ ، اﻟﻼﻋﺑﯾن أﻟﻌﺎب ﺑﻌض ﻓﻲ اﻟﻔﺎﺋز ﺗﺣدﯾد ﻣﻊ ﺗﺗواﻓﻖ . ﻟﻠ اﻟﻛﻣوﻣﯾﺔ اﻟﻣﺷﻲ ﻣﺳﺎرات اﺳﺗﺧدام ًﺎﺿأﯾ ﯾﻣﻛن ﻋﻠﻰ ﻟﻠﻐﺎﯾﺔ ﻋﺎم ﺗﺳرﯾﻊ ﻋﻠﻰ ﺣﺻول ﻋﺑﺎرة ھﻲ اﻟﻣﻧﻔﺻﻠﺔ ﻣﺎرﻛوف ﺳﻠﺳﻠﺔ .ﻣﺎرﻛوف ﺳﻼﺳل ﻋﻠﻰ اﻟﻘﺎﺋﻣﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت اﻻﻧﺗﻘﺎل ﻣﺻﻔوﻓﺔ ﺗﺣددھﺎ ﻋﺷواﺋﯾﺔ ﺧطﯾﺔ ﺧرﯾطﺔ ﻋن P ، ﺣﯾث xy P ﻣن اﻻﻧﺗﻘﺎل اﺣﺗﻣﺎل ھﻲ اﻟﺣﺎﻟﺔ x اﻟﺣﺎﻟﺔ إﻟﻰ y . اﻟﺑﺣث ﺧوارزﻣﯾﺎت ﻣن اﻟﻌدﯾد ﻋن اﻟﺗﻌﺑﯾر ﯾﻣﻛن ﻛﻣﺣﺎﻛﺎة اﻟﻛﻼﺳﯾﻛﯾﺔ ﻟﺳﻠﺳﻠﺔ Markov ﻋﻧﺻر إﻟﻰ ﯾﺗم اﻻﻧﺗﻘﺎل ﻛﺎن إذا ﻣﻣﺎ واﻟﺗﺣﻘﻖ ، اﻟﺧطوات ﻣن ﻣﻌﯾن ﻟﻌدد ھﻲ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺔ ھذه ﻛﻔﺎءة ﺗﺣدد اﻟﺗﻲ اﻟرﺋﯾﺳﯾﺔ اﻟﻣﻌﻠﻣﺔ .ﻋﻧﮫ ﻧﺑﺣث اﻟذي ""ﻣﻠﺣوظ اﻟطﯾﻔﯾﺔ اﻟﻔﺟوة δ ﻣﺎرﻛوف ﻟﺳﻠﺳﻠﺔ ( اﻷﻛﺑ واﻟﺛﺎﻧﻲ اﻷﺿﺧم اﻟﻘﯾم ﺑﯾن اﻟﻔرق ، أي اﻟﻘﯾم ﻣن ر اﻟذاﺗﯾﺔ P ). ﻋﻠﻰ اﻻﻋﺗﻣﺎد ﺗﺣﺳﯾن ﻋﻠﻰ ﺗﻌﻣل واﻟﺗﻲ ، اﻟﻛم ﻣﺳﺎرات إﻟﻰ ﺗﺳﺗﻧد ﻣﻣﺎﺛﻠﺔ ﺧوارزﻣﯾﺎت ھﻧﺎك ad ﻣن ، اﻟﺗرﺑﯾﻌﯾﺔ اﻟﻧﺎﺣﯾﺔ ﻣن 1 / 1 إﻟﻰ 1 54 δ. / ، 55 ، 56 ﻟﻠﺣﺻول اﻹطﺎر ھذا اﺳﺗﺧدام ﺗم
- 39. 39 ، اﻟﻣﺷﻛﻼت ﻣن ﻣﺗﻧوﻋﺔ ﻟﻣﺟﻣوﻋﺔ ﻛﻣوﻣﯾﺔ ﺳرﻋﺎت ﻋﻠﻰ 4 ﺗﺣدﯾد ﺑﯾن ﺗﺗراوح ﻛﺎﻧت إذا ﻣﺎ ﻣﻣﯾزة اﻟﺻﺣﯾﺣﺔ اﻷﻋداد ﻗﺎﺋﻣﺔ 54 اﻟﺑﯾﺎﻧﯾﺔ اﻟرﺳوم ﻓﻲ ﻣﺛﻠﺛﺎت ﻋن اﻟﺑﺣث إﻟﻰ 57 . اﻟﺻﻠﺔ ذات واﻟﻣﮭﺎم اﻟﺧطﯾﺔ اﻟﻣﻌﺎدﻻت ﺣل اﻟﻣﻌﺎدﻻت أﻧظﻣﺔ ﺣل اﻟﻌﻠوم ﻣﺟﺎﻻت ﻣن واﻟﻌدﯾد واﻟﮭﻧدﺳﺔ اﻟرﯾﺎﺿﯾﺎت ﻓﻲ اﻷﺳﺎﺳﯾﺔ اﻟﻣﮭﺎم ﻣن ﻣﺻﻔوﻓﺔ إﻋطﺎؤﻧﺎ ﯾﺗم .اﻟﺧطﯾﺔ N × N وﻧﺎﻗﻼت ، b∈ℝN إﺧراج ﻣﻧﺎ ُطﻠبﯾو ، x ﺑﺣﯾث A x = b . ﻓﻲ اﻷﺣﯾﺎن ﻣن ﻛﺛﯾر ﻓﻲ اﻟﻣﺷﻛﻠﺔ ھذه ﺣل ﯾﻣﻛن N اﻟﺟﺑر أﺳﺎﻟﯾب ﺧﻼل ﻣن ًﺻﻌﺑﺎ ھذا ﯾﺑدو ھذا؟ ﻣن أﻓﺿل ﻧﻔﻌل أن ﯾﻣﻛﻧﻧﺎ ھل .اﻟﺟﺎوس ﻋﻠﻰ اﻟﻘﺿﺎء ﻣﺛل ﻣﺑﺎﺷرة اﻟﺧطﻲ اﻹﺟﺎﺑﺔ ﺗدوﯾن ﺣﺗﻰ ﻷﻧﮫ ، x اﻟﺗرﺗﯾب ﻣن ًﺎﺗوﻗ ﺳﯾﺗطﻠب N. ﻣن اﻟﻛم ﺧوارزﻣﯾﺔ Harrow و Hassidim و (HHL) 58 Lloyd ﻣن اﻟﻣﺷﻛﻠﺔ ھذه ﺗﺗﺟﻧب اﻟﺧطﯾﺔ اﻟﻣﻌﺎدﻻت أﻧظﻣﺔ ﻟﺣل اﻟﻛﻣوﻣﯾﺔ اﻟﺣﺎﻟﺔ إﻧﺷﺎء ﻋﻠﻰ اﻟﻘدرة إﻟﻰ ﺑﺎﻟﻧظر :اﻟﻐرﯾب اﻟﻛﻣﻲ ﺑﺎﻟﻣﻌﻧﻰ اﻟﻣﻌﺎدﻻت ""ﺣل ﺧﻼل | b〉 = ∑i = 1Nbi | i〉 إﻟﻰ واﻟوﺻول ، A ﻣﻊ ًﺎﺑﺗﻘرﯾ ﻣﺗﻧﺎﺳﺑﺔ ﺣﺎﻟﺔ اﻟﺧوارزﻣﯾﺔ ُﻧﺗﺞﺗ ، | x〉 = ∑i = 1Nxi | i〉. اﻟﻛم ﺣﺎﻟﺔ ھو ھذا N- اﻟﺑﺗﺎت ﻓﻲ ﺗﺧزﯾﻧﮭﺎ ﯾﻣﻛن واﻟﺗﻲ ، اﻷﺑﻌﺎد O ( ﺳﺟل N ). اﻟﻣﺻﻔوﻓﺔ أن ﺑﺎﻓﺗراض ، ﺑﻛﻔﺎءة اﻟﺧوارزﻣﯾﺔ ﺗﻌﻣل A ﯾﻛون أن ﯾﺟب ، ًأوﻻ .اﻟﻘﯾود ﺑﻌض ﺗﻠﺑﻲ ا ًﻣﺗﻧﺎﺛر - اﻟﻌﻧﺎﺻر أﻛﺛر ﻋﻠﻰ ﺻف ﻛل ﯾﺣﺗوي أن ﯾﺟب d اﻟﻧﻘﺎط ﻟﺑﻌض ﺑﺎﻟﻧﺳﺑﺔ ، d . أن ﯾﺟب ﯾ إﻟﻰ اﻟوﺻول ﻣﻧﺣﻧﺎ ﺗم A اﻟﺻف رﻗم ﺗﻣرﯾر ﺧﻼﻟﮭﺎ ﻣن ﯾﻣﻛﻧﻧﺎ داﻟﺔ ﻋﺑر r واﻟﻔﮭرس i ﻣﻊ ، 1 ⩽ i ⩽ d اﻟﺻف ﻓﻲ اﻟﺻﻔري ﻏﯾر اﻟﻌﻧﺻر ُرﺟﻊﺗ واﻟﺗﻲ ، r . رﻗم ﯾﻛون أن ﯾﺟب ، ًﺎﺿأﯾ اﻟﺷرط κ = ∥A − 1∥∥A∥ ﻟـ اﻟﻌددي اﻻﺳﺗﻘرار ﻋدم ﺗﻘﯾس ﻣﻌﻠﻣﺔ ، A ﺑﺎﻓﺗراض .ا ًﺻﻐﯾر ، ﯾﻣﻛن ، اﻟﻘﯾود ھذه إﻧﺗﺎج | x〉 اﻟﺳﺟل ﻓﻲ اﻟزﻣﻧﯾﺔ اﻟﺣدود ﻛﺛﯾر ﻓﻲ ًﺎﺑﺗﻘرﯾ N و d و κ 58 . ، 59 ﻛﺎﻧت إذا d و κ ﻓﻲ .اﻟﻘﯾﺎﺳﯾﺔ اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺧوارزﻣﯾﺎت ﻓﻲ ﻛﺑﯾر ﺗﺣﺳن ﻓﮭذا ، ﺻﻐﯾرة أﺟﮭزة أن ﯾﻌﻧﻲ ﻛﻼﺳﯾﻛﻲ ﺑﺷﻛل ﻣﻣﺎﺛل ﺗﺷﻐﯾل وﻗت ﺗﺣﻘﯾﻖ أن ﯾوﺿﺢ أن ﻟﻠﻣرء ﯾﻣﻛن ، اﻟواﻗﻊ ﻣﺣﺎ ﯾﻣﻛﻧﮭﺎ اﻟﺗﻘﻠﯾدﯾﺔ اﻟﻛﻣﺑﯾوﺗر ﺑﻛﻔﺎءة اﻟﻣﻧﺎﺳب اﻟوﻗت ﻓﻲ اﻟﺣدود ﻣﺗﻌدد ﻛﻣّﻲ ﺣﺳﺎب أي ﻛﺎة 58 . ﻛﺎﻣل ﻛﺈﺧراج إﻋطﺎء ﻣن ًﺑدﻻ ، اﻟﺣﺎل ﺑطﺑﯾﻌﺔ x ﻛﻣﯾﺔ ﺣﺎﻟﺔ اﻟﺧوارزﻣﯾﺔ ُﻧﺗﺞﺗ ، N- dimensional | x〉 اﻟﺣل ﻹﺧراج ؛ x ﻣن اﻟﻌدﯾد إﺟراء ذﻟك ﺑﻌد ﺳﯾﺗﺿﻣن ، ﻧﻔﺳﮫ ﻣن ًﺎﺗوﻗ ﯾﺗطﻠب ﻣﻣﺎ ، ﺗﻣﺎﻣًﺎ اﻟﺣﺎﻟﺔ ﻟﺗوﺻﯾف اﻟﻘﯾﺎﺳﺎت اﻟﺗرﺗﯾب N ﻻ ﻗد ، ذﻟك وﻣﻊ .ﻋﻣوﻣًﺎ ھذه ﺗﺣدﯾد ﯾﻣﻛن .ﻟذﻟك اﻟﻌﺎﻟﻣﯾﺔ اﻟﺧﺻﺎﺋص ﺑﻌض ﺑﺎﻷﺣرى وﻟﻛن ، اﻟﺣل ﺑﻛﺎﻣل ﻣﮭﺗﻣﯾن ﻧﻛون ﻋﻠﻰ ﻗﯾﺎﺳﺎت إﺟراء طرﯾﻖ ﻋن اﻟﺧﺻﺎﺋص | x〉. ﺧوارزﻣﯾﺔ ﺗﺳﻣﺢ ، اﻟﻣﺛﺎل ﺳﺑﯾل ﻋﻠﻰ HHL اﻟﺣل ﻧﻔس ﻟﮭﺎ اﻟﺧطﯾﺔ اﻟﻣﻌﺎدﻻت ﻣن ﻣﺟﻣوﻋﺗﺎن ﻛﺎﻧت إذا ﻣﺎ ﺑﺗﺣدﯾد ﻟﻠﻔرد ، 59 اﻷﺧرى اﻟﺑﺳﯾطﺔ اﻟﻌﺎﻟﻣﯾﺔ اﻟﺧﺻﺎﺋص ﻣن اﻟﻌدﯾد إﻟﻰ ﺑﺎﻹﺿﺎﻓﺔ 60 .
- 40. 40 ﺧوارزﻣﯾﺔ ﺗﺟد أن اﻟﻣرﺟﺢ ﻣن HHL إﻧﺷﺎء ﯾﺗم ﺣﯾث اﻹﻋدادات ﻓﻲ ﺗطﺑﯾﻘﺎت اﻟﻣﺻﻔوﻓﺔ A واﻟﻧﺎﻗل b اﻹﻋدادات ھذه أﺣد .ﺻرﯾﺢ ﺑﺷﻛل ﻛﺗﺎﺑﺗﮭﺎ ﻣن ًﺑدﻻ ، ﺣﺳﺎﺑﯾﺔ ﺑطرﯾﻘﺔ اﻟﻣﺣددة اﻟﻌﻧﺎﺻر طرﯾﻘﺔ ھو (FEM) أ .اﻟﮭﻧدﺳﺔ ﻓﻲ ﻛﻼدر ﺑﮫ ﻗﺎم اﻟذي اﻷﺧﯾر اﻟﻌﻣل ظﮭر ﺧوارزﻣﯾﺔ أن وﺳﺑروس وﺟﺎﻛوﺑس HHL ﯾﻣﻛن ، ﻣﺳﺑﻖ ﺷرط ﻣﻊ دﻣﺟﮭﺎ ﯾﺗم ﻋﻧدﻣﺎ ، ﻋﺑر اﻟﻛﮭروﻣﻐﻧﺎطﯾﺳﻲ اﻻﻧﺗﺛﺎر ﻣﺷﻛﻠﺔ ﻟﺣل اﺳﺗﺧداﻣﮭﺎ 60 FEM. أو ، اﻟﺧوارزﻣﯾﺔ ﻧﻔس اﻟﻣﻌﺎ ﺗﺗﺟﺎوز اﻟﺗﻲ اﻟﻣﺷﻛﻼت ﻋﻠﻰ ًﺎﺿأﯾ ﺗطﺑﯾﻘﮭﺎ ﯾﻣﻛن ، اﻟوﺛﯾﻘﺔ اﻟﺻﻠﺔ ذات اﻷﻓﻛﺎر دﻻت ، اﻟﺗﻔﺎﺿﻠﯾﺔ اﻟﻣﻌﺎدﻻت ﻣن اﻟﻛﺑﯾرة اﻟﻧظم ﺣل ھذه وﺗﺷﻣل .ﻧﻔﺳﮭﺎ اﻟﺧطﯾﺔ 61 ، 62 اﻟﺑﯾﺎﻧﺎت اﻟﻣﻧﺎﺳب 63 اﻵﻟﻲ اﻟﺗﻌﻠم ﻓﻲ اﻟﻣﺧﺗﻠﻔﺔ واﻟﻣﮭﺎم 64 . اﻟﻛﻣوﻣﯾﺔ اﻟﺧوارزﻣﯾﺔ أن ﻋﻠﻰ اﻟﺗﺄﻛﯾد ﯾﺟب ﺧوارزﻣﯾﺔ ﺑﮫ ﺗﺣل اﻟذي اﻟﻣﻌﻧﻰ ﺑﻧﻔس اﻟﻣﺷﻛﻼت ھذه ""ﺗﺣل اﻟﺣﺎﻻت ھذه ﺟﻣﯾﻊ ﻓﻲ HHL: ﻓﮭﻲ ﻟـ ﻣﻌﻘول ﺗﻌرﯾف ھو ھذا ﻛﺎن إذا ﻣﺎ .ﻛﻣﺧرﺟﺎت ﻛواﻧﺗﯾﺔ ﺣﺎﻟﺔ وﺗﻧﺗﺞ ﻛواﻧﺗﯾﺔ ﺑﺣﺎﻟﺔ ﺗﺑدأ وﻣرة ، اﻟﺗطﺑﯾﻖ ﻋﻠﻰ ﯾﻌﺗﻣد ""اﻟﺣل ًﺎﯾﺣﺳﺎﺑ اﻹدﺧﺎل إدﺧﺎل ﯾﺗم ﻛﺎن إذا ﻣﺎ ﻋﻠﻰ ﯾﻌﺗﻣد ﻗد أﺧرى ﺗﻌﺳﻔﯾﺔ ﻛﺑﯾﺎﻧﺎت ً ﺻراﺣﺔ ﺗﻘدﯾﻣﮫ ﺗم أو 65 . ﻗﻠﯾﻠﺔ ﺗطﺑﯾﻘﺎت qubit اﻟﺗﺟرﯾﺑﯾﺔ واﻟﺗطﺑﯾﻘﺎت ﻋﻠﻰ ﻣﺎ طرﯾﻖ أﻣﺎﻣﻧﺎ ﯾزال ﻻ أﻧﮫ إﻻ ، ًﺎﺳرﯾﻌ ﻛﺎن اﻟﺗﺟرﯾﺑﻲ اﻟﻛم ﺣﺳﺎب ﻓﻲ اﻟﺗﻘدم أن ﻣن اﻟرﻏم ﺣﺎﻟﯾﺔ ﺗطﺑﯾﻘﺎت ﻣﻊ ، اﻟﻌﺎﻣﺔ ﻟﻸﻏراض اﻟﻧطﺎق واﺳﻊ ﻛﻣوﻣﻲ ﻛﻣﺑﯾوﺗر ﻋﻠﻰ ﻧﺣﺻل أن ﻗﺑل ﻣن أﻛﺛر ﻋﻠﻰ ﯾﻌﻣل ﻛﻣﻲ ﺣﺳﺎب أي ﻣﺣﺎﻛﺎة ﯾﻣﻛن .اﻟﺑﺗﺎت ﻣن ﻗﻠﯾل ﻋدد ﻣن ﺗﺗﻛون 20 - 30 ﺑت اﻟداﺋرة ﻧﻣوذج ﻓﻲ ﯾﺟب ، ﻟذﻟك .ﺣدﯾث ﻛﻼﺳﯾﻛﻲ ﻛﻣﺑﯾوﺗر ﺟﮭﺎز ﻋﻠﻰ ﺑﺳﮭوﻟﺔ اﻟﻘﯾﺎﺳﯾﺔ اﻟﻛﻣوﻣﯾﺔ إظﮭﺎر ﻣن ًﺑدﻻ اﻟﻣﺑدأ ﻋﻠﻰ ﻛدﻟﯾل اﻟﻛﻣوﻣﯾﺔ ﻟﻠﺧوارزﻣﯾﺎت اﻟﺣﺎﻟﯾﺔ اﻟﺗطﺑﯾﻘﺎت إﻟﻰ ﯾﻧظر أن اﻟﺟدول ﻓﻲ .ﻟﻠﻔن اﻟﻛﻼﺳﯾﻛﯾﺔ اﻟﺣﺎﻟﺔ ﻋﻠﻰ ﺣﻘﯾﻘﯾﺔ ﺳرﻋﺎت 3 ﺑﻌض ﻋﻠﻰ اﻟﺿوء ﻧﺳﻠط ، ﻟﻠﺧوارزﻣﯾﺎت اﻟﺗﺟرﯾﺑﯾﺔ اﻟﺗطﺑﯾﻘﺎت أﺣﺟﺎم أﻛﺑر ﻋﻠﻰ اﻟﺗرﻛﯾز ﻣﻊ ، ھﻧﺎ ﻣﻧﺎﻗﺷﺗﮭﺎ ﺗﻣت اﻟﺗﻲ ﻋﻧد اﻟﺣذر ﺗوﺧﻲ ﯾﺟب أﻧﮫ ﻣﻼﺣظﺔ ﻣن اﻟرﻏم )ﻋﻠﻰ اﻵن ﺣﺗﻰ ﺑﺣﺛﮭﺎ ﺗم اﻟﺗﻲ اﻟﻣﺷﻛﻼت اﻟﻛم ﻛﻣﺑﯾوﺗر ﺟﮭﺎز ﻋﻠﻰ ﺣل ﻓﻲ "ﺻﻌوﺑﺔ ﻋن ﻛﺑدﯾل "اﻟﻣﺷﻛﻠﺔ "ﺣﺟم اﺳﺗﺧدام ). 66 "
- 41. 41 اﻟﺜﺎﻟﺚ اﻟﻔﺼﻞ اﻟﻜﻤﻮﻣﻲ اﻟﺤﺎﺳﻮب ﻋﻤﻞ اﻟﯿﺔ When building a novel type of computer, like a quantum computer, one can use an architecture that is based on one of the (presented) classical architectures [26] to avoid having to design a fundamentally different kind of architecture. Furthermore, facilitating scalability in quantum computer hardware is one of the most challenging tasks of quantum computer architectures. In this section, the quantum von Neumann architecture is introduced which combines the classical von Neumann architecture with the requirements of the DiVincenzo-criteria in QC [43] resulting in quantum hardware which incorporates scalability. In a massively parallel quantum computer, the DiVincenzo criteria have to be fulfilled at every site that holds a qubit. In order to simplify the hardware of a quantum computer, one can fabricate hardware specialized on only one criteria and move the quantum information between these specialized hardware components to perform QC [20]. The schematic diagram of the quantum von Neumann architecture is depicted in Fig. 6. Like any quantum computer, it will require a classical control unit which controls the quantum computer. A quantum bus system allows moving quantum information between the different parts of the quantum computer. The manipulation of the quantum information is executed in the quantum arithmetic logic unit (QALU) which is the most hardware demanding11 part of the quantum computer as quantum gate operations are executed here. The quantum information is stored in the quantum memory which should rely on multiplexing technology for large storage capability. Furthermore, an input and output region acts as an interface to the classical world in which the qubit state is initialized and/or detected. In large-scale quantum computers, one has to achieve big quantum data storage capacities with low (classical) hardware demand in the quantum memory. If the hardware demand scaled linearly with the number of qubits that were stored, it would not obey Rent’s rule and the control hardware would get too complicated and too expensive for large-scale QC with thousands or millions of qubits. Reducing the hardware demand can be achieved with multiplexing circuits, as depicted in Fig. 7 b. Therefore, one needs to have the ability to store quantum information with a set of constant parameters. For example, to store an ion chain
- 42. 42 in a segmented Paul trap, one only needs a negative DC voltage at the position of the ion string and positive DC voltages surrounding it which form an axial confinement for the ion string. These few voltages can in principle be used to store arbitrarily many ion strings. During storage, this set of parameters (for trapped ions that would be a set of DC voltages) is applied to all qubits in the quantum memory. In order to access a specific memory cell, multiplexing technology allows a change of this set of parameters to another set which can be controlled independently. This independent set of parameters enables movement of the quantum information of an arbitrary memory cell out of the quantum memory. Quantum information transport One of the most critical features of this quantum von Neumann architecture is the quantum bus system for quantum information transport, which has to be performed with high fidelity to allow fault-tolerant QC. As quantum information cannot be copied [57], quantum information can only be transported by physically moving the qubits, quantum teleportation [58] or via coupling to photons [59, 60]. Atomic or molecular qubit systems enable quantum information transport via physical movement of the qubit from one location in space to another. For example in trapped ion systems with segmented Paul traps [61, 55], ions or ion strings can be moved by changing the confining axial DC potential. In solid state systems, such movement is not possible in general. However, there are solid state systems which allow qubit movement, like spins in silicon [44, 62, 63]. Quantum teleportation [58] requires an entangled qubit pair, of which one qubit is at the location from where the quantum information is taken and the second is the qubit at the destination. Furthermore, it requires a qubit measurement with a classical channel to the destination where a conditional quantum gate has to be performed. In order to store and read quantum information in the quantum memory, it implies read-out- and quantum- gate-capability at every site in the memory. This is in contradiction to a specialized hardware for each DiVincenzo criteria and, thus, more hardware demanding than physical movement. But it could be a strategy in many solid-state systems. Mapping qubits to photons was demonstrated in atomic or molecular qubit systems [64, 65] as well as in solid-state systems [60]. Like in quantum teleportation, this approach requires quantum logic at every site in the memory
- 43. 43 and is therefore hardware demanding. Quantum information transport with quantum teleportation or mapping to photons have one advantage over qubit movement: it is possible to change from one qubit system to another. For example, QIP could be performed with superconducting circuit QED systems [12, 13] and for long storage in the quantum memory, one could use nitrogen vacancy centers in diamond [66]. The disadvantage of these technologies compared to systems, which allow qubit movement, is the high hardware demand in the memory, as quantum gate operations and quantum state readout are required at every site in the quantum memory. If this cannot be overcome, quantum teleportation and mapping to photons will only be applicable to small- and medium-scale systems. Large-scale systems with low hardware demand per stored qubit may have to move the qubits in the quantum computer [20]. 4.3. Parallelism in quantum von Neumann architectures In order to work with an increasing number of qubits in a quantum von Neumann architecture, one has to increase the κ value to compensate decoherence in the quantum memory. Therefore, one can either increase the coherence time or decrease the time per quantum gate operation. If both options are not feasible, one has to parallelize QIP. Similar to classical multiprocessor systems, one can use multiple QALUs in one quantum computer
- 44. 44 A quantum von Neumann architecture for trapped ion quantum computation This section covers how one can build the different parts of a quantum von Neumann architecture in a trapped ion system. The next section will combine these individual parts to build a model trapped ion quantum computer based on quantum von Neumann architecture called Quantum 4004. The guideline for development of the architecture is as follows: (1) Trapped ions QC was chosen because ion traps are a technology with high κ values. (2) If it is possible, one should only use operations that have already been demonstrated with high fidelity. (3) This document covers only the hardware of the quantum computer. (4) Simplicity of the hardware, especially for scaling of the quantum computer, is favored over optimization for higher abstraction layer tasks, containing things like QEC or quantum algorithms, throughout this section. (5) As there is no functioning fault-tolerant quantum computer yet, one cannot expect a first- generation quantum computer to work with high computation speed. Thus, computation speed has low priority in the development of the architecture. If a fault-tolerant quantum computer can be built and if Moore’s law is applicable to quantum computer development, the computation speed (and quantum memory size) will increase exponentially over time. In the quantum charged coupled device (QCCD) principle [55], shown in Fig. 9, a segmented ion trap is used to move ions to different positions on the trap by changing the axially confining DC voltages. This allows using one part of the trap as a quantum memory and another part as a processing zone, or QALU. The QCCD [55] is a general concept for trapped ion QC and resembles a quantum von Neumann architecture, as there are separate regions for the different DiVincenzo criteria [43] and it enables qubit movement (along the RF rails of the segmented Paul trap). In the following, the QCCD is used as the underlying principle of a quantum von Neumann architecture for trapped ion QC For the QCCD, ideas for QEC and higher level architectures12 have been proposed [69]. However, trapped ions offer a variety of different gate operations and, thus, it makes sense to adapt at the abstraction layer scheme for trapped ion QC. Gates can be performed using local RF fields [70, 23, 71, 72], global RF fields [73] or optical fields [74, 54]. Even for optical entangling gates, there are multiple types of gates [75, 76, 77]. Similarly, multiple procedures for efficient ion movement have been demonstrated [78, 79, 80]. In the following, the lowest abstraction
- 45. 45 layer of the scheme described in Section 3 (and reference [35]) is split into two. The new lowest level is then called the hardware layer, and on top of the hardware layer, a firmware layer is inserted. This new layer contains the firmwire, such as the type of quantum gates and ion movements. Since the top layers have only weak hardware dependence, they do not need to be adapted. The quantum von Neumann architecture, presented in this section, covers only the hardware abstraction layer. As the exact performance of the hardware is not known and, thus, the optimum QEC scheme cannot be identified13, it does not make sense to discuss the higher abstraction layers for this architecture at this point. The different design challenges for such a quantum von Neumann architecture with trapped ions are • vacuum pressure, • decoherence in the quantum memory, • multiplexing to enable large quantum memories, • quantum gates, • read out and initialization, and • choice of qubits, which are discussed in the following subsections. Reduce collisions with background gas In order to maximize the coherence time in trapped ion systems, collisions with background gas should not limit the coherence times, as they can lead to ion loss or to loss of quantum information in the ion chain. Although these losses can be corrected with QEC, it is advisable to suppress such collisions as much as possible. In room temperature setups, collisions with residual background gas occur roughly once per hour per ion at typical UHV pressures of 10−11 mbar [81]. That means when working with, for example 3600, ions in room temperature setups, one will have approximately one collision per second. In a cryogenic ion trap experiment at a temperature of 4 K, a residual background pressure of 10−16 mbar has been observed [82]. Such pressures reduce the collision rate by 5 orders of magnitude compared to room temperature setups. Hence in cryogenic experiments, one can work with more ions than in room temperature setups while at the same time reducing the collisions with background gas. This suggests that large-scale QC with trapped ions will have to be performed in a cryogenic environment. Ideally, one wants to
- 46. 46 be able to neglect collisions with background gas as a source of qubit loss or decoherence. Therefore, one can look at the two elements with the lowest boiling point (or triple point), hydrogen and helium. As the exact vacuum pressure in an experiment strongly depends on the used materials, whether they were baked before, and so on, one can only perform a worst-case analysis by looking at the vapor pressure of hydrogen and helium. For the vapor pressure, one assumes at the whole vacuum chamber is covered with at least one monolayer of the element in question. Hydrogen has a sublimation equilibrium pressure of 10−6 mbar at a temperature of 4.2 K, and 10−12 mbar at a temperature of 2.6 K [83, 84]. Hence at a temperature around 2 K, hydrogen can no longer sublimate and will definitely be frozen out. If helium is also a source for collision with the ions, one will have to cool even further, as 4He has a sublimation equilibrium pressure of 10−6 mbar at a temperature of 0.46 K, and 10−12 mbar at a temperature of 0.24 K [83]. 3He shows a sublimation equilibrium pressure of 10−6 mbar already at a temperature of 0.22 K, and 10−12 mbar at a temperature of 0.1 K [83]. This does not imply that the whole experiment has to be performed at a temperature of 0.1 K to not be limited by collisions with 3He. But at least one surface in the cryostat will have to be that cold to exclude collisions with background gas from the sources of qubit loss or decoherence. 5.2. Decoherence in the quantum memory and magnetic shielding In trapped ion QC, the qubit can either be encoded in an optical qubit [85, 74] or a ground state qubit [86, 87, 88]. In the optical qubit, one state of the qubit is a meta-stable D-state of the ion whereas the other one is in the ground state. The qubit transition frequency is in the optical regime and thus it is called optical qubit. As the live-time of this qubit is limited by the life-time of the meta-stable state, which is typically on the order of 1 s [86], the coherence time will ultimately be limited by its spontaneous decay. Therefore, to achieve a long coherence time and a high κ value of the system, the qubit has to be encoded in the ground state of the ion, which does not suffer from such decoherence. For ground state qubits, the main source of decoherence is magnetic field fluctuations. Therefore, generating a constant magnetic field and magnetic shielding are the most critical challenges to achieve long coherence times in trapped ion systems. Decoherence sources like spin-spin interaction [89] must be suppressed, e.g. by the choice of an |F1, MF = 0i to |F2, MF = 0i transition qubit, or by the choice of a qubit at a ’clock transition’, for which the energy separation does to first order not depend on the magnetic field [86]. Other
- 47. 47 decoherence sources like leakage of resonant light must be reduced such that they can be neglected in the quantum memory, which is discussed in Section 5.5.5. Quantum gate operations in trapped ion systems take between 10 and 100 µs [23, 54]. Experimentally, coherence times of more than 100 ms have been shown with mu-metal magnetic shielding [87] and dressed states [90]. All trapped ion experiments with coherence times of more than 100 s [22, 24] were performed with hyperfine qubits at a clock transition [86] and without external magnetic shielding. Hence 14 with appropriate magnetic shielding, one should be able to increase the coherence by several orders of magnitude. This results in coherence times of hours or days and κ values14 greater than 106 . As the main magnetic field noise in a laboratory environment is from alternating current (AC) sources, one way to shield against AC magnetic field is using skin-effect in a highly conducting material surrounding the experiment [91]. Another way is to encapsulate the experiment in a mu-metal shield [92], which provides shielding against AC and DC magnetic fluctuations. However, slow magnetic field drifts such as changes in earth’s magnetic field [93] still penetrate a magnetic shield made out of a highly conducting material or mu-metal15. Thus, these simple magnetic shielding schemes will not allow the desired coherence times of hours or days. A consequence of Meissner effect [94] is that superconductors are perfect diamagnets and thus perfect magnetic shields. Inside a hollow superconductor, the magnetic field is constant and shielded from external magnetic fields. When placing the ion trap (equivalent to the whole quantum computer) in such an environment, the desired coherence times should be feasible with clock transitions in hyperfine qubits. In practice, it is not straightforward to define a certain magnetic field strength inside a superconductor, as required for clock transitions in hyperfine qubits. During the phase transition into the superconducting regime, local magnetic flux can get pinned16. To avoid this pinning, the suggested solution is to have the superconductor undergo the phase transition in a zero-field environment [95]. For such a cool-down, the experiment has to be located inside a magnetically shielded room (MSR) [96]. Once the entire shield is superconducting, external magnetic field changes will no longer be able to penetrate the shield. Cables, fibers, etc. to operate the Paul trap will have to enter the superconducting shield through holes to which superconducting tubes should be attached. The shielding of such superconducting cylinders depends exponentially on its length (for a given diameter) [97]. Hence, long and thin
- 48. 48 cylinders are desired for high shielding against the environment. The bias magnetic field at the position of the ions can be generated by superconducting coils inside the magnetic shield, as depicted in Fig. 10 a. During the cool-down in a zero-field environment, the superconducting coils do not contain persistent current [98]. With additional normally conducting coils, one can generate a magnetic field inside in the shield, shown in Fig. 10 b. When the superconducting coils are heated locally, as illustrated in Fig. 10 c, the generated magnetic field can penetrate the superconducting coils. After they are cooled back down into a superconducting regime, the magnetic field produced by the normally conducting coils can be switched off. The resulting persistent current in the superconducting coils will generate an ultra-stable magnetic field inside the superconducting shield. The zero-field environments in MSRs with a residual field of less than 1.5 nT have been demonstrated [99]. If the pinning of magnetic flux in the superconductor were to increase the residual magnetic field by a factor of 100, the magnetic field strength would be on the order of 100 nT. The magnetic field strength for clock transitions in hyperfine qubits is generated by the superconducting coils inside the superconducting shield and is on the order of 10 mT [100, 23]. Hence, the pinned magnetic field in the center of the superconducting coils (at the position of the ion trap) can only produce a relative offset of 14As previously discussed, one will only be able to use a small fraction of the stated coherence time, which is typically a 1/e value of a coherence measure. Although the exact κ value depends on the logical qubit encoding, a stated coherence time of about 105 s with gate times of about 10 to 100 µs may lead to κ ≈ 106 . 15A typical value of the DC attenuation of magnetic field of a mu-metal shield is about 30 dB. 16This local flux can get pinned to grain boundaries, strains, etc. inside the superconductor which alters the magnetic field inside the superconductor [95]. The measured magnetic field strength inside a superconducting cylinder can reach 100 times the externally applied magnetic field strength. 15 10−5 of the total magne c field, which leaves hyperfine qubits safely in the regime with only quadratic Zeeman shift. Such a setup will provide a temporally stable magnetic field to reach the desired coherence times of hours or days. In general, it is not necessary to completely eliminate magnetic gradients in trapped ion QC. If the magnetic field at each storage point is well known, one can calculate the phase evolution of all
- 49. 49 qubits. However, techniques like decoherence free subspace (DFS) encoding [101] require the same magnetic field for multiple ions. Therefore, it is desirable but not necessary to have high homogeneity. Spatial homogeneity is discussed in the appendix in Appendix A.1 in more detail. 5.3. Local oscillator stability The transition frequencies of hyperfine transitions are typically on the order of 1-10 GHz [102, 100, 23]. If one wants to achieve coherence times of up to days, a frequency reference with a stability of about 10−15 will be required. In order to achieve the required stability of the reference clock, one can sacrifice some ions of the quantum computer to act as a precise long-term frequency reference. Although one has to remove some ions from QIP for the clock signal generation, such a scheme allows stabilizing the local oscillator. It will even enable using the quantum computer for atomic clock measurements. 5.4. Multiplexing: ion storage and movement An idling ion string accumulates on the order of 10 quanta/s and thus about a million phonons during a day of uncooled storage. These high phonon numbers will cause a melting of the ion crystal and the order in the ion string will be lost after a refreeze. Hence, ion storage times of hours or days require sympathetic cooling with a second ion specie Besides working with two ion species, sympathetic cooling implies that one needs cooling beams at each storage position. The illumination of each storage zone can either be accomplished by integrating fibers into the trap [105] or by illuminating multiple storage zones with a beam parallel to the trap surface, as displayed in Fig. 11. Integrated fiber optics facilitate cooling of ion strings. However, one fiber per storage position will complicate the trap design whereas cooling multiple storage zones with a single beam will simplify the optical setup. These beams along the surface can even be reused by reflecting the light from one line of storage zones to the next line of storage zones, similar to the ideas discussed in reference [106] and shown in Fig. 15 b. One thing that has to be kept in mind when designing a large-scale quantum computer in a cryogenic environment is the heat load. Large-scale QC will require thousands of storage sites. If light is coming from a fiber at every storage site, it will be hard to couple the light back into fibers to avoid heating the cryostat due to the light absorption. Whereas, light parallel to the surface cools multiple sites and is easier to couple back into a fiber. A trap suitable for QIP with thousands of ions will require the control over thousands of segments and thus over thousands of voltages with digital-to-analog
- 50. 50 converter (DAC) channels. In order to reduce this hardware demand, one can use analog multiplexers. By employing such analog switches, one DAC channel can control multiple segments. An example of how this can be incorporated in ion movement is shown in Fig. 12. At first, the ion is stored on the left side by controlling three segment pairs. During the shuttling, one has to control at maximum four segment pairs. When moving the ion right, the control of an unused segment pair on the left can be exchanged to control over the next segment pair on the right17 . Hence, with this multiplexing scheme, it is possible to move ions in an arbitrarily big segmented trap with DC control over only four segment pairs and digital multiplexing logic. Furthermore, it is possible to adapt the voltage ramps for each segment individually which enables the compensation of stray fields on all parts of the trap Quantum gates A major problem with entangling gates which use Coulomb interaction [75, 76], thus phonons in an ion crystal, is motional heating [109]. A lot of effort has been made to characterize heating [110], especially its dependence on the distance of the ion to the surface of the trap, and it has been shown that the heating rate is reduced in cryogenic environments [111, 112]. Experimentally, heating rates as low as 0.33 ph/s have been observed in surface traps [113]. Due to sympathetic cooling in the memory region and short transport times between the quantum 18 memory region and the QALU of less than about 1 ms, heating only affects QIP in the QALU. The quantum computer based on this quantum von Neumann architecture for trapped ions has to be operated in a cryogenic environment and, thus, heating rate should be low enough to allow for fault-tolerant QC. . RF or optical drive fields RF fields enable qubit operations with the lowest infidelity in trapped ion systems to date [23]. Entangling operations via Coulomb interaction require high field gradients due to the low Lamb-Dicke parameter of RF fields. These high field gradients are typically generated with high RF amplitudes. If the QALU is surrounded by memory zones, one must protect the qubits in the quantum memory from the resonant and near-resonant RF fields. There is research on minimizing RF surrounding the processing zones of traps.
- 51. 51 However, it is unclear how well this RF field suppression would work for a large- scale quantum computer with tens of thousands of qubits or more surrounding the QALU. Experimentally, one has to stabilize the phase of the RF in QALU for high fidelity operation such that the length between the RF source and the ion does not fluctuate on a (tens of) micrometer scale. On the other hand, high fidelity quantum operations can be performed with optical drive fields as well [54, 36]. There, the demonstrated infidelity is about one order of magnitude worse than with RF fields. However, unwanted fields can be avoided by inhibiting direct line of sight between the quantum memory and surfaces of the QALU that scatter light, see the Section 5.5.5 for details. Experimentally, the most challenging part is amplitude and phase control of the light field at the position of the ion. Given that optical frequencies are much higher than the RF frequencies, one has to stabilize the phase of the light with sub-nanometer precision. Suggestions on the phase stabilization is given in Appendix A.3. Furthermore, in order to avoid long distances between the quantum memory region and the QALU, the processing zone will be in the center of the trap. Single ion addressing with laser beams will require a numerical aperture (NA) of 0.2 or higher for ion-to-ion distances of about 5 µm. Therefore, the trap needs to be slotted in the region of the QALU to allow high NA addressing perpendicular to the trap surface. 5.5.3. Physical requirements for the gate operations So far, this architecture requires (at least) two ion chains to be loaded into the QALU for QIP, where gate operations are performed. The type of gates [76, 77, 70, 23] that are executed is defined in the firmware layer of the architecture. For a full set of quantum operations, single ion addressing capability is required. As the length of path between the drive field’s source and the ions should not fluctuate for a stable phase reference, vibration isolation of the superconducting magnetic shield will be required, e.g. by suspending the shield with ropes from the vacuum chamber. Please, refer to Appendix A.2 for more details. With RF gates, the trap can be used as part of the transmission line which simplifies the setup. For optical gates, light can be guided via fibers into the magnetic shield and optical alignment in the shield will enable enough optical access to perform the required gate operations. Furthermore, vibration isolation will reduce beam pointing instabilities and thus undesired varying optical crosstalk between the ions. The tight focusing, required for single ion addressing, results in a high local light intensity at the position of the ion. In reference [114], the authors state that between 1 and 10 mW optical power is
- 52. 52 required for single qubit gates with a gate infidelity of 10−4 employing Raman transitions. Moreover, between 100 mW and 1 W optical power is required for entangling gates21 using a Gaussian beam with w0 = 20 µm. If all gates in a quantum von Neumann setup are performed with highly focused Gaussian beams with w0 ≈ 1 µm, the required total optical power will drop by a factor of 400 compared to their stated values. This lower optical power reduces problems like bleaching of fibers, which is worse at higher powers. The crosstalk onto neighboring ions is a coherent process and thus can be eliminated by calibration and composite pulses [74]. If the crosstalk on all ions is known, one can construct a pulse sequence that performs all single qubit operations required by the quantum algorithm and at the same time corrects for the crosstalk [41]. Such calibration requires precise control over the amplitude of the driving field at the position of the ion. For operation with RF gates, this implies a clever segment structure of the trap. For operation with optical gates, beam pointing instabilities and imperfections in amplitude and timing control must be negligibly small. Thermal drifts might still cause spatial drifts on time scales of seconds or minutes. Therefore, it might be necessary to regularly place ”calibration ions” in the QALU to track drifts of the crosstalk. In order to protect idling qubits, it is possible to shelve populations from the clock state to other states in the Zeeman manifold [74] in which the QIP is performed. With this scheme, gate operations are not resonant with the clock transition in which quantum information is stored in the quantum memory. However, the imperfect shelving operations introduce leakage from the qubit states which needs to be considered in the employed QEC. 5.5.4. Pipelining Since ions which arrive in the QALU from the quantum memory are only Doppler cooled, they have to be groundstate-cooled for high fidelity QIP. If cooling and QIP are executed in the same processing zone of the QALU, the processing cycle will be slowed down by the required initial cooling. Following the pipelining approach from classical computer science, one can use separate regions in the processing zone for the individual tasks required for efficient QIP. These tasks could be: 1. Combining two (or more) ion strings to a single string 2. Sympathetic Doppler cooling 3. Sympathetic ground state cooling: e.g. by using electromagnetically-induced- transparency (EIT) cooling 4. Qubit decoding, e.g. map from a DFS basis back to a single ion basis 5. Map ions for QIP from clock states, or dressed states, to
- 53. 53 processing states 6. Perform QIP 7. Map ions back from processing state to clock states, or dressed states 8. Qubit encoding, e.g. map the single ion basis back into DFS basis 9. Split the ion string into multiple parts for storage Fig. 16 depicts such a pipelining approach which enables the execution of multiple tasks on multiple ion strings simultaneously. The thick black lines illustrate the RF rails along which ion strings can be moved. Fig. 16 a shows a QALU architecture for which two (or more) ion strings, which shall interact during QIP, are loaded from the quantum memory and combined to a single ion string. As Doppler cooling typically lasts milliseconds, whereas QIP is performed in tens of microseconds, the ion string passes through multiple stages of sympathetic Doppler cooling to ensure that the ions are at the Doppler limit before further processing is performed. After Doppler cooling, the ion string is ground state cooled with sympathetic EIT cooling. In the next step, the quantum information is decoded for example by transferring from the DFS encoding to the bare physical qubit. After qubit decoding, QIP is performed on the ion string. This enables interaction between arbitrary qubits of the quantum memory. After QIP, the ion string is encoded, e.g. with DFS encoding. At last, the long ion string is split into multiple ion strings which can then be sent back to the quantum memory. Another QALU architecture is depicted in Fig. 16 b. It has the same cooling and QIP procedure as the previous one. However, the different ion strings loaded from the quantum memory are not combined in the first pipeline step but cooled individually. After ground state cooling, the cooling ions can be separated from the qubit ions. This simplifies the mode structure of the ion crystal but requires efficient ion splitting of ground state cooled ion strings. To simplify the mode structure even further, the qubit ions used only for DFS encoding are separated from the ones containing the quantum information after DFS decoding. In the QIP region, the two ion strings are combined and QIP can be performed. For DFS encoding, the ions that were split off can be reused. At last, the qubit ions are recombined with the cooling ions before ion strings can be sent back to the quantum memory. Qubit encoding/decoding and QIP require single ion addressing. With optical gates, if there is not enough optical access to perform single ion addressing at multiple locations, these tasks may have to be performed at different positions on the trap. Having different regions for the different parts required for QIP is not yet pipelining. In the pipelining process, an ion string is moved from one processing region to the next, while the next ion string is moved into the previous processing
- 54. 54 region22. Thus, the number of processing regions defines the depth of the pipeline. The parameters of the cooling and processing time have to be chosen such that they can be synchronized. The time of one execution cycle defines the speed of the processing. The distance between the different processing regions should be short so that ion movement does not increase the execution time of one pipeline step considerably. In the processing regions, micromotion [115] has to be compensated for effective cooling and QIP. This will require many independently controlled voltages in the processing zone. However, in the shuttling regions between the processing regions, micromotion is not crucial and one can use multiplexing, as shown in Fig. 13, to reduce the number of DC voltages which need to be controlled in the QALU. In this general pipelining approach, there are no restrictions on the ion strings processed in the QALU. In order to keep the vibrational mode structure of the ion strings simple, one has to limit the length of the ion strings. By choosing the ion string loaded from the quantum memory such that the qubit ions are surrounded by the cooling ions, one can detect ion loss during Doppler cooling. For this, one uses a camera to detect the number and positions of the cooling ions. From the spacing between the cooling ions, the number of processing ions can be inferred. Ion loss can be compensated by adding ions to the ion string either in the QALU or in a special zone outside the QALU. 5.5.5. Trap constraints In order to minimize axial micromotion (which cannot be compensated), it is imperative to design the trap in the processing zone as symmetric as possible, e.g. as illustrated in Fig. 16 a and b. 21 In both the quantum memory and the QALU, the tracks along ions can be shuttled will form loops. Hence, inter-layer connectivity (vias) will be required for the fabrication of such trap structures. Modern traps with vias23 typically route the signal lines underneath the trap surface to the segment. These traps use vias to connect the actual segments with the routing tracks. This enables placing ground planes at areas on the trap surface which are not used for electrodes. These ground planes shield against electric fields from the lower lying routing layer, thereby, reduce the cross-talk between segments For the operation with optical gates, stray light that is (near-)resonant to a qubit transition is a serious problem for the long coherence times required for a quantum von Neumann architecture. A main source of stray light is light scatter at the slot, required for QIP with high NA, in the QALU, and it can be minimized by
- 55. 55 blocking direct line of sight between the quantum memory and the QALU, for example with walls on the segmented traps, as depicted in Fig. 17. The height of the walls should be higher than the distance from an ion to the surface of the trap. These walls should not be perpendicular to the trap surface but under an angle so that reflections on the wall’s surface reflect the light away from the trap surface. If the walls are made of a conducting material, they can be grounded and will have little impact on the trapping potentials. For the operation with RF gates, blocking of stray fields is not possible. It can only be minimized by clever segment structures. 5.6. Detection and initialization For QIP with optical gates on ground state qubits, Raman transitions are incur porated to couple the quantum states [114]. These transitions are off-resonant with a typical detuning in the GHz or low THz regime. Because of this large detuning, a single photon is very unlikely to affect a qubit. Thus, it is safe it assume that reflections somewhere in the vacuum chamber can be neglected and it is sufficient to place a wall around the QIP zone in the QALU to shield the quantum memory from stray light. However, detection requires resonant light which causes fluorescence which is resonant as well. Furthermore, initialization produces resonant fluorescence. In the case of resonant photons, even a single photon can affect the information in the qubits, and one should try to avoid photons resonant with a state used for storing quantum information. This problem can be circumvented by using a second ion species for detection. For this, the state of the ion to be detected has to be transferred onto the detection ion of a different species. Entanglement between two ions of different species has been demonstrated [116]. The swapping operation, illustrated in Fig. 18 a in the circuit model representation [11], requires only near-resonant driving fields but no resonant fields. For detection, it transfers the quantum information to another ion species, while initializing the main qubit for further processing. Therefore, both state detection and initialization can be performed with ions of the second ion species and one does not have to worry about stray light resonant to the qubits in the quantum memory. This implies that initialization fidelity will depend on the fidelity of entangling operations. In order to increase the initialization fidelity for qubits which have a quadrupole transition, one can reinitialize the qubits additionally by optical pumping via the quadrupole transition.
- 56. 56 High fidelity state detection needs to be performed fast which requires high photon collection efficiency. For example, in Ca+, the qubit information is usually stored in the ground state of the ion and, thus, an electron shelving pulse is required to transfer the population of one qubit state into the D5/2 state. The D5/2 state has a limited lifetime and thus spontaneous emission causes errors in the detection. The life-time of the D5/2 state in Ca+ is about 1 s [117] which means that the detection has to be performed in 10 µs 24 to achieve it with a detection infidelity of 10−5 . With a sca er rate of about 10 MHz in Ca+, an ion emits about 100 photons during 10 µs. If one requires 5 clicks on the detector for reliable detection, one has to collect about 10 % of the photons with a typical detector efficiency of about 50 %. A collection efficiency of 10 % requires the detection optics to have NA > 0.6. QEC requires ancilla qubits which have to be detected to extract information on the occurred errors, and thus the detection region has to be close to the QALU on the trap. This might limit the optical access to the QALU. To increase the number of scattered photons in a certain period of time, one can use the fluorescence of multiple ions by employing Greenberger- Horne-Zeilinger (GHZ) states [119], as demonstrated in reference [120]. The circuit representation of this detection scheme can be seen in Fig. 18 b. The input state |ψi = α |0i + β |1i is transferred onto N ancilla qubits of a second ion species to generate the GHZ state α |00 · · · 0i + β |11 · · · 1i. With N ancilla qubits, the count rate increases by a factor of N compared to the detection with just one ancilla qubit. For detection in the same time interval, the collection efficiency can be lower by a factor of N compared to the case with one ancilla qubit. It is also possible to increase the detection fidelity for longer detection times by performing a majority vote. As an example, if one chooses a detection time of 100 µs for detection of Ca+, this will result in an infidelity of ≈10−4 due to spontaneous decay. If one chooses 5 ancilla qubits and one can detect how many ions are bright, 3 qubits will need to decay from the D-state to the S-state for a wrong state detection. The probability for this to happen is 10−12. Hence, the overall detection process will more likely be limited by how efficiently one can generate the GHZ state than by detection itself. Pipelining can also be incorporated in the detection/initialization zone, as illustrated Fig. 18 c. The incoming qubits are cooled to the ground state of motion before they are moved to the swapping zone.
- 57. 57 There, the CNOT-gates for GHZ state generation and the swap gate are performed with initialized ancilla qubits of a second ion species. After the swap operation, the initialized qubits are moved to another initialization zone where one can compensate the initialization error due to imperfect gates or leakage into other states during QIP. After the initialization, the ions are shuttled back to other parts of the trapped ion quantum computer. During the compensation of the initialization error, the ancilla qubits of the second ion species are moved to a detection zone where the (GHZ) state is detected. After detection, the ions are cooled and initialized in separate zones before they can be reused in the swap zone. Experimentally, the challenge will lie in protecting the quantum information between the swap and the detection zone from (resonant) stray light of the cooling and initialization zones. 5.7. Choice of ion species At first, one has to decide how many species one needs for this architecture. One ion species is required for the qubit ions. Another ion species is required for sympathetic cooling. The ions for detection can either be from the same ion species as the ions for sympathetic cooling, or one can use a third ion species. If one only uses two ion species, cooling in the memory region and detection have to be pulsed so that resonant stray fields from the memory region does not affect the quantum state in the detection zone. Whereas, using three ion species makes the detection zone independent from the memory region. In the following, the three ion species architecture will be discussed Gold has a work function of 5.3 eV [121], which corresponds to 234 nm. Aluminum has a work function of 4.08 eV [122], which corresponds to 304 nm. • Mass ratio: for sympathetic cooling the mass ratio of the ion species in the ion string should be close to 1 [104, 123, 124], so that all modes of a mixed ion crystal can be efficiently cooled. Experimentally, sympathetic cooling of two-ion crystals with a mass ratio of 3 has been demonstrated [125]. • Mass: with the same electric field, lighter ions are accelerated faster, which is advantageous for ion movement. In the same trapping potential, lighter ions have higher trap frequencies, which allows faster gate operations and less power is required for the entangling gate operations [114]. The criteria for the choice of the ion species of the cooling ions are: • Mass ratio: as described for the qubit ion species.
- 58. 58 • Wavelength: as described for the qubit ion species. • No nuclear spin: this simplifies the level structure and the laser system, if one does not require two beams with GHz detuning from one another. The criteria for the choice of the ion species of the detection/initialization ions are: • Mass ratio: as described for the qubit ion species. • Wavelength: as described for the qubit ion species. • No nuclear spin: as described for the cooling ion species. • Long lived D-state: there are several different detection schemes like electron shelving [126, 127, 128], or using sigma polarized light to cyclically drive a single transition [61]. Both schemes allow high-fidelity state detection. But in the same setup, electron shelving with an ion species which has a long lived D5/2 state usually yields higher fidelity than a detection scheme which is limited by off- resonant excitations
- 59. 59 اﻟﺨﺎﻣﺲ اﻟﻔﺼﻞ اﻟﻜﻤﻮﻣﻲ اﻟﺤﺎﺳﻮب ﺗﻮاﺟﮫ اﻟﺘﻲ واﻟﺘﺤﺪﯾﺎت اﻟﻤﺸﻜﻼت ﯾﻠﻲ ﻛﻤﺎ ﻟﻠﻐﺎﯾﮫ ﻣﮭﻤﺔ ﻧﻘﺎط اﻟﻰ اﻟﻜﻤﻮﻣﻲ اﻟﺤﺎﺳﺐ ﻣﺸﺎﻛﻞ ﺗﻠﺨﯿﺺ ﯾﻤﻜﻦ 1 - ا ﻣﺸﻜﻠﺔ ﯾﺴﺎوي اﻟﺬي اﻟﻤﻄﻠﻖ اﻟﺼﻔﺮ ﻣﻦ ﻗﺮﯾﺒﺔ ﺗﺒﺮﯾﺪ درﺟﺔ اﻟﻰ اﻟﻜﻤﻲ اﻟﺤﺎﺳﺐ ﯾﺤﺘﺎج ﺣﯿﺚ ,ﻟﺘﺒﺮﯾﺪ - 273,15 اﻟﺤﺎﻟﻲ اﻟﻮﻗﺖ ﻓﻲ ﻣﺴﺘﺤﯿﻞ ﺷﺒﮫ اﻟﺒﺮوده ھﺬه ﻻﻧﺘﺎج اﻟﻼزم اﻟﻄﺎﻗﮫ وﺣﺠﻢ ﺳﯿﻠﯿﻠﻮز 2 - ﻓﻘﺪان ﻓﻲ وﺗﺘﺴﺒﺐ اﻟﻜﯿﻮﺑﺖ ﻣﯿﺰة اﻟﻜﻤﻲ اﻟﺤﺎﺳﺐ ﺗﻔﻘﺪ ان ﯾﻤﻜﻨﮭﺎ اﻟﮭﻮاء ﺟﺰﯾﺌﺎت ﺑﯿﻦ اﻟﺘﺼﺎدم ﻋﻤﻠﯿﺔ اﻟ ﺑﻌﺾ اﻻﺟﮭﺰه ھﺬه ﺣﺴﺎﺳﯿﺔ ﻟﺸﺪة ﺒﯿﺎﻧﺎت 3 - واﻟﻤﻮﺟﺒﮫ اﻟﺴﺎﻟﺒﮫ اﻟﻘﯿﻢ ﺑﺘﻐﯿﯿﺮ ﺑﻌﻀﮭﺎ ﺑﯿﻦ رﺳﺎﺋﻞ ﺗﺮﺳﻞ اﻻﻟﻜﺘﺮوﻧﺎت ان ﺣﯿﺚ اﻟﻜﻤﻮﻣﻲ اﻟﺘﺸﺎﺑﻚ ﻣﺸﻜﻠﺔ اﻟﻤﺤﯿﺮ اﻟﻠﻐﺰ ھﺬا ﻓﻚ اﻟﻜﻢ ﻣﯿﻜﺎﻧﯿﻜﺎ ﻋﻠﻤﺎء ﯾﺴﺘﻄﻊ ﻟﻢ اﻻن واﻟﻰ اﻟﺪوران ﻋﻤﻠﯿﺔ وﺗﻐﯿﯿﺮ ﻛﺬﻟﻚ واﻟﻌﻜﺲ
- 60. 60 اﻟﻔﺼﻞ اﻟﺴﺎدس واﻟﺘﻮﺻﯿﺎت اﻻﻗﺘﺮاﺣﺎت ﻓﻲ ﺧﻼﺻﺔ وﺧﺘﺎم ھﺬه ،اﻟﺪراﺳﺔ ﺣﺎوﻟﻨﺎ إﻟﻘﺎء اﻟﻀﻮء ﻋﻠﻰ اﻟﻤﻔﺎھﯿﻢ ﻟﻤﻔﮭﻮم اﻟﻤﺆﺳﺴﺔ اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻤﻮﻣﻲ ﺧﺎﺻﺔ ﺗﻠﻚ اﻟﻤﺘﻌﻠﻘﺔ ﺑﺒﻮاﺑﺎﺗﮫ اﻟﻤﻨﻄﻘﯿﺔ اﻟﻜﻤﻮﻣﯿﺔ ( ھﺬا ﻣﻊ إدراﻛﻲ أن ً دراﺳﺔ واﺣﺪة وأﻛﺜﺮ ﻏﯿﺮ ﻛﺎﻓﯿﺔ ﻟﻺﻟﻤﺎم ﺑﮫ ﻧﻈﺮي ﻛﻌﻠﻢ ﻣﻊ ﺗﻄﺒﯿﻘﺎﺗﮫ اﻟﺘﻘﻨﯿﺔ اﻵن؛ إذ إن QLG اﻟﻤﻨﻄﻘﺔ اﻟﻌﺮﺑﯿﺔ ﻻ زاﻟﺖ ﻗﻠﯿﻠﺔ ﺑﺎﻟﻌﻠﻮم اﻻھﺘﻤﺎم اﻟﻌﺼﺮﯾﺔ ،ھﺬه ُرﺪوﺗﻨ ﺗﻠﻚ اﻟﻤﺮاﻛﺰ اﻟﺒﺤﺜﯿﺔ اﻟﻤﺘﺨﺼﺼﺔ ﻓﻲ ھﺬا ،اﻟﻤﺠﺎل ﻟﺬﻟﻚ ﯾﺒﺪو ﻣﻦ اﻟﺼﻌﻮﺑﺔ ﺑﻤﻜﺎن إﻧﺘﺎج اﻟﺠﺪﯾﺪ ﻓﯿﮫ . ﻋﻠﻰ أي ،ﺣﺎل وﻓﻲ ﺧﺎﺗﻤﺔ دراﺳﺘﻨﺎ ﯾﻤﻜﻨﻨﺎ اﻗﺘﺮاح واﺳﺘﺨﻼص ﻣﺎ ﯾﻠﻲ : • ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ ) QC ( ، ﯾﻤﻜﻦ اﻟﻘﻮل إن اﻋﺘﻤﺎد ﻋﺪد اﻟﻜﯿﻮﺑﺘﺎت اﻟﻘﻠﯿﻠﺔ اﻟﺘﻲ ﯾﻤﻜﻨﮭﺎ إﻧﺠﺎز ﻣﮭﻤﺎت ﻻ ﯾﺴﺘﻄﯿﻊ إﻧﺠﺎزھﺎ اﻟﺤﺎﺳﺐ اﻟﻜﻼﺳﯿﻜﻲ ﺑﺂﺧﺮ ﻧﺴﺨﺔ ﻣﺘﻄﻮرة ﻟﮫ ﻟﯿﺲ ًﻞﺣ ًﺎﯿﻧﮭﺎﺋ ،ًﺎﯿوﻛﺎﻓ ﻓﺤﺘﻰ إن ﻛﺎن ﻋﺪد ًﻞاﻟﻜﯿﻮﺑﺘﺎﺗﻘﻠﯿ ًاﺪﺟ ﻓﻲ اﻟﺤﺎﺳﺐ اﻟﻜﻤﻮﻣﻲ ًﺎﺳﻗﯿﺎ ﺑﺎﻟﻌﺪد اﻟﮭﺎﺋﻞ ﻣﻦ اﻟﺘﺮﻧﺰﺳﺘﻮرات ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ ،اﻟﻜﻼﺳﯿﻜﻲ إﻻ أن إﻣﻜﺎﻧﯿﺔ اﻟﺘﺤﻜﻢ واﻟﺴﯿﻄﺮة ﻋﻠﻰ ﺣﺎﻻت اﻟﺘﺸﺎﺑﻚ واﻟﺘﺪاﺧﻞ اﻟﻜﻤﻮﻣﻲ ﺗﺒﺪو ﺻﻌﺒﺔ ًﺎﯿﺗﻘﻨ ،اﻟﯿﻮم ﻟﻜﻨﮭﺎ ﺗﺒﻘﻰ ﻣﺤﺎوﻻت ﻣﺘﻘﺪﻣﺔ ًﺎﯿﺗﻘﻨ . ﺗﺘﻢ اﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ ﻓﻲ ﺑﻨﺎء اﻟﺒﻮاﺑﺎت اﻟﻤﻨﻄﻘﯿﺔ ،ﻟﻠﻜﻤﺒﯿﻮﺗﺮ ،اﻟﯿﻮم ًاداﻋﺘﻤﺎ ﻋﻠﻰ ﺑﯿﺌﺔ اﻟﻌﻤﻞ اﻟﻜﻼﺳﯿﻜﯿﺔ اﻟﺘﻲ ﺑﻨﯿﺖ ﻋﻠﯿﮭﺎ ﺑﻮاﺑﺎت اﻟﻜﻤﺒﯿﻮﺗﺮ ،ذاﺗﮭﺎ وﺑﺎﻟﻀﺮورة ﺛﻤﺔ ﻓﺮض ﻋﻠﻤﻲ ﻣﻔﺎده أن ﻣﻦ اﻟﻤﻤﻜﻦ اﻟﻌﻤﻞ اﻟﻨﻈﺮي ﻋﻠﻰ إﻧﺘﺎج ﻧﻈﺎم ﻋﺪ ﻛﻤﻮﻣﻲ ) Quantum Code System, QCS ( ﯾﺘﻨﺎﺳﺐ واﺗﺴﺎع ظﻮاھﺮ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ واﺣﺘﻤﺎﻻﺗﮭﺎ ،اﻟﻤﺘﻌﺪدة ﺑﺤﯿﺚ ﻻ ﺗﺘﻘﯿﺪ ﻓﻘﻂ ﺑﻄﺮق اﻟﻌﺪ اﻟﻜﻼﺳﯿﻜﯿﺔ ﻓﻲ أﻧﻈﻤﺔ اﻟﻌﺪ ،اﻟﺜﻨﺎﺋﻲ وﺗﺒﺪو ھﺬه ﻣﻦ اﻟﻨﻘﺎط اﻟﻤﻤﻜﻦ اﻟﻌﻤﻞ ﻋﻠﯿﮭﺎ ًﺎﯾﻧﻈﺮ ﻋﻠﻰ أﺳﺲ اﻟﻤﯿﻜﺎﻧﯿﻚ اﻟﻜﻤﻮﻣﻲ اﻟﻜﻮاﻧﺘﻲ؛ ﻓﺎﻟﺒﻘﺎء ﺿﻤﻦ ﺑﯿﺌﺔ اﻟﻌﻤﻞ اﻟﻜﻼﺳﯿﻜﯿﺔ ًﺎﯿﻣﻨﻄﻘ وﺑﻨﺎء اﻟﺒﻮاﺑﺎﺗﺎﻟﻜﻤﻮﻣﯿﺔ ﻋﻠﻰ أﺳﺎﺳﮭﺎ ﯾﺒﺪو أﻧﮭﻤﺎ ﻣﻦ اﻟﻌﻮاﻣﻞ اﻟﺘﻲ ﺗﺆﺧﺮ اﻟﺘﻘﺪم ﻓﻲ اﻟﻜﻤﺒﯿﻮﺗﺮ اﻟﻜﻤﻮﻣﻲ وﺗﺤﻮﯾﻠﮫ ﻣﻦ ﺣﺎﻻت ﺗﺠﺮﯾﺒﯿﺔ ﻣﺨﺒﺮﯾﺔ إﻟﻰ ﻛﻤﺒﯿﻮﺗﺮ ﻣﺘﺎح ﻟﻠﻌﻤﻮم ﺑﻤﻮاﺻﻔﺎت ﻣﺬھﻠﺔ ﺣﺎل ﺗﺤﻘﻘﮫ . • ﯾﻤﻜﻦ إﺟﺮاء دراﺳﺎت ﻣﺘﻘﺪﻣﺔ ﺗﻘﻮم ﻋﻠﻰ اﻟﺠﻤﻊ ﺑﯿﻦ ﺣﺎﻟﺘﯿﻦ ﻛﻤﻮﻣﯿﺘﯿﻦ ﻣﺨﺘﻠﻔﺘﯿﻦ ) Qubits 2 ( ﻓﻲ ﺑﻮاﺑﺔ ﻣﻨﻄﻘﯿﺔ ﻛﻤﻮﻣﯿﺔ ،واﺣﺪة ﻛﺎﻟﺴﺒﯿﻦ اﻟﻜﻤﻮﻣﻲ اﻟﻨﺎﺗﺞ ﻣﻦ اﻟﺘﺠﺎوب اﻟﻤﻐﻨﺎطﯿﺴﻲ اﻟﻨﻮوي ) NMR ( ﺑﺤﻘﻞ ﻣﻐﻨﺎطﯿﺴﻲ ﺧﺎرﺟﻲ ﺑﻜﯿﻮﺑﺖ ،أوﻟﻲ واﻹﺛﺎرة اﻟﺬرﯾﺔ ﺑﻤﻨﺒﻊ ﻟﯿﺰري ذي طﻮل ﻣﻮﺟﺔ ﻣﺤﺪد ﺑﻜﯿﻮﺑﺖ ، ٍ ﺛﺎن وﯾﺒﺪو ھﺬا اﻷﻣﺮ ﻣﺠﺎل دراﺳﺔ ﻛﻤﻮﻣﯿﺔ ﻗﺪ ﺗﻜﻮن واﻋﺪة ﻓﻲ اﻟﻤﺴﺘﻘﺒﻞ اﻟﻘﺮﯾﺐ . ًﺎﯾأ ﺗﻜﻦ اﻟﻨﺘﺎﺋﺞ اﻟﺤﺎﻟﯿﺔ ﻓﻲ ﻣﺴﺘﻘﺒﻞ اﻟﺤﻮﺳﺒﺔ ،اﻟﻜﻤﻮﻣﯿﺔ ﻓﺈﻧﮫ ﻣﻦ اﻟﻀﺮوري اﻟﺘﻮﺻﯿﺔ ﺑﻀﺮورة دﺧﻮل ھﺬا اﻟﻤﺠﺎل اﻟﻌﺼﺮي ،ًﺎﯿﻋﺮﺑ إذ ﻧﻌﺘﻘﺪ أﻧﮫ ﺣﺎن اﻟﻮﻗﺖ اﻟﻤﻨﺎﺳﺐ ﻷن ﺗﺒﺎدر اﻟﺠﺎﻣﻌﺎت اﻟﻌﺮﺑﯿﺔ وﻣﺮاﻛﺰ اﻟﺒﺤﺚ اﻟﻤﺘﺨﺼﺼﺔ ﻟﻮﻟﻮج ھﺬا اﻟﻤﺠﺎل ﻣﻦ اﻟﺒﺤﻮث واﻟﻌﻠﻮم اﻟﺤﺪﯾﺜﺔ اﻟﻤﺘﻌﻠﻘﺔ ﺑﺎﻟﺤﻮﺳﺒﺔ اﻟﻜﻤﻮﻣﯿﺔ؛ ﺑﺤﯿﺚ ﯾﺘﻢ ﺗﺸﻜﯿﻞ ﻓﺮق ﻋﻤﻞ ﻋﻠﻤﯿﺔ وﺗﻘﻨﯿﺔ ﻣﺘﻌﺪدة ،وﻣﺘﻮاﺻﻠﺔ ﺗﺒﺤﺚ ﻓﻲ ﺷﻄﺮي اﻟﺒﺤﺚ اﻟﻌﻠﻤﻲ : اﻟﻨﻈﺮي اﻟﻜﻤﻮﻣﻲ ،اﻟﻤﺠﺮد واﻟﺘﻄﺒﯿﻘﻲ اﻟﺘﻘﻨﻲ اﻟﻤﺨﺒﺮي . وھﻲ ﻣﮭﻤﺔ ُﻠﻘﻰﺗ ﻋﻠﻰ ﻋﺎﺗﻖ اﻟﺒﺎﺣﺜﯿﻦ اﻟﻌﺮب ﻣﻦ ،ﺟﮭﺔ وﻋﻠﻰ اﻟﻤﺮاﻛﺰ اﻟﺒﺤﺜﯿﺔ اﻟﻌﻠﻤﯿﺔ اﻟﻌﺮﺑﯿﺔ وﻣﻨﻈﻤﺎﺗﮭﺎ اﻟﻌﻤﻠﯿﺔ وﺣﻜﻮﻣﺎﺗﮭﺎ اﻟﺪاﻋﻤﺔ ﻣﻦ ﺟﮭﺔ أﺧﺮى؛ إذ إﻧﮫ ﻋﻠﻰ أﻗﻞ ،ﺗﻘﺪﯾﺮ ﯾﻤﻜﻦ اﻟﻘﻮل إن اﻟﺒﺤﺚ اﻟﻌﻤﯿﻖ ﻓﻲ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ وﺗﻄﺒﯿﻘﺎﺗﮭﺎ اﻟﺤﺪﯾﺜﺔ ٌ ﺣﺎﻟﺔ ﻋﻠﻤﯿﺔ ﻣﮭﻤﺔ ﯾﺠﺐ ،ﺗﻌﻤﯿﻤﮭﺎ ﻛﻤﺎ أن ﻧﻘﻞ اﻟﻔﯿﺰﯾﺎء اﻟﻜﻤﻮﻣﯿﺔ إﻟﻰ ﻋﻤﻮم اﻟﻨﺎس ﻋﺒﺮ اﻟﺤﻮاﺳﯿﺐ اﻟﻜﻤﻮﻣﯿﺔ اﻟﻤﻤﻜﻨﺔ ﺑﺎﻻﺳﺘﺨﺪام واﻻﺳﺘﺜﻤﺎر اﻟﯿﻮﻣﻲ ﺳﯿﻜﻮن ﻟﮫ ﻧﺘﺎﺋﺞ ﻣﮭﻤﺔ ﻋﻠﻰ اﻟﺘﻔﻜﯿﺮ اﻟﻌﻠﻤﻲ ،ﺧﺎﺻﺔ واﻟﺒﺸﺮي ﻋﺎﻣﺔ؛ ﺣﯿﻦ ﯾﺒﺪأ اﻟﺒﺸﺮ ﺑﺘﻠﻤﺲ ﻧﺘﺎﺋﺞ ھﺬا اﻟﻌﻠﻢ اﻟﺬي ﻻ زال ا ًﺣﻜﺮ ﻋﻠﻰ اﻷﺧﺼﺎﺋﯿﯿﻦ اﻟﻔﯿﺰﯾﺎﺋﯿﯿﻦ اﻟﻨﻈﺮﯾﯿﻦ واﻟﺘﻄﺒﯿﻘﯿﯿﻦ ﻓﻘﻂ . ،وﺧﺘﺎﻣًﺎ إن دﺧﻮل ھﺬا اﻟﻤﻌﺘﺮك اﻟﻌﻠﻤﻲ ًﺎﯿﻋﺮﺑ ﺳﯿﺸﻜﻞ ﻧﻘﻠﺔ ﻧﻮﻋﯿﺔ ﻓﻲ إطﺎر اﻟﺘﻨﻤﯿﺔ واﻟﺘﻘﺪم اﻟﺘﻘﻨﻲ ،واﻟﻌﻠﻤﻲ وﺧﻄﻮة ﻋﺼﺮﯾﺔ ﻣﮭﻤﺔ أﺻﺒﺢ ﻻ ﺑﺪ ،ﻣﻨﮭﺎ ﺑﺪل اﻻﻛﺘﻔﺎء ﺑﺎﻟﻨﻘﻞ واﺳﺘﯿﺮاد اﻟﺘﻘﻨﯿﺔ ﺟﺎھﺰة .
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