Quantum Computing Fundamentals 2023-04-14
- 1. 2023-04-14 Gerald Scharitzer 1 Quantum Computing Fundamentals How quantum goes beyond classic computing Meetup of Quantum Computing Vienna
- 2. 2023-04-14 Gerald Scharitzer 2 Classic Information ● The fundamental unit of information is the "bit". ● Its value space is 0 and 1. ● All information is encoded in sequences of bits. – 01000001b Latin capital letter A encoded in UTF-8 – 01000001b Decimal number 65 encoded as binary integer – 100001001111b Color purple encoded in 12-bit RGB – 1001000100001110b Instruction "add" encoded in RISC-V C
- 3. 2023-04-14 Gerald Scharitzer 3 Classic Computing ● All computation is modifying bit sequences. ● 1-bit operations like "set", "clear", and "not" ● 2-bit operations like "and", "or", "xor", and "nand" ● Processor instructions like "add", "compare", and "load" ● Programming languages like Python, Java, and Rust ● Memory load/store and device input/output ● Sensors, emitters, and actuators interact physically.
- 4. 2023-04-14 Gerald Scharitzer 4 Classic Computers ● Modern (but classic) computers contain – processors based on MOSFETs with doped silicon – cache based on static RAM (transistors) – memory based on dynamic RAM (capacitators) – storage (disk) on floating-gate MOSFETs (flash) or magnetic disk – communication (net) over electric (copper) or optic (glass) cable, or radio waves (wireless)
- 5. 2023-04-14 Gerald Scharitzer 5 Enter Quantum Computing ...
- 6. 2023-04-14 Gerald Scharitzer 6 Quantum Information ● The fundamental unit of information is the "qubit". ● Its value space is a|0> + b|1> where – |0> and |1> are the classic 0 and 1 – a and b are complex numbers – and |a|² + |b|² = 1. ● Observing (measuring) a qubit turns it into 0 or 1. ● |a|² is the probability to measure 0, |b|² to measure 1.
- 7. 2023-04-14 Gerald Scharitzer 7 Quantum Computing ● is probabilistic instead of deterministic. ● You need an efficient classic algorithm to decide whether the outcome is a solution to your problem. ● It utilizes the quantum effects of superposition, entanglement, and phase shift. ● Quantum operations are unitary matrices with 2n rows and 2n columns operating on n qubits.
- 8. 2023-04-14 Gerald Scharitzer 8 Superposition ● enables n qubits to be in 2n states at the same time. ● One frequent method is to initialize all qubits to 0 and then use the Hadamard gate to reach a uniform probability distribution over all possible states. ● H|0> = 2-1/2 (|0> + |1>) ● P(0) = P(1) = |2-1/2 |2 = 2-1 = 50 % ● This enables 2n concurrent computations.
- 9. 2023-04-14 Gerald Scharitzer 9 Entanglement ● Non-entangled qubits do not interact and their probabilities are entirely independent. ● Entanglement makes qubits and their probabilities depend on each other. ● A Bell state like 2-1/2 (|00> + |11>) or 2-1/2 (|01> + |10>) ensures that measuring one qubit provides information on the other qubit, and vice versa. ● This is one way to program quantum computers.
- 10. 2023-04-14 Gerald Scharitzer 10 Phase Shift ● You can shift the phases of qubit states, such that constructive (amplifying) and destructive (dampening) interference can occur. ● This interference can increase the probability of measuring the relevant information. ● The complex numbers in the quantum states describe these phase differences. ● That is another way to program quantum computers.
- 11. 2023-04-14 Gerald Scharitzer 11 Measurement ● Reading a quantum state requires interacting with it. ● This causes it to adopt a classic state based on its probability distribution. ● Programming this probability distribution significantly increases the probability of measuring a relevant result. ● Quantum algorithms were found that are significantly faster than the best know classic algorithms for certain classes of problems.
- 12. 2023-04-14 Gerald Scharitzer 12 Quantum Computers ● differ by computational model – gate array, measurement-based, adiabatic, and topological ● by technology – superconducting, trapped ion, photonic, nuclear magnetic resonance (NMR), and many more ● and by processing capacity (aka quantum volume) – qubit count, connectivity (topology), coherence time, error rate, fidelity, and frequency (computing speed)
- 13. 2023-04-14 Gerald Scharitzer 13 Onward from here ● Quantum Computing in a Nutshell – https://qiskit.org/documentation/qc_intro.html ● Quantum Computing Field Guide – https://quantum-computing.ibm.com/composer/docs/iqx/guide/ ● Quantum Computing Qiskit Textbook – https://qiskit.org/learn/
- 14. 2023-04-14 Gerald Scharitzer 14 Quantum Computing Fundamentals Comments, feedback, or questions?