Taking Quantum Computing for a Spin: What is Imaginary and What is Real?
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The document discusses the fundamental principles of quantum computing, contrasting it with classical computing concepts such as binary arithmetic and logic gates. It outlines the capabilities of quantum computing, such as superposition and entanglement, which enable it to address complex problems that classical computers struggle with, including integer factorization and optimization challenges. Additionally, it highlights recent advancements in quantum computing hardware and algorithms, including applications in biomedicine and the emergence of quantum programming languages.
Taking Quantum Computing for a Spin: What is Imaginary and What is Real?
- 1. TAKING QUANTUM COMPUTING FOR A SPIN: WHAT IS IMAGINARY AND WHAT IS REAL? Michael Hogarth, MD, FACP, FACMI Faculty, Department of Biomedical Informatics Clinical Research Information Officer (CRIO) UC San Diego Health
- 2. OVERVIEW • Classical computing • Basic Principles of Quantum Computing • Suuperposition • Entanglement • Quantum Logic Gates • Exploring Quantum Circuits and Algorithms • Current state of Quantum Computing
- 3. BINARY COMPUTATION – THE KEY TO THE MODERN COMPUTER • Binary numeral system – invented by mathematician Gottfried Leibniz (17th century) • Mathematical Functions • One can perform basic mathematical computation with the binary numeral system • Storing information • One can also store a ‘state’ (number) in binary
- 4. CLAUDE SHANNON – THE REAL “FATHER” OF CLASSICAL COMPUTING • Explored performing binary ‘arithmetic’ using electric circuits (in the form of ‘switches’ – on/off) • MIT Master’s Thesis: “A Symbolic Analysis of Relay and Switching Circuits” (1936) • described using electronic relays and switches to perform Boolean algebra and binary arithmetic. • Other notable accomplishments • the father of “information theory” which outlines the basic theory behind communication systems (1948) • coined the term “bit”, for “binary information digit” (he attributed term to John Tukey of Bell Labs)
- 5. “LOGIC CIRCUITS”: A KEY CONCEPT IN SHANNON’S THESIS:
- 6. THE BINARY NATURE OF TRANSISTORS Transistors are just very very small on/off ‘switches’!Switches can be used to perform Boolean logic!
- 7. BASIC “LOGIC GATES” Does this look familiar to something you saw in Shannon’s thesis?
- 8. LOGIC CIRCUITS = ”LOGIC GATES” AND MATH FUNCTIONS
- 9. MULTI-GATE TRANSISTOR CIRCUITS– THE ”INTEGRATED CIRCUIT” (IC) http://www.electronics-tutorials.ws/combination/comb_7.html 74LS83 chip performs addition with carry!
- 10. FROM LOGIC GATES TO A MOTHERBOARD
- 11. THE “CLASSICAL COMPUTER” • A modern CPU is just a binary arithmetic “machine” that uses boolean logic and binary computation to perform a broad array of functions • Can be “programmed” --- it can step through a set of “instructions” that cause the classical computer central processing unit (CPU) to perform different boolean logic steps and computation by invoking different circuits --- a universal computing machine • Versatile as it can be “programmed” to do a broad array of things • Can be used to control other devices (GPU, video card, hard drive, random access memory cards, etc..) and receive information from other devices (keyboard, mouse, network card) Intel 4004 – 1971 (2,300 transistors)
- 12. EXAMPLES OF CHALLENGING COMPUTATION FOR CLASSICAL COMPUTERS • Even with the current crop of super computers, there are computing problems that are not tractable • Virtual Climate – climate models, predicting potential effects of global warming. Current supercomputers can only render down to 14 kilometers squared • Digital cells - modeling the movement and interaction of molecules in a cell. • Combustion (fuel) simulation • Simulating astrophysical phenomena • Integer factorization – determining the prime numbers multiplied to create an integer (can be solved in a quantum computer in polynomial time)
- 13. A ROLE FOR QUANTUM COMPUTING Quantum computing is emerging as a possible approach to “NP Hard” computational problems NP – class of problems in which a solution can be verified in polynomial time by a classical computer An algorithm is polynomial (or has polynomial running time) if the running time on inputs of “n” is at most O(n)k Algorithms with exponential running times are not polynomial Example of an NP-hard problem – finding the least cost route through nodes of a graph (the traveling salesman)
- 15. RICHARD FEYNMAN – FIRST TO SUGGEST A ‘QUANTUM COMPUTER’ WOULD BEST SIMULATE QUANTUM MECHANICAL SYSTEMS • Nobel prize in physics in 1965 - for work on quantum electrodynamics • “it is impossible to represent the results of quantum mechanics with a classical universal device” • Feynman proposed simulating quantum mechanical system using a computer based on the same principles (a quantum computer) MIT Endicott House Conference on the physics of computation (May 1981)
- 16. THE POTENTIAL POWER IN USING QUANTUM MECHANICS TO COMPUTE • A sub-atomic particle (electron, photon, etc..) behaves according to quantum mechanical principles • If you use such particle as a “bit”, due to ”superposition”, the bit can be in more than one state at a time --- it can be BOTH ”1” and ”0” at the same time • If you make one “bit” state dependent on another, superposition of the controlling “bit” means two possible computations can happen at the same time… massive parallelism for “bits”
- 17. TWO KEY CONCEPTS IN QUANTUM COMPUTING PARALLELISM • Superposition • Entanglement
- 18. BORROWING FROM QUANTUM MECHANICS • Modeling the ‘state’ of a ‘quantum bit’ (“qubit”) • Borrow existing modeling methods in quantum mechanics • A ‘qubit’ can generically be represented as an electron with “spin” leading to a vector within a sphere. • Dirac Notation (bra-ket notation) – a standard notation to describe “quantum states”, which can be modeled as abstract vectors in mathematics • Angle brackets < and >, and vertical bars (|) denote the linear function on a vector in complex space
- 19. WELCOME TO THE “QUBIT” https://www.cbinsights.com/blog/quantum-computing-explainer/ ● A qubit = The basic unit of information storage/processing in a quantum based computing system ● The figure on the left is an idealized model with: ● |1> = “spin down” ● |0>= “spin up” ● What isHint: what is the vector along the equator? Remember the pythagorean theorem and how to calculate a vector using angles…
- 20. QUANTUM SUPERPOSITION • Quantum particles • photon, Majorana fermion, electron, electron spin, or magnetic field • Superposition means their state is in multiple “directions” or have “multiple simultaneous spins” at the same time • When measured, the qubit ‘collapses’ to a 1 or 0 probabilistically
- 21. A QUBIT STATE DESCRIBED AS A COMPLEX VECTOR COMPOSED OF IMAGINARY AND REAL COMPONENTS • Equation describes the vector • Infinite possible states (not just 1 or 0 An Example state: Lies on the equator, along the y-axis
- 22. COMPUTING WITH QUBITS c t c’ t’ 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 c = control c ‘= c t = target t’ = c XOR t The controlled NOT gate: -c controls whether t is flipped or not. If c is 1, then it flips.
- 23. WHAT HAPPENS WHEN C IS IN SUPERPOSITION? c t c’ t’ 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 c = control c ‘= c t = target t’ = c XOR t If c is in superposition, does t get flipped or not? It does BOTH! If t = 0, and c=0, then t = 0 If t=0, and c=1, then t=1 c=|0> + |1> t = |0> |00>+|11> They are “entangled”
- 24. PARALLEL COMPUTING WITH SUPERPOSITION AND ENTANGLEMENT Qubit 1 Qubit 2 U Answer 1 and Answer 2 U is a function that takes in 1 input and provides 1 output (answer) If one puts qubit 1 into superposition, it causes qubit 2 to be in two states at the same time and yield two calculations simultaneously
- 25. QUANTUM PARALLELISM EXPLAINED https://youtu.be/UUpqnBzBMEE 2013 (the year DWave announced the DWave Two with 512 qubits)
- 26. REVISITING “LOGIC GATES” AS A PARADIGM FOR COMPUTING Does this look familiar to something you saw in Shannon’s thesis?
- 27. HADAMARD GATE (THE SIMPLEST GATE) • Hadamard gate – acts on a single qubit and maps the basis state (0 or 1) to a superposition qubit 1
- 28. THE PAULI-X GATE (NOT GATE) • Puts the qubit ‘spin’ or ‘state’ in an orthogonally opposite direction
- 30. ADIABATIC ANNEALING QUANTUM COMPUTER • A set of magnets are arranged on a grid • Magnetic fields of each influences all the other magnets, which flip to arrange themselves to minimize the energy stored in the overall magnetic field • You can control how strongly the magnetic field from each affects the others • Start with high energy so fields can flip back and forth • Let the system “cool” (or anneal) and loose energy, it will ‘settle’ at the lowest energy state
- 31. QUANTUM “ANNEALING” • “a method for finding solutions to combinatorial optimization problems and ‘ground states’ of systems” • By letting a system cool and go through sequential states, it will “anneal”, one can find the lowest energy state • What it does at the quantum level -- finds the lowest energy state in a system • Uses equations that describe the total energy of a system - a “Hamiltonian” Finnila, Gomez, Sebenik, Stenson, Doll. Quantum annealing: A new method for minimizing multidimensional functions. Chem Physics Letters. 219(1994) 343-348
- 32. ANNEALING - REACHING THE LOWEST ENERGY POINT WITH A SPECIALLY DESIGNED QUANTUM COMPUTER
- 34. OVER 50 EXISTING “QUANTUM ALGORITHMS”
- 35. GROVER’S ALGORITHM • Lou Grover 1996 • Uses qubits in superposition to compute ‘searches’ much faster than classical computers • “Searches” = generalized search • Finding an item in an *unstructured* list
- 36. https://www.youtube.com/watch?v=hK6BBluTGhU Grover’s algorithm is a quantum algorithm that will perform search in less time -- lowers it by the square root of the total items in the list
- 37. PETER SHOR’S ALGORITHM AND PRIME NUMBERS https://science.mit.edu/research/faculty/shor-peter-williston Look out RSA encryption!!
- 38. PRACTICAL APPLICATIONS FOR QUANTUM COMPUTING TODAY • Combinatorial optimization • “traveling salesman problem” • Integer factorization (breaks RSA) • Search in unsorted databases (Grover’s) • Pattern recognition • Protein folding
- 40. EXAMPLES OF QUANTUM ALGORITHMS RELEVANT TO BIOMEDICAL INFORMATICS
- 41. DEEP LEARNING MODEL AND QUANTUM ANNEALING
- 42. PROTEINS AND MODELING STRUCTURE • Understanding how proteins fold • Modeling malfunctioning proteins and their physical structures http://www.atelier.net/en/trends/articles/quantum-computing-set-revolutionise-health-sector_437915
- 44. OPTIMIZING/AUGMENTING AUTOMATED CLASSIFICATION • Classification of patients • Poor prognosis • Good prognosis
- 46. CURRENT COMMERCIAL QUANTUM COMPUTING DESIGNS • DWave Quantum Annealing computer (2013) • IBM 5-20 qubit “universal quantum computer” (2015) • Microsoft’s “Topological” Quantum Computer (March 2017) • Intel’s Quantum 17-qubit CPU (Oct 2017) • Atos Quantum Machine Learning computer (Nov 2017)
- 47. D-WAVE – THE FIRST COMMERCIALLY AVAILABLE QUANTUM COMPUTER
- 48. THE D-WAVE QUANTUM TRANSISTOR - THE SQUID ● Superconducting QUantum Interference Device (SQUID) ● Made of niobium, becomes superconducting at low temperatures ● A very sensitive magnetometer that can measure very subtle magnetic fields, based on superconducting loops containing Josephson junctions ● The transistor behavior: ● The SQUID stores two magnetic fields, which either point up (+1) or down (-1) ● Each SQUID is a qubit that can be controlled and put into a superposition of the two states
- 49. D-WAVE COUPLING – QUBIT ENTANGLEMENT ● Multi-qubit D-Wave processor has qubits connected to each other through couplers ● Couplers cause qubits to influence each other ● Mathematically, these elements couple together qubits, set as variables, providing parallelized solutions to multi-dimensional computation ○ Ie, optimization problems where changing one element requires re- computing of the others ● Readout device attached to each qubit - inactive during computation (do not affect qubit behavior), but read output once computation has finished 8 qubit loops with 16 couplers ‘connecting’ each qubit with 4 others
- 50. IBM QUANTUM COMPUTING – AS A WEB SERVICE? Free access to IBM 16- qubit machin eIBM Quantu m Computi ng Service
- 51. IBM Q COMPOSER: QUANTUM COMPUTING FOR THE MASSES
- 52. MICROSOFT QUANTUM INITIATIVE • Nadela – first major tech CEO to mention quantum computing in the company’s major conference (May 2017) • Topological quantum design • Less error (decoherence) • End-to-end quantum computing • From hardware to software • Developed a programming language • Built new language into Visual Studio IDE with full debugging and simulation support
- 53. TOPOLOGICAL QUANTUM COMPUTING • Relies on a particle called a Majorana fermion, first predicted by Ettore Majorana in 1937 • Appear as “quasiparticle excitations” • Design reduces the number of qubit interactions (gates) needed to perform certain computations (logical quantum gates) • First actually detected in 2017… • “It doesn’t really matter what exactly these excitations are, as long as they are measurable, and they can be used to perform calculations” – Elizabeth Gibney (Nature) https://www.nature.com/news/inside-microsoft-s-quest-for-a- topological-quantum-computer-1.20774
- 54. INTEL ANNOUNCES 17-QUBIT SUPERCONDUCTING CHIP • Oct 10, 2017 (4 weeks ago) • Intel announced delivery of a 17-qubit superconducting test chip to QuTech (Intel’s quantum research partner in the Netherlands) • Design – “spin qubits in silicon” in a superconducting environment • “single electronic transistor” (SET)
- 55. ATOS “QUANTUM LEARNING MACHINE” • Nov 13, 2017 (yesterday!) • Oak Ridge National Lab (ORNL) purchases an Atos Quantum Learning Machine • Ultracompact 30-qubit machine • Universal quantum programming language
- 56. QUANTUM COMPUTING IN THE REST OF THE WORLD
- 61. IBM QISKIT • SDK for working with OpenQASM • QASM – A text format language for describing ‘acylclic’ quantum circuits • Example programs: https://www.media.mit.edu/quanta/qas m2circ/ QASM program that puts a single qubit into a superposition then
- 62. A MICROSOFT QUANTUM PROGRAMMING LANGUAGE • LIQUi|> (Liquid) • Based on F# • Functions, variables, branches, quantum specific elements • Simulates up to 30 qubits • Largest number factored to date is a 13-bit number, 5 days runtime
- 63. WHAT I PREDICT – QUANTUM AUGMENTED HYBRID COMPUTING PLATFORMS • Combination of a quantum computing infrastructure with classical computing infrastructure • A ‘programming language’ that is ‘interpreted’ by a cloud computing infrastructure, which decides what to have computed and in what equipment • CPU • GPU • Quantum CPU Super computer Quantum computer Hybrid Exascale Computing Language Interpreter/controller Exascale Computing Platform
- 64. QUESTIONS?