Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice

Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a novel computing platform designed to solve NP-hard optimization problems. Starting with a 16-qubit prototype announced in 2007, the company has launched and sold increasingly larger models: the 128-qubit D-Wave One system was announced in 2010 and the 512-qubit D-Wave Two system arrived on the scene in 2013. A 1,000-qubit model is expected to be available in 2014. This monograph presents an introductory overview of this unusual and rapidly developing approach to computation. We start with a survey of basic principles of quantum computation and what is known about the AQC model and the QA algorithm paradigm. Next we review the D-Wave technology stack and discuss some challenges to building and using quantum computing systems at a commercial scale. The last chapter reviews some experimental efforts to understand the properties and capabilities of these unusual platforms. The discussion throughout is aimed at an audience of computer scientists with little background in quantum computation or in physics.

[1]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[2]  Daniel A. Lidar,et al.  Defining and detecting quantum speedup , 2014, Science.

[3]  Eleanor G. Rieffel,et al.  J an 2 00 0 An Introduction to Quantum Computing for Non-Physicists , 2002 .

[4]  M. W. Johnson,et al.  Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor , 2010, 1004.1628.

[5]  G. Rose,et al.  Finding low-energy conformations of lattice protein models by quantum annealing , 2012, Scientific Reports.

[6]  Bikas K. Chakrabarti,et al.  Quantum Annealing and Other Optimization Methods , 2005 .

[7]  Andrew M. Childs,et al.  Robustness of adiabatic quantum computation , 2001, quant-ph/0108048.

[8]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[9]  M. W. Johnson,et al.  Quantum annealing with manufactured spins , 2011, Nature.

[10]  E. Tosatti,et al.  Quantum annealing of the traveling-salesman problem. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[12]  Colin P. Williams.  Explorations in Quantum Computing, Second Edition , 2011, Texts in Computer Science.

[13]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[14]  Seth Lloyd,et al.  Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation , 2007, SIAM J. Comput..

[15]  Jérémie Roland,et al.  Anderson localization makes adiabatic quantum optimization fail , 2009, Proceedings of the National Academy of Sciences.

[16]  Endre Boros,et al.  Local search heuristics for Quadratic Unconstrained Binary Optimization (QUBO) , 2007, J. Heuristics.

[17]  David P. DiVincenzo,et al.  The complexity of stoquastic local Hamiltonian problems , 2006, Quantum Inf. Comput..

[18]  A. Young,et al.  Size dependence of the minimum excitation gap in the quantum adiabatic algorithm. , 2008, Physical review letters.

[19]  Vicky Choi,et al.  Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design , 2010, Quantum Inf. Process..

[20]  Ray,et al.  Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations. , 1989, Physical review. B, Condensed matter.

[21]  Jeremy Hsu.  D-Wave's year of computing dangerously [News] , 2013 .

[22]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Umesh V. Vazirani,et al.  How powerful is adiabatic quantum computation? , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[24]  Daniel A. Lidar,et al.  Error-corrected quantum annealing with hundreds of qubits , 2013, Nature Communications.

[25]  Sergio Boixo,et al.  Spectral Gap Amplification , 2011, SIAM J. Comput..

[26]  M. W. Johnson,et al.  Entanglement in a Quantum Annealing Processor , 2014, 1401.3500.

[27]  Ben Reichardt,et al.  The quantum adiabatic optimization algorithm and local minima , 2004, STOC '04.

[28]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[29]  Erio Tosatti,et al.  Optimization by quantum annealing: lessons from hard satisfiability problems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Vicky Choi,et al.  Different adiabatic quantum optimization algorithms for the NP-complete exact cover problem , 2010, Proceedings of the National Academy of Sciences.

[31]  Frank Thomson Leighton,et al.  Protein folding in the hydrophobic-hydrophilic (HP) is NP-complete , 1998, RECOMB '98.

[32]  Masayuki Ohzeki,et al.  Quantum annealing: An introduction and new developments , 2010, 1006.1696.

[33]  V. Fock,et al.  Beweis des Adiabatensatzes , 1928 .

[34]  Daniel A. Lidar,et al.  Experimental signature of programmable quantum annealing , 2012, Nature Communications.

[35]  M. W. Johnson,et al.  Experimental demonstration of a robust and scalable flux qubit , 2009, 0909.4321.

[36]  Todd A. Brun,et al.  Quantum Computing , 2011, Computer Science, The Hardware, Software and Heart of It.

[37]  Fabián A. Chudak,et al.  Experimental determination of Ramsey numbers with quantum annealing , 2012 .

[38]  Firas Hamze,et al.  Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines , 2014, 1401.1546.

[39]  N. Mermin.  Quantum Computer Science: An Introduction , 2007 .

[40]  Barbara M. Terhal,et al.  The complexity of quantum spin systems on a two-dimensional square lattice , 2008, Quantum Inf. Comput..

[41]  T. Hogg,et al.  Experimental implementation of an adiabatic quantum optimization algorithm. , 2003, Physical review letters.

[42]  L. Clark,et al.  Ramsey numbers and adiabatic quantum computing. , 2011, Physical review letters.

[43]  Rodney Van Meter,et al.  A blueprint for building a quantum computer , 2013, Commun. ACM.

[44]  H. Nishimori,et al.  Quantum annealing in the transverse Ising model , 1998, cond-mat/9804280.

[45]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[46]  M. Amin,et al.  Algorithmic approach to adiabatic quantum optimization , 2011, 1108.3303.

[47]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[48]  Kathryn A. Dowsland,et al.  Simulated Annealing , 1989, Encyclopedia of GIS.

[49]  Fabián A. Chudak,et al.  Investigating the performance of an adiabatic quantum optimization processor , 2010, Quantum Inf. Process..

[50]  Fred S. Roberts,et al.  Applications of Ramsey theory , 1984, Discret. Appl. Math..

[51]  B. Apolloni,et al.  Quantum stochastic optimization , 1989 .

[52]  Terufumi Yokota.  Infinite range Ising spin glass model with a transverse field , 1987 .

[53]  Marcus Schaefer.  Graph Ramsey Theory and the Polynomial Hierarchy , 2001, J. Comput. Syst. Sci..

[54]  M. Sipser,et al.  Quantum Computation by Adiabatic Evolution , 2000, quant-ph/0001106.

[55]  Paul R. Cohen,et al.  Using Finite Experiments to Study Asymptotic Performance , 2000, Experimental Algorithmics.

[56]  Fabián A. Chudak,et al.  Experimental determination of Ramsey numbers. , 2012, Physical Review Letters.

[57]  M. W. Johnson,et al.  Thermally assisted quantum annealing of a 16-qubit problem , 2013, Nature Communications.

[58]  Parongama Sen,et al.  Dynamical frustration in ANNNI model and annealing , 2005 .

[59]  Vicky Choi,et al.  Minor-embedding in adiabatic quantum computation: I. The parameter setting problem , 2008, Quantum Inf. Process..

[60]  W. Macready,et al.  Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization , 2008, 0804.4457.

[61]  H. Nishimori,et al.  Mathematical foundation of quantum annealing , 2008, 0806.1859.

[62]  Daniel A. Lidar,et al.  Evidence for quantum annealing with more than one hundred qubits , 2013, Nature Physics.

[63]  Cong Wang,et al.  Experimental evaluation of an adiabiatic quantum system for combinatorial optimization , 2013, CF '13.

[64]  Sorin Istrail,et al.  Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces (extended abstract) , 2000, STOC '00.

[65]  J. Doll,et al.  Quantum annealing: A new method for minimizing multidimensional functions , 1994, chem-ph/9404003.

[66]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[67]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[68]  H.-G. Meyer,et al.  Adiabatic Quantum Computation With Flux Qubits, First Experimental Results , 2007, IEEE Transactions on Applied Superconductivity.

[69]  J. Biamonte,et al.  Realizable Hamiltonians for Universal Adiabatic Quantum Computers , 2007, 0704.1287.

[70]  Thomas Jansen,et al.  Introduction to the Theory of Complexity and Approximation Algorithms , 1997, Lectures on Proof Verification and Approximation Algorithms.

[71]  Dario Tamascelli,et al.  An introduction to quantum annealing , 2011, RAIRO Theor. Informatics Appl..

[72]  R. Feynman.  Simulating physics with computers , 1999 .

[73]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[74]  T. Hogg.  Adiabatic Quantum Computing for Random Satisfiability Problems , 2002, quant-ph/0206059.