Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network

We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential equations. We also discuss the advanced CIM with quantum measurement-feedback control and various problems which can be solved by CIM.

[1]  Drummond,et al.  Quantum dynamics of the parametric oscillator. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[2]  J. Bajorath,et al.  Docking and scoring in virtual screening for drug discovery: methods and applications , 2004, Nature Reviews Drug Discovery.

[3]  Sergiy Butenko,et al.  On greedy construction heuristics for the MAX-CUT problem , 2007, Int. J. Comput. Sci. Eng..

[4]  R. Byer,et al.  Network of time-multiplexed optical parametric oscillators as a coherent Ising machine , 2014, Nature Photonics.

[5]  Yoshihisa Yamamoto,et al.  Quantum correlation in degenerate optical parametric oscillators with mutual injections , 2015, 1506.00135.

[6]  Seth Lloyd,et al.  Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation , 2008, SIAM Rev..

[7]  Johan Håstad,et al.  Some optimal inapproximability results , 2001, JACM.

[8]  John C. Lindon,et al.  Encyclopedia of spectroscopy and spectrometry , 2000 .

[9]  H. Nishimori Statistical Physics of Spin Glasses and Information Processing , 2001 .

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

[11]  Yoshihisa Yamamoto,et al.  Large-scale Ising spin network based on degenerate optical parametric oscillators , 2016, Nature Photonics.

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

[13]  George L. Nemhauser,et al.  A polynomial algorithm for the max-cut problem on graphs without long odd cycles , 1984, Math. Program..

[14]  F. Barahona On the computational complexity of Ising spin glass models , 1982 .

[15]  Klaudia Frankfurter Computers And Intractability A Guide To The Theory Of Np Completeness , 2016 .

[16]  John E. Hopcroft,et al.  Complexity of Computer Computations , 1974, IFIP Congress.

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

[18]  K. McNeil,et al.  Non-equilibrium Transitions in Sub/second Harmonic Generation: II. Quantum Theory , 1980 .

[19]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[20]  Andrew Lucas,et al.  Ising formulations of many NP problems , 2013, Front. Physics.

[21]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[22]  Yoshihisa Yamamoto,et al.  Mapping of Ising models onto injection-locked laser systems. , 2011, Optics express.

[23]  R. Car,et al.  Theory of Quantum Annealing of an Ising Spin Glass , 2002, Science.

[24]  L. Holmes,et al.  ENCYCLOPEDIA OF SPECTROSCOPY AND SPECTROMETRY , 2001 .

[25]  C. Gardiner,et al.  Generalised P-representations in quantum optics , 1980 .

[26]  M. Scully,et al.  Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations , 2003 .

[27]  Martin Grötschel,et al.  Weakly bipartite graphs and the Max-cut problem , 1981, Oper. Res. Lett..

[28]  R. Glauber Coherent and incoherent states of the radiation field , 1963 .

[29]  Yoshihisa Yamamoto,et al.  Binary phase oscillation of two mutually coupled semiconductor lasers. , 2015, Optics express.

[30]  髙田 健太,et al.  Quantum Theory and Experimental Demonstration of a Coherent Computing System with Optical Parametric Oscillators , 2015 .

[31]  Siam J. CoMPtrr,et al.  FINDING A MAXIMUM CUT OF A PLANAR GRAPH IN POLYNOMIAL TIME * , 2022 .

[32]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[33]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[34]  Jin-Kao Hao,et al.  Breakout Local Search for the Max-Cutproblem , 2013, Eng. Appl. Artif. Intell..

[35]  Yoshihisa Yamamoto,et al.  Data search by a coherent Ising machine based on an injection-locked laser network with gradual pumping or coupling , 2014 .

[36]  Oliver Thomas,et al.  Dynamically probing ultracold lattice gases via Rydberg molecules , 2015, 1506.05955.

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

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

[39]  R. Byer,et al.  Coherent Ising machine based on degenerate optical parametric oscillators , 2013, 1311.2696.

[40]  Shoko Utsunomiya,et al.  Truncated Wigner theory of coherent Ising machines based on degenerate optical parametric oscillator network , 2016, 1605.08655.

[41]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[42]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[43]  Shoko Utsunomiya,et al.  Transient time of an Ising machine based on injection-locked laser network , 2012 .

[44]  Jan Vondrák,et al.  Optimization via enumeration: a new algorithm for the Max Cut Problem , 2001, Math. Program..