Gaussian optical Ising machines

It has recently been shown that optical parametric oscillator (OPO) Ising machines, consisting of coupled optical pulses circulating in a cavity with parametric gain, can be used to probabilistically find low-energy states of Ising spin systems. In this work, we study optical Ising machines that operate under simplified Gaussian dynamics. We show that these dynamics are sufficient for reaching probabilities of success comparable to previous work. Based on this result, we propose modified optical Ising machines with simpler designs that do not use parametric gain yet achieve similar performance, thus suggesting a route to building much larger systems.

[1]  Gerardo Adesso,et al.  Continuous Variable Quantum Information: Gaussian States and Beyond , 2014, Open Syst. Inf. Dyn..

[2]  R J Lipton,et al.  DNA solution of hard computational problems. , 1995, Science.

[3]  Ken-ichi Kawarabayashi,et al.  A coherent Ising machine with quantum measurement and feedback control , 2015 .

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

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

[6]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[7]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

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

[9]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[10]  Kae Nemoto,et al.  Efficient classical simulation of continuous variable quantum information processes. , 2002, Physical review letters.

[11]  Ken-ichi Kawarabayashi,et al.  A coherent Ising machine for 2000-node optimization problems , 2016, Science.

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

[13]  Gerard J. Milburn,et al.  Production of squeezed states in a degenerate parametric amplifier , 1981 .

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

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

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

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

[18]  Ken-ichi Kawarabayashi,et al.  Uncertain behaviours of integrated circuits improve computational performance , 2015, Scientific Reports.

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

[20]  Kazuyuki Aihara,et al.  A fully programmable 100-spin coherent Ising machine with all-to-all connections , 2016, Science.

[21]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.