A coherent Ising machine with quantum measurement and feedback control

An optical parametric oscillator network driven by a quantum measurement-feedback circuit, composed of optical homodyne detectors, analog-to-digital conversion devices and field programmable gate arrays (FPGA), is proposed and analysed as a scalable coherent Ising machine. The new scheme has an advantage that a large number of optical coupling paths, which is proportional to the square of a problem size in the worst case, can be replaced by a single quantum measurement-feedback circuit. There is additional advantage in the new scheme that a three body or higher order Ising interaction can be implemented in the FPGA digital circuit. Noise associated with the measurement-feedback process is governed by the standard quantum limit. Numerical simulation based on c-number coupled Langevin equations demonstrate a satisfying performance of the proposed Ising machine against the NP-hard MAX-CUT problems.

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

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

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

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

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

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

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

[8]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

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

[10]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

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

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

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

[14]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

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

[16]  Viktor Dotsenko,et al.  Introduction to the Replica Theory of Disordered Statistical Systems: Preface , 2000 .

[17]  Dmitri V. Averin,et al.  Decoherence induced deformation of the ground state in adiabatic quantum computation , 2012, Scientific Reports.

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