Coherent Ising machines with error correction feedback

Abstract

A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial optimization problems. However, there are two challenges in the previously proposed approach: (1) The machine can be trapped by local minima which increases exponentially with problem size and (2) the machine fails to map a target Hamiltonian correctly on the loss landscape of a neural network due to oscillator amplitude heterogeneity. Both of them lead to erroneous solutions rather than correct answers. In this paper, we show that it is possible to overcome these two problems partially but simultaneously by introducing error detection and correction feedback mechanism. The proposed machine achieves efficient sampling of degenerate ground states and low-energy excited states via its inherent migration property during a solution search process.

12 pages, 7 figures

References in corpus (16)

• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• On the impossibility of distilling Gaussian states with Gaussian operations
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators
• Realizing the $XY$ Hamiltonian in polariton simulators
• Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer
• Destabilization of local minima in analog spin systems by correction of amplitude heterogeneity
• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Hysteretic Optimization
• Quantum correlation in degenerate optical parametric oscillators with mutual injections
• Networks of non-equilibrium condensates for global optimization
• A Quantum Model for Coherent Ising Machines: Discrete-time Measurement Feedback Formulation
• Truncated Wigner function theory of coherent Ising machines based on degenerate optical parametric oscillator network
• A Quantum Model for Coherent Ising Machine: Stochastic Differential Equations with Replicator Dynamics
• Entanglement and quantum discord in optically coupled coherent Ising machines

Cited by in corpus (13)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Coherent Ising machines -- Quantum optics and neural network perspectives
• Can nonlinear parametric oscillators solve random Ising models?
• Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine
• A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization
• Combinatorial optimization solving by coherent Ising machines based on spiking neural networks
• Effective implementation of $l_0$-Regularised Compressed Sensing with Chaotic-Amplitude-Controlled Coherent Ising Machines
• Mean-field Coherent Ising Machines with artificial Zeeman terms
• Dawn and fall of non-Gaussianity in the quantum parametric oscillator
• Highly Versatile FPGA-Implemented Cyber Coherent Ising Machine
• Frustration Elimination and Excited State Search in Coherent Ising Machines
• Requirements on bit resolution in optical Ising machine implementations
• Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning