Coherent Ising machines -- Quantum optics and neural network perspectives

Abstract

A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the "strongest" collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump rate or network coupling rate is increased from below to above threshold, however, the eigenvectors with a smallest eigenvalue of Ising coupling matrix [J_ij] appear near threshold and impede the machine to relax to true ground states. Two complementary approaches to attack this problem are described here. One approach is to utilize squeezed/anti-squeezed vacuum noise of OPOs below threshold to produce coherent spreading over numerous local minima via quantum noise correlation, which could enable the machine to access either true ground states or excited states with eigen-energies close enough to that of ground states above threshold. The other approach is to implement real-time error correction feedback loop so that the machine migrates from one local minimum to another during an explorative search for ground states. Finally, a set of qualitative analogies connecting the CIM and traditional computer science techniques are pointed out. In particular, belief propagation and survey propagation used in combinatorial optimization are touched upon.

arXiv comment32 pages and 7 figures

References in corpus (33)

• Quantum Mechanics helps in searching for a needle in a haystack
• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Inseparability criterion for continuous variable systems
• Quantum random walks - an introductory overview
• Emergent complex neural dynamics
• Are biological systems poised at criticality?
• Dynamical synapses causing self-organized criticality in neural networks
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• Quantum versus classical correlations in Gaussian states
• Statistical physics of inference: Thresholds and algorithms
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators
• Large-scale photonic Ising machine by spatial light modulation
• Realizing the $XY$ Hamiltonian in polariton simulators
• Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer
• The statistics of critical points of Gaussian fields on large-dimensional spaces
• Optimization hardness as transient chaos in an analog approach to constraint satisfaction
• Destabilization of local minima in analog spin systems by correction of amplitude heterogeneity
• Heuristic Recurrent Algorithms for Photonic Ising Machines
• Dynamics of Random Neural Networks with Bistable Units
• Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Statistical mechanics of complex neural systems and high dimensional data
• Hysteretic Optimization
• Quantum correlation in degenerate optical parametric oscillators with mutual injections
• Networks of non-equilibrium condensates for global optimization
• Topological field theory and computing with instantons
• 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
• Dynamical TAP approach to mean field glassy systems
• Coherent Ising machines with error correction feedback
• Statistical Mechanics of High-Dimensional Inference

Cited by in corpus (18)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Applications and Techniques for Fast Machine Learning in Science
• A Ferroelectric Compute-in-Memory Annealer for Combinatorial Optimization Problems
• Multidimensional hyperspin machine
• Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine
• Controlled asymmetric Ising model implemented with parametric micromechanical oscillators
• On computational capabilities of Ising machines based on nonlinear oscillators,
• The coherent Ising machine with quantum feedback: the total and conditional master equation methods
• Mean-field Coherent Ising Machines with artificial Zeeman terms
• Dawn and fall of non-Gaussianity in the quantum parametric oscillator
• Equalized Hyperspin Machine
• Zeno-effect Computation: Opportunities and Challenges
• A general learning scheme for classical and quantum Ising machines
• Three Strongly Coupled Kerr Parametric Oscillators Forming a Boltzmann Machine
• Entropy Computing, A Paradigm for Optimization in Open Photonic Systems
• Emergent Equilibrium in All-Optical Single Quantum-Trajectory Ising Machines
• Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization
• Explicitly Quantum-parallel Computation by Displacements