Heuristic Recurrent Algorithms for Photonic Ising Machines

Abstract

The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort recently toward developing novel, application-specific hardware, across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the true potential of such novel architectures requires the development of featured algorithms which optimally exploit their fundamental properties. We here present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures that allows for fast and efficient sampling from distributions of combinatorially hard Ising problems. Since the PRIS relies essentially on vector-to-fixed matrix multiplications, we suggest the implementation of the PRIS in photonic parallel networks, which realize these operations at an unprecedented speed. The PRIS provides sample solutions to the ground state of arbitrary Ising models, by converging in probability to their associated Gibbs distribution. By running the PRIS at various noise levels, we probe the critical behavior of universality classes and their critical exponents. In addition to the attractive features of photonic networks, the PRIS relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work suggests speedups in heuristic methods via photonic implementations of the PRIS. We also hint at a broader class of (meta)heuristic algorithms derived from the PRIS, such as combined simulated annealing on the noise and eigenvalue dropout levels. Our algorithm can also be implemented in a competitive manner on fast parallel electronic hardware, such as FPGAs and ASICs.

Main text : 10 pages, 4 figures; Supplementary Information: 33 pages, 16 figures

References in corpus (10)

• Deep Learning with Coherent Nanophotonic Circuits
• All-Optical Machine Learning Using Diffractive Deep Neural Networks
• Neuromorphic Silicon Photonic Networks
• Efficient, Compact and Low Loss Thermo-Optic Phase Shifter in Silicon
• Large-Scale Optical Neural Networks based on Photoelectric Multiplication
• Large-scale photonic Ising machine by spatial light modulation
• Reprogrammable Electro-Optic Nonlinear Activation Functions for Optical Neural Networks
• Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer
• Monolayer Graphene as Saturable Absorber in Mode-locked Laser
• Deep optical neural network by living tumour brain cells

Cited by in corpus (16)

• Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons
• Nanophotonic spin-glass for realization of a coherent Ising machine
• Coherent Ising machines -- Quantum optics and neural network perspectives
• Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine
• Scalable spin-glass optical simulator
• Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity
• Collective and synchronous dynamics of photonic spiking neurons
• Ising Machines' Dynamics and Regularization for Near-Optimal Large and Massive MIMO Detection
• Antiferromagnetic spatial photonic Ising machine through optoelectronic correlation computing
• Quadrature Photonic Spatial Ising Machine
• Fock State-enhanced Expressivity of Quantum Machine Learning Models
• On-demand Photonic Ising Machine with Simplified Hamiltonian Calculation by Phase encoding and Intensity Detection
• Observation of Distinct Phase Transitions in a Nonlinear Optical Ising Machine
• Solving the max-3-cut problem using synchronized dissipative networks
• Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning
• A CMOS-compatible Ising Machine with Bistable Nodes