Hyperscaling in the coherent hyperspin machine

Abstract

Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability of success in finite-size scaling. We show that by exploiting high dimensional embedding of the Ising Hamiltonian and subsequent dimensional annealing, the drop is counteracted by an exponential improvement in the performance. Our analysis relies on extensive statistics of the convergence dynamics by high-performance computing. We propose a realistic experimental implementation of the new annealing device by off-the-shelf coherent Ising machine technology. The hyperscaling heuristics can also be applied to other quantum or classical Ising machines by engineering nonlinear gain, loss, and non-local couplings.

6 pages, 4 figures

References in corpus (5)

• Large-scale photonic Ising machine by spatial light modulation
• Can nonlinear parametric oscillators solve random Ising models?
• Coherent dynamics in frustrated coupled parametric oscillators
• Observing a Phase Transition in a Coherent Ising Machine
• 10-GHz-clock time-multiplexed non-degenerate optical parametric oscillator network with a variable planar lightwave circuit interferometer

Cited by in corpus (6)

• Dawn and fall of non-Gaussianity in the quantum parametric oscillator
• Using continuation methods to analyse the difficulty of problems solved by Ising machines
• Frustration Elimination and Excited State Search in Coherent Ising Machines
• Equalized Hyperspin Machine
• Quantum hyperspins: Highly nonclassical collective behavior in quantum optical parametric oscillators
• Metrics for spin-based computing