Hyperscaling in the coherent hyperspin machine

TL;DR

This paper introduces a high-dimensional embedding and dimensional annealing approach for Ising machines, significantly improving their success probability and scalability in optimization tasks.

Contribution

It proposes a novel hyperscaling method that counteracts exponential success probability drop in Ising machines through high-dimensional embedding and annealing techniques.

Findings

Exponential improvement in success probability with high-dimensional embedding.

Feasible experimental implementation using existing coherent Ising machine technology.

Applicable to both quantum and classical Ising machines through engineered nonlinearities.

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.