Multidimensional hyperspin machine

TL;DR

The paper introduces a hyperspin machine capable of simulating multidimensional continuous spin models, enabling flexible interpolation between models and improving success probabilities in combinatorial optimization tasks.

Contribution

It presents a novel hyperspin machine that can simulate arbitrary multidimensional spins and interpolate between models, expanding the capabilities of spin-based computational systems.

Findings

Hyperspin machine successfully simulates high-dimensional spin models.

Dimensional annealing improves success probability in optimization.

Machine can be realized with existing hardware for large-scale applications.

Abstract

From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and study NP-hard graphs of hyperspins. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call "dimensional annealing". When interpolating between the XY and the Ising model, the dimensional annealing impressively increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.