3-Regular 3-XORSAT Planted Solutions Benchmark of Classical and Quantum Heuristic Optimizers

TL;DR

This paper benchmarks various classical and quantum heuristic optimizers on a specific hard constraint satisfaction problem, revealing their relative performance and scaling behaviors.

Contribution

It provides the first comprehensive comparison of multiple hardware and algorithmic approaches on 3-regular 3-XORSAT problems, highlighting their strengths and limitations.

Findings

SATonGPU and DAU have the smallest scaling exponents.

SATonGPU has a significant parallelism advantage with the smallest prefactor.

The benchmark offers an objective assessment of hardware performance on a hard problem class.

Abstract

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving Quadratic Unconstrained Binary Optimization (QUBO) problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (3-regular 3-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's Digital Annealer Unit (DAU), the D-Wave Advantage quantum annealer, a Virtual MemComputing Machine, Toshiba's Simulated Bifurcation Machine (SBM), the SATonGPU algorithm from Bernaschi et al., and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.