Practical engineering of hard spin-glass instances

TL;DR

This paper presents a practical method for engineering extremely hard spin-glass Ising problems to serve as effective benchmarks for quantum annealers and classical algorithms, addressing the need for more challenging test instances.

Contribution

The authors introduce a heuristic algorithm to generate hard optimization problems without random sampling, enabling better benchmarking of quantum and classical optimization methods.

Findings

Generated instances exhibit genuine thermal hardness.

Energy landscape analysis confirms problem difficulty.

State-of-the-art algorithms perform poorly on these instances.

Abstract

Recent technological developments in the field of experimental quantum annealing have made prototypical annealing optimizers with hundreds of qubits commercially available. The experimental demonstration of a quantum speedup for optimization problems has since then become a coveted, albeit elusive goal. Recent studies have shown that the so far inconclusive results, regarding a quantum enhancement, may have been partly due to the benchmark problems used being unsuitable. In particular, these problems had inherently too simple a structure, allowing for both traditional resources and quantum annealers to solve them with no special efforts. The need therefore has arisen for the generation of harder benchmarks which would hopefully possess the discriminative power to separate classical scaling of performance with size, from quantum. We introduce here a practical technique for the engineering of extremely hard spin glass Ising-type problem instances that does not require `cherry picking' from large ensembles of randomly generated instances. We accomplish this by treating the generation of hard optimization problems itself as an optimization problem, for which we offer a heuristic algorithm that solves it. We demonstrate the genuine thermal hardness of our generated instances by examining them thermodynamically and analyzing their energy landscapes, as well as by testing the performance of various state-of-the art algorithms on them. We argue that a proper characterization of the generated instances offers a practical, efficient way to properly benchmark experimental quantum annealers, as well as any other optimization algorithm.