On the hardness of quadratic unconstrained binary optimization problems

TL;DR

This paper investigates the solution landscape of small QUBO problems using enumeration and explores how the success probability of a quantum annealer correlates with Hamming distance distributions, providing insights into problem hardness.

Contribution

It introduces a method to characterize QUBO solutions via Hamming distances and links these properties to quantum annealer performance on larger instances.

Findings

Hamming distance distributions predict quantum annealer success probabilities

Enumeration characterizes solution landscapes of small QUBO problems

Quantum annealer performance correlates with problem hardness metrics

Abstract

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a QUBO correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.