Solving QUBOs with a quantum-amenable branch and bound method

TL;DR

This paper presents an exact classical branch and bound solver for QUBO problems that leverages quantum-inspired bounds and high-performance techniques, demonstrating competitive performance against state-of-the-art solvers.

Contribution

It introduces a novel classical solver for QUBO leveraging quantum-inspired bounds and advanced heuristics, validated through extensive empirical analysis.

Findings

The solver matches or exceeds performance of existing QUBO solvers.

Quantum speedup in branch and bound faces significant practical challenges.

High-performance heuristics significantly improve solver efficiency.

Abstract

Due to the expected disparity in quantum vs. classical clock speeds, quantum advantage for branch and bound algorithms is more likely achievable in settings involving large search trees and low operator evaluation costs. Therefore, in this paper, we describe and experimentally validate an exact classical branch and bound solver for quadratic unconstrained binary optimization (QUBO) problems that matches these criteria. Our solver leverages cheap-to-implement bounds from the literature previously proposed for Ising models, including that of Hartwig, Daske, and Kobe from 1984. We detail a variety of techniques from high-performance computing and operations research used to boost solver performance, including a global variable reordering heuristic, a primal heuristic based on simulated annealing, and a truncated computation of the recursive bound. We also outline a number of simple and inexpensive bound extrapolation techniques. Finally, we conduct an extensive empirical analysis of our solver, comparing its performance to state-of-the-art QUBO and MaxCut solvers, and discuss the challenges of a speedup via quantum branch and bound beyond those faced by any quadratic quantum speedup.