Reducing Binary Quadratic Forms for More Scalable Quantum Annealing

TL;DR

This paper investigates preprocessing techniques to reduce the size of quadratic binary problems, enabling more efficient use of limited qubits in quantum annealers for solving NP-hard graph problems.

Contribution

It introduces methods for identifying persistent variables in quadratic binary programs, significantly reducing problem size for quantum annealing.

Findings

Preprocessing can substantially decrease the number of variables needed.

Strong and weak persistencies are highly instance-specific.

Reductions improve scalability of quantum annealing for NP-hard problems.

Abstract

Recent advances in the development of commercial quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary programs. However, the relatively small number of available qubits (around 1000 for the D-Wave 2X quantum annealer) poses a severe limitation to the range of problems that can be solved. This paper explores the suitability of preprocessing methods for reducing the sizes of the input programs and thereby the number of qubits required for their solution on quantum computers. Such methods allow us to determine the value of certain variables that hold in either any optimal solution (called strong persistencies) or in at least one optimal solution (weak persistencies). We investigate preprocessing methods for two important NP-hard graph problems, the computation of a maximum clique and a maximum cut in a graph. We show that the identification of strong and weak persistencies for those two optimization problems is very instance-specific, but can lead to substantial reductions in the number of variables.