Optimized QUBO formulation methods for quantum computing

TL;DR

This paper introduces novel methods to reduce variables in QUBO formulations, enabling more efficient use of NISQ quantum devices for solving complex combinatorial optimization problems.

Contribution

It presents new techniques, the iterative quadratic polynomial and master-satellite methods, for efficient QUBO reformulation without approximating constraints.

Findings

Reduced variable count in QUBO formulations improves quantum optimization efficiency.

Demonstrated effectiveness on a real-world financial optimization problem.

Compared performance of D-wave Advantage and Advantage2 quantum annealers.

Abstract

Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for these QUBO reformulations in order to unlock the possibility to efficiently obtain optimal solutions for a class of optimization problems with NISQ devices. This is achieved by introducing novel tools that allow an efficient use of slack variables, even for problems with non-linear constraints, without the need to approximate the starting problem. We divide our new techniques in two independent parts, called the iterative quadratic polynomial and the master-satellite methods. Hence, we show how to apply our techniques in case of an NP-hard optimization problem inspired by a real-world financial scenario called Max-Profit Balance Settlement. We follow by submitting several instances of this problem to two D-wave quantum annealers, comparing the performances of our novel approach with the standard methods used in these scenarios. Moreover, this study allows to appreciate several performance differences between the D-wave Advantage and Advantage2 quantum annealers.