Towards solving large QUBO problems using quantum algorithms: improving the LogQ scheme

TL;DR

This paper introduces a new parameterization of the LogQ quantum algorithm for QUBO problems, enabling more efficient optimization and enhancing its scalability for large industrial problems.

Contribution

A novel LogQ parameterization that allows gradient-inspired optimization, reducing resource requirements compared to traditional methods.

Findings

Effective on analytical models

Scalable results on MaxCut problems

Improved optimization efficiency

Abstract

The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a challenge related to the optimization of its free parameters, which requires the usage of resource intensive evolutionary or even global optimization algorithms. We propose a new LogQ parameterization that can be optimized with a gradient-inspired method, which is less resource-intensive and thus strengthens the advantage of LogQ over QAOA for large/industrial problems. We illustrate the features of our method on an analytical model and present larger scale numerical results on MaxCut problems.