Systematic improvement of the quantum approximate optimisation ansatz for combinatorial optimisation using quantum subspace expansion

TL;DR

This paper enhances the quantum approximate optimisation algorithm (QAOA) with a generator coordinate method, leading to systematic improvements in solution quality for combinatorial problems on quantum computers, especially for larger graphs.

Contribution

The paper introduces a GCM-based enhancement to QAOA, demonstrating significant performance improvements and potential scalability for combinatorial optimisation on quantum hardware.

Findings

Improved approximation ratio and fidelity for maximal independent set problems.

Surpasses standard QAOA for graphs larger than 75 nodes with only eight trial states.

Potential applicability to other combinatorial problems.

Abstract

The quantum approximate optimisation ansatz (QAOA) is one of the flagship algorithms used to tackle combinatorial optimisation on graphs problems using a quantum computer, and is considered a strong candidate for early fault-tolerant advantage. In this work, I study the enhancement of the QAOA with a generator coordinate method (GCM), and achieve systematic performances improvements in the approximation ratio and fidelity for the maximal independent set on Erd\"os-R\'enyi graphs. The cost-to-solution of the present method and the QAOA are compared by analysing the number of logical CNOT and $T$ gates required for either algorithm. Extrapolating on the numerical results obtained, it is estimated that for this specific problem and setup, the approach surpasses QAOA for graphs of size greater than 75 using as little as eight trial states. The potential of the method for other combinatorial optimisation problems is briefly discussed.