A quantum walk assisted approximate algorithm for bounded NP optimisation problems

TL;DR

This paper introduces a quantum walk-assisted approximate algorithm based on QAOA for efficiently solving bounded NP optimization problems, integrating quantum walks with variational schemes to improve solution quality.

Contribution

It generalizes QAOA with quantum walks and phase shifts, enabling better handling of problem constraints in NPO problems, demonstrated on minimum vertex cover.

Findings

Promising results with few optimization parameters

Effective integration of quantum walks for constraint handling

Potential for improved approximate solutions in NPO problems

Abstract

This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts, and use the quantum walks to integrate the problem constraints of NPO problems. We apply the recent concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. The algorithm is applied to the problem of minimum vertex cover, showing promising results using only a fixed and low number of optimisation parameters.