Advantages of multistage quantum walks over QAOA

TL;DR

This paper demonstrates that multistage quantum walks (MSQW) outperform the quantum approximate optimization algorithm (QAOA) in solving Ising Hamiltonian-based optimization problems, even with minimal stages and heuristic parameters.

Contribution

The work provides a comparative analysis showing MSQW's advantages over QAOA, including performance with fewer stages and without classical optimization.

Findings

MSQW outperforms QAOA with equivalent resources.

MSQW performs well even with few stages and heuristic parameters.

No classical optimization needed for effective MSQW performance.

Abstract

Methods to find the solution state for optimization problems encoded into Ising Hamiltonians are a very active area of current research. In this work we compare the quantum approximate optimization algorithm (QAOA) with multi-stage quantum walks (MSQW). Both can be used as variational quantum algorithms, where the control parameters are optimized classically. A fair comparison requires both quantum and classical resources to be assessed. Alternatively, parameters can be chosen heuristically, as we do in this work, providing a simpler setting for comparisons. Using both numerical and analytical methods, we obtain evidence that MSQW outperforms QAOA, using equivalent resources. We also show numerically for random spin glass ground state problems that MSQW performs well even for few stages and heuristic parameters, with no classical optimization.