Parameters Fixing Strategy for Quantum Approximate Optimization Algorithm

TL;DR

This paper introduces a parameters fixing strategy for QAOA that improves approximation ratios at large circuit depths by leveraging optimal parameters from previous iterations, enhancing performance on graph problems.

Contribution

The paper proposes a novel parameters fixing strategy for QAOA that maintains high approximation ratios at large depths by using prior optimal parameters.

Findings

High approximation ratios achieved at large circuit depths

Effective on Max-cut problems of specific graph classes

Strategy improves QAOA performance in near-term quantum devices

Abstract

The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical hybrid structure. Its quantum part consists of a parameterized alternating operator ansatz, and its classical part comprises an optimization algorithm, which optimizes the parameters to maximize the expectation value of the problem Hamiltonian. This expectation value depends highly on the parameters, this implies that a set of good parameters leads to an accurate solution. However, at large circuit depth of QAOA, it is difficult to achieve global optimization due to the multiple occurrences of local minima or maxima. In this paper, we propose a parameters fixing strategy which gives high approximation ratio on average, even at large circuit depths, by initializing QAOA with the optimal parameters obtained from the previous depths. We test our strategy on the Max-cut problem of certain classes of graphs such as the 3-regular graphs and the Erd\"{o}s-R\'{e}nyi graphs.