QAOA Performance in Noisy Devices: The Effect of Classical Optimizers and Ansatz Depth

TL;DR

This study investigates how noise affects the performance of classical optimizers and the optimal depth of QAOA circuits on NISQ devices, highlighting that noise influences optimizer choice and optimal circuit depth.

Contribution

It provides an analysis of optimizer performance under realistic noise conditions and identifies optimal circuit depth for QAOA in noisy environments.

Findings

Adam and AMSGrad perform best with shot noise.

SPSA, Adam, and AMSGrad excel under real device noise.

Optimal QAOA depth is around six layers for 5-qubit problems.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimiz\-ation problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost function, computed on the quantum device. This paper presents an investigation into the impact of realistic noise on the classical optimizer and the determination of optimal circuit depth for the Quantum Approximate Optimization Algorithm (QAOA) in the presence of noise. We find that, while there is no significant difference in the performance of classical optimizers in a state vector simulation, the Adam and AMSGrad optimizers perform best in the presence of shot noise. Under the conditions of real noise, the SPSA optimizer, along with ADAM and AMSGrad, emerge as the top performers. The study also reveals that the quality of solutions to some 5 qubit minimum vertex cover problems increases for up to around six layers in the QAOA circuit, after which it begins to decline. This analysis shows that increasing the number of layers in the QAOA in an attempt to increase accuracy may not work well in a noisy device.