Analysis of Quantum Approximate Optimization Algorithm under Realistic Noise in Superconducting Qubits

TL;DR

This paper investigates how realistic noise in superconducting qubits affects the performance of the Quantum Approximate Optimization Algorithm (QAOA), revealing that hardware limitations constrain optimal circuit depth rather than the benefits of increased depth.

Contribution

The study provides a comprehensive analysis of noise impacts on QAOA performance both through simulation and real quantum hardware, highlighting hardware noise as a limiting factor for optimal circuit depth.

Findings

Optimal QAOA depth is limited by hardware noise.

Noise sources like gate error and coherence time affect performance.

Higher circuit depth does not always mean better results under realistic noise.

Abstract

The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.