Reliable Optimization Under Noise in Quantum Variational Algorithms

TL;DR

This paper investigates the impact of sampling noise on Variational Quantum Eigensolver (VQE) optimization, benchmarking classical optimizers, and proposing adaptive metaheuristics and bias correction techniques for more reliable quantum chemistry calculations.

Contribution

It introduces a comprehensive analysis of noise effects on VQE optimization and proposes practical strategies, including adaptive metaheuristics and bias correction, to improve reliability under noisy conditions.

Findings

Adaptive metaheuristics outperform traditional optimizers in noisy regimes.

Bias correction via population mean improves optimizer stability.

Guidelines for co-designing ansatz and optimizer enhance VQE robustness.

Abstract

The optimization of Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise, which distorts the cost landscape, creates false variational minima, and induces statistical bias called winner's curse. We investigate this phenomenon by benchmarking eight classical optimizers spanning gradient-based, gradient-free, and metaheuristic methods on quantum chemistry Hamiltonians H$_2$, H$_4$ chain, LiH (in both full and active spaces) using the truncated Variational Hamiltonian Ansatz. We analyze difficulties of gradient-based methods (e.g., SLSQP, BFGS) in noisy regimes, where they diverge or stagnate. We show that the bias of estimator can be corrected by tracking the \textit{population mean}, rather than the biased best individual when using population based optimizer. Our findings, which are shown to generalize to hardware-efficient circuits and condensed matter models, identify adaptive metaheuristics (specifically CMA-ES and iL-SHADE) as the most effective and resilient strategies. We conclude by presenting a set of practical guidelines for reliable VQE optimization under noise, centering on the co-design of physically motivated ansatz and the use of adaptive optimizers.