The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry

TL;DR

This paper investigates how noise impacts the performance and ranking of hardware efficient ansatze in variational quantum algorithms for quantum chemistry, revealing that noise alters optimal circuit choices and expressibility is not a reliable metric.

Contribution

It provides a comprehensive analysis of noise effects on ansatz performance, evaluates the expressibility measure's relevance, and highlights the importance of hardware-specific considerations.

Findings

Noise changes the ranking of ansatz performance.

Expressibility weakly correlates with VQE results.

Hardware noise models influence optimal ansatz selection.

Abstract

Variational quantum algorithms are suitable for use on noisy quantum systems. One of the most important use-cases is the quantum simulation of materials, using the variational quantum eigensolver (VQE). To optimize VQE performance, a suitable parameterized quantum circuit (ansatz) must be selected. We investigate a class of ansatze that incorporates knowledge of the quantum hardware, namely the hardware efficient ansatze. The performance of hardware efficient ansatze is affected differently by noise, and our goal is to study the effect of noise on evaluating which ansatz gives more accurate results in practice. First, we study the effect of noise on the different hardware efficient ansatze by benchmarking and ranking the performance of each ansatz family (i) on a chemistry application using VQE and (ii) by the recently established metric of "expressibility". The results demonstrate the ranking of optimal circuits does not remain constant in the presence of noise. Second, we evaluate the suitability of the expressibility measure in this context by performing a correlation study between expressibility and the performance of the same circuits on a chemistry application using VQE. Our simulations reveal a weak correlation and therefore demonstrate that expressibility is not an adequate measure to quantify the effectiveness of parameterized quantum circuits for quantum chemistry. Third, we evaluate the effect of different quantum device noise models on the ordering of which ansatz family is best. Interestingly, we see that to decide which ansatz is optimal for use, one needs to consider the specific hardware used even within the same family of quantum hardware.