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

Abstract

Variational quantum algorithms are hybrid quantum classical algorithms suitable for use on Noisy Intermediate Scale Quantum (NISQ) devices. The most promising variational quantum algorithm for quantum simulation of materials on existing quantum computers, is the Variational Quantum Eigensolver (VQE). To optimise the performance of the VQE algorithm, a suitable parameterised quantum circuit (ansatz) must be selected that represents the solution space well. Several ansatz have been shown to perform well for quantum chemistry problems on near term quantum computers. We investigate a class of such ansatzes that incorporates knowledge of the quantum hardware, referred to as the hardware efficient ansatz. Since the performance of the hardware efficient ansatz is affected differently by noise, our goal is to see how noise changes which ansatz is the best for a quantum chemistry problem. First, we study the effect of noise on the different hardware efficient ansatz by benchmarking and ranking the performance of each ansatz family on a chemistry application using VQE and by a recently established metric called “expressibility”. The results demonstrate, the ranking of optimal circuits does not remain constant in the presence of noise. Second, we evaluate the validity of the expressibility measure, by statistically analysing the correlation between expressibility and the performance of the circuits applied to a quantum chemistry application using VQE. Our simulations reveal a weak correlation and therefore demonstrate that expressibility is not an adequate measure to quantify the potential effectiveness of parameterised quantum circuits for quantum chemistry. In addition, we explore the underlying reasons for this weak correlation by demonstrating that simple non-uniform parameter sampling significantly boosts the expressibility of a given fixed circuit. Such non-uniform sampling begins to capture the intertwined nature between the ansatz, the molecule and the classical optimizer component of VQE. Third, we evaluate the effect of realistic noise models of quantum hardware 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 even within the same family of quantum hardware.