The Effect of Noise on the Optimality of Variational Algorithms for Quantum Chemistry
Variational quantum algorithms are hybrid quantum-classical algorithms suitable for use on noisy intermediate scale quantum devices (NISQ), and appear to provide the most promising near term application of quantum computers. One of the most important use-cases is the quantum simulation of materials, specifically, using the variational quantum eigensolver (VQE). A crucial component of VQE, is the selection of a parameterised ansatz circuit. Here we study the effect of noise on evaluating which ansatz circuit gives more accurate results in practice. First, we examine the metric to evaluate the performance. One commonly used metric is that of ``expressibility'', and we statistically assess the correlation between expressibility and the performance of the circuits applied to VQE for small molecules. Simulations are performed classically and on noisy IBM quantum simulators to understand and compare the performance of the methods under realistic noisy conditions. 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 a 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. Second, we evaluate the effect of noise 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.