The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

TL;DR

This paper investigates how errors impact the variational quantum eigensolver (VQE) in quantum chemistry, offering strategies to optimize resource use and improve energy calculation accuracy on noisy quantum hardware.

Contribution

It provides an analysis of error effects on VQE and proposes optimized protocols for resource allocation to enhance result precision on current noisy quantum devices.

Findings

Allow some noise in intermediate evaluations for efficiency

High final readout precision is crucial

Running experiments quickly avoids parameter drift

Abstract

Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE) -- an algorithm to calculate the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE, and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, as well as physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal way of running the hybrid classical-quantum optimization is to (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but require high final readout precision, (ii) emphasize efficient problem encoding and ansatz parametrization, and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently it is quite difficult to obtain trustworthy calculations of molecular energies.