Reducing runtime and error in VQE using deeper and noisier quantum circuits

TL;DR

This paper introduces Robust Amplitude Estimation, a method that enables more accurate and faster expectation value estimation in VQE on NISQ devices by using deeper, noisier circuits, thus improving quantum algorithm efficiency.

Contribution

The paper presents Robust Amplitude Estimation, a novel technique that reduces runtime and error in VQE by leveraging deeper quantum circuits and improved measurement strategies.

Findings

Robust Amplitude Estimation improves expectation value precision.

Deeper circuits can yield more accurate results despite higher error rates.

The method reduces the number of measurements needed for a given accuracy.

Abstract

The rapid development of noisy intermediate-scale quantum (NISQ) devices has raised the question of whether or not these devices will find commercial use. Unfortunately, a major shortcoming of many proposed NISQ-amenable algorithms, such as the variational quantum eigensolver (VQE), is coming into view: the algorithms require too many independent quantum measurements to solve practical problems in a reasonable amount of time. This motivates the central question of our work: how might we speed up such algorithms in spite of the impact of error on NISQ computations? We demonstrate on quantum hardware that the estimation of expectation values, a core subroutine of many quantum algorithms including VQE, can be improved in terms of precision and accuracy by using a technique we call Robust Amplitude Estimation. Consequently, this method reduces the runtime to achieve the same mean-squared error compared to the standard prepare-and-measure estimation method. The surprising result is that by using deeper, and therefore more error-prone, quantum circuits, we realize more accurate quantum computations in less time. As the quality of quantum devices improves, this method will provide a proportional reduction in estimation runtime. This technique may be used to speed up quantum computations into the regime of early fault-tolerant quantum computation and aid in the realization of quantum advantage.