PNNL

Abstract

The still maturing noisy intermediate-scale quantum (NISQ) technology places strict limitations on the algorithms that can be implemented efficiently. In the realm of quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become ubiquitous, with many variations. Common to these approaches is use of the functional form of the ansatz as a degree of freedom, whose parameters are determined variationally in a feedback loop between the quantum processor and its conventional counterpart. Alternatively, a promising new avenue has been unraveled by the quantum variations of connected moments expansions (CMX). Contrasting with VQE-based methods, CMX uses an energy functional that is guaranteed to approach the exact ground state energy, provided the state prepared by the circuit has non-vanishing overlap with the true ground state. However, for a given nite CMX order, the circuit may bear a significant impact on the energy accuracy. Here we use ADAPT-VQE algorithm to test shallow circuit construction strategies that are not expected to impede their implementation in quantum hardware, while granting sizable accuracy improvement in the computed ground state energies. We also show that we can take advantage of the fact that the terms in the connected moments are highly recurring in different powers, incurring a sizable reduction in the number of necessary measurements. By coupling this measurement caching with a threshold that determines whether a given term is to be measured based on its associated scalar coefficients, we observe further reduction in the number of circuit implementations while allowing for tunable accuracy.