Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes

TL;DR

This paper explores how different coordinate systems and measurement schemes can significantly reduce the measurement overhead in estimating vibrational states on quantum computers, enabling more efficient quantum simulations of molecules.

Contribution

It introduces methods to optimize measurement schemes for vibrational states by utilizing coordinate transformations, reducing measurement requirements compared to traditional approaches.

Findings

Average of 3-fold reduction in measurements for three-mode molecules.

Up to 7-fold reduction in measurement count for certain molecules.

Automated construction of qubit Hamiltonians from vibrational data.

Abstract

One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structure of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.