Refining resource estimation for the quantum computation of vibrational molecular spectra through Trotter error analysis

TL;DR

This paper provides a detailed analysis of quantum resource requirements for vibrational molecular spectra simulations, focusing on Trotter error analysis to improve resource estimation accuracy for fault-tolerant quantum computers.

Contribution

It introduces a refined method for estimating quantum resources needed for vibrational structure calculations, emphasizing Trotter error analysis and practical applications to specific molecules.

Findings

Quantitative estimates of logical qubits and gates for vibrational spectra

Analysis of Trotter errors using nested commutators

Guidance on quantum advantage potential in vibrational simulations

Abstract

Accurate simulations of vibrational molecular spectra are expensive on conventional computers. Compared to the electronic structure problem, the vibrational structure problem with quantum computers is less investigated. In this work we accurately estimate quantum resources, such as number of logical qubits and quantum gates, required for vibrational structure calculations on a programmable quantum computer. Our approach is based on quantum phase estimation and focuses on fault-tolerant quantum devices. In addition to asymptotic estimates for generic chemical compounds, we present a more detailed analysis of the quantum resources needed for the simulation of the Hamiltonian arising in the vibrational structure calculation of acetylene-like polyynes of interest. Leveraging nested commutators, we provide an in-depth quantitative analysis of trotter errors compared to the prior investigations. Ultimately, this work serves as a guide for analyzing the potential quantum advantage within vibrational structure simulations.