Short-time simulation of quantum dynamics by Pauli measurements

TL;DR

This paper introduces a hybrid quantum-classical method for simulating short-time quantum dynamics using Pauli measurements and a truncated Taylor series, with rigorous error bounds and potential applications in Hamiltonian learning and device verification.

Contribution

It presents a novel measurement-based simulation approach for quantum dynamics that is efficient for short times and includes rigorous error analysis.

Findings

Method provides rigorous error bounds for short-time simulations.

Applicable to Hamiltonian learning and quantum device verification.

Enables estimation of low-order Taylor approximations of quantum functions.

Abstract

Simulating the dynamics of complex quantum systems is a central application of quantum devices. Here, we propose leveraging the power of measurements to simulate short-time quantum dynamics of physically prepared quantum states in classical post-processing using a truncated Taylor series approach. While limited to short simulation times, our hybrid quantum-classical method is equipped with rigorous error bounds. It is extendable to estimate low-order Taylor approximations of smooth, time-dependent functions of tractable linear combinations of measurable operators. These insights can be made use of in the context of Hamiltonian learning and device verification, short-time imaginary time evolution, or the application of intractable operations to sub-universal quantum simulators in classical post-processing.