A comparison of three ways to measure time-dependent densities with quantum simulators

TL;DR

This paper compares three methods for measuring time-dependent densities in quantum simulations, finding that direct measurement is generally preferable, with potential uses for Bayesian phase estimation and harmonic inversion in specific contexts.

Contribution

It provides a comparative analysis of measurement techniques for quantum simulations of time-dependent densities, highlighting the advantages of direct measurement and exploring alternative methods.

Findings

Direct measurement is the most effective method tested.

Bayesian phase estimation and harmonic inversion may be useful in specific scenarios.

Tests conducted on Rigetti's quantum virtual device support the conclusions.

Abstract

Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized. In fact, many of the modern hybrid-classical approaches are essentially quantum measurements of states with short quantum circuit descriptions. Here, we compare and examine three methods of extracting the time-dependent one-particle probability density from a quantum simulation: direct $Z$-measurement, Bayesian phase estimation and harmonic inversion. We have tested these methods in the context of the potential inversion problem of time-dependent density functional theory. Our test results suggest that direct measurement is the preferable method. We also highlight areas where the other two methods may be useful and report on tests using Rigetti's quantum virtual device. This study provides a starting point for imminent applications of quantum computing.