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

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.

References in corpus (21)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum algorithm for solving linear systems of equations
• Quantum Simulation
• Quantum Chemistry in the Age of Quantum Computing
• Quantum Algorithms Revisited
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Finding Density Functionals with Machine Learning
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Quantum measurements and the Abelian Stabilizer Problem
• Finding Exponential Product Formulas of Higher Orders
• Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
• Robust Online Hamiltonian Learning
• Quantum Hamiltonian Complexity
• Universal simulation of Hamiltonian dynamics for qudits
• Implementing unitary operators in quantum computation
• QInfer: Statistical inference software for quantum applications
• Computational complexity of time-dependent density functional theory
• Solver for the electronic V-representation problem of time-dependent density functional theory
• A Method to Calculate Correlation for Density Functional Theory on a Quantum Processor

Cited by in corpus (2)

• Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Toward Density Functional Theory on Quantum Computers?