Quantum Dynamical Emulation of Imaginary Time Evolution

TL;DR

This paper presents a new quantum algorithm called Imaginary Time Quantum Dynamical Emulation (ITQDE) that maps non-unitary imaginary time evolution to unitary operations, enabling estimation of ground states, spectra, and thermodynamic properties.

Contribution

The paper introduces ITQDE, a novel method for emulating imaginary time evolution using unitary operations, and develops algorithms for Hamiltonian spectrum estimation and thermodynamic analysis.

Findings

Validated ITQDE through numerical simulations.

Implemented ITQDE on quantum hardware.

Demonstrated estimation of ground and thermal states.

Abstract

We introduce a constructive method for mapping non-unitary dynamics to a weighted set of unitary operations. We utilize this construction to derive a new correspondence between real and imaginary time, which we term Imaginary Time Quantum Dynamical Emulation (ITQDE). This correspondence enables an imaginary time evolution to be constructed from the overlaps of states evolved in opposite directions. We develop ITQDE as a tool for estimating the ground and thermal state properties associated with a given Hamiltonian. We additionally provide a prescription for leveraging ITQDE to estimate the complete Hamiltonian spectrum. We go on to develop a quantum algorithm for computing Hamiltonian spectra based on ITQDE, which we validate through numerical simulations and quantum hardware implementations. We conclude with a discussion of how ITQDE can be utilized more broadly to derive novel thermodynamic results, including a generalisation of the Hubbard-Stratonovich transformation.