Fast quantum imaginary time evolution

TL;DR

Fast QITE significantly accelerates quantum imaginary time evolution by reducing its complexity from exponential to linear, enabling quantum advantage in sampling matrix exponentials and improving finite temperature simulations.

Contribution

The paper introduces Fast QITE, a novel implementation that drastically reduces the computational scaling of QITE from exponential to linear.

Findings

Achieves linear scaling in QITE algorithmic cost

Enables quantum advantage in sampling diagonal matrix elements

Discusses application to finite temperature simulations

Abstract

A fast implementation of the quantum imaginary time evolution (QITE) algorithm called Fast QITE is proposed. The algorithmic cost of QITE typically scales exponentially with the number of particles it nontrivially acts on in each Trotter step. In contrast, a Fast QITE implementation reduces this to only a linear scaling. It is shown that this speed up leads to a quantum advantage when sampling diagonal elements of a matrix exponential, which cannot be achieved using the standard implementation of the QITE algorithm. Finally the cost of implementing Fast QITE for finite temperature simulations is also discussed.