Quantum algorithm for the microcanonical Thermal Pure Quantum method

TL;DR

This paper introduces a quantum algorithm that efficiently constructs thermal pure quantum states at low temperatures, enabling accurate evaluation of thermodynamic properties in quantum systems.

Contribution

It presents a novel quantum algorithm combining quantum singular value transformation to improve the construction of TPQ states at finite temperatures.

Findings

Efficient realization of multiple Hamiltonian products.

Systematic construction of low-temperature TPQ states.

Enhanced evaluation of thermodynamic quantities.

Abstract

We present a quantum algorithm for the microcanonical thermal pure quantum (TPQ) method, which has an advantage in evaluating thermodynamic quantities at finite temperatures, by combining with some recently developed techniques derived from quantum singular value transformation. When the ground energy of quantum systems has already been obtained precisely, the multiple products of the Hamiltonian are efficiently realized and the TPQ states at low temperatures are systematically constructed in quantum computations.