Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers

TL;DR

This paper introduces an efficient quantum algorithm for calculating the Gibbs partition function using imaginary time evolution, requiring fewer qubits and measurements than previous methods, suitable for near-term quantum computers.

Contribution

The authors propose a novel scheme that computes the Gibbs partition function with minimal qubit resources and avoids extensive state extrapolation, improving feasibility on near-term quantum devices.

Findings

Requires only 2N qubits for N-qubit systems.

Uses overlap measurements of Gibbs states at different temperatures.

Reduces resource costs compared to existing methods.

Abstract

The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-team quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, and these could be costly performed on the near-term quantum computers. Here, we propose an efficient scheme to calculate the Gibbs function with the imaginary time evolution. To calculate the Gibbs function of $N$ qubits, only $2N$ qubits are required in our scheme. After preparing Gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, and this allows us to calculate the Gibbs partition function.