# Critical behavior of Ising model by preparing thermal state on quantum computer

## TL;DR

This paper demonstrates simulating the critical behavior of the Ising model using a quantum computer to prepare thermal states via variational quantum imaginary time evolution, showing results consistent with exact methods.

## Contribution

It introduces a systematic method for designing variational ansatz in QITE and applies it to study critical phenomena in the Ising model on a quantum computer.

## Key findings

- Successful simulation of Ising criticality on small lattices
- Quantum results agree with exact diagonalization near critical points
- Method demonstrates potential for quantum simulation of phase transitions

## Abstract

We simulate the critical behavior of the Ising model utilizing a thermal state prepared using quantum computing techniques. The preparation of the thermal state is based on the variational quantum imaginary time evolution (QITE) algorithm. The initial state of QITE is prepared as a classical product state, and we propose a systematic method to design the variational ansatz for QITE. We calculate the specific heat and susceptibility of the long-range interacting Ising model and observe indications of the Ising criticality on a small lattice size. We find the results derived by the quantum algorithm are well consistent with the ones from exact diagonalization, both in the neighbourhood of the critical temperature and the low-temperature region.