Exact Ising model simulation on a quantum computer

TL;DR

This paper demonstrates an exact simulation of a 1D transverse Ising model on quantum computers, introducing an efficient circuit for eigenstate preparation, and testing it on IBM and Rigetti devices.

Contribution

It presents a novel quantum circuit that diagonalizes the Ising Hamiltonian, enabling exact eigenstate and thermal state simulations on current quantum hardware.

Findings

Successfully simulated ground state magnetization

Performed time evolution simulations

Compared results across different quantum devices

Abstract

We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for $n=4$ spins, we compute the expected value of the ground state magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.