Simulating the Ising Model with a Quantum Computer

Abstract

This work is based on replicating the results achieved in the paper ”Exact Ising Model Simulation on a quantum computer” by Alba Cervera-Lierta et al. (2018) and comparing them with the ones given by current quantum machines. First, we present a way to analytically diagonalize the onedimensional Ising Hamiltonian. Next, we create a quantum circuit that diagonalizes the Hamiltonian and simulates its eigenstates. Furthermore, thanks to the Ising model being solvable, the circuit can serve as a benchmark for evaluating the reliability of quantum machines. Through the application of this circuit, we have obtained the energy spectrum and ground state magnetization of the onedimensional Ising Model.