Exact Ising model simulation on a quantum computer

Understand

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.