Simulating the Quantum Ising Model with Cloud Quantum Computers

The 1D quantum Ising model is a prototype for quantum phase transition that involves a chain of interacting spins in a transverse magnetic field. The 1D Ising model has been studied extensively to explore the magnetic properties of solids in relation to varying transverse magnetic field strengths and temperatures, while also serving as a pedagogical stepping stone for solving problems in higher dimensions. We utilize IBM’s cloud quantum computer to simulate a quantum Ising model with a broad range of magnetic field strength. In the simulation, we start from an initial state that is the quantum ground state in the large transverse field limit and then we simulate the dynamic evolution of the system using the quantum computer. Our results demonstrate that at a finite magnetic field, the simulated model evolves according to the quantum Ising Hamiltonian. Comparing the results from Qiskit and from the cloud quantum computer, we discover that the discrepancies between the results stem from environmental noise and control errors, which reduces the fidelity of the simulation. The deviation of results between Qiskit and the cloud quantum computer represents the ongoing challenge faced by physicists to minimize the presence of noise in quantum computers and attain higher quantum fidelity.