Quantum Circuit Implementation of the First-Order Perturbation in Transverse-field Ising Systems

Abstract

The transverse-field Ising (TI) model is the standard prototype from which the properties of magnetic systems are often scrutinized. In addition, inhomogeneities in these systems can be treated as perturbations to the TI model. Incorporating perturbation escalates the difficulty of simulating such magnetic systems, specially if it is accompanied by an increase in system size or when higher dimensions or more complex lattice structures are considered. In this work, a quantum computational approached is demonstrated to carry out perturbation theory in a TI system consisting of four spins with nearest neighbor interactions along the x-axis with a transverse field along the z-axis. Considered separately as perturbations were the next-nearest neighbor interactions along the x-axis and the nearest neighbor interactions along the y-axis. Through a series of simple quantum gates implemented in Qiskit, IBM’s quantum computing software platform, the first order correction to the ground state of the TI system was obtained in both cases. This work on quantum circuits provides a foundation upon which more complex magnetic systems can be simulated.