Simulation of XY model in a quantum computer

Abstract

The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, with the aim of efficiently simulating and comprehending the complexities of quantum physics. In this paper, we address this need by utilizing a scheme proposed in previous works for the exact simulation of the 1-D XY model on a quantum computer. Using the Qibo software, we successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Among all possibilities this opens, we have computed the transverse magnetization’s expected value for the ground state which allows the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers