Born Machines for Periodic and Open XY Quantum Spin Chains

TL;DR

This paper demonstrates that a quantum-inspired Born machine, based on matrix product states, can effectively learn and represent quantum phases of the XY spin chain, including near critical points, under different boundary conditions.

Contribution

It introduces a novel application of Born machines to model quantum phases in spin chains, highlighting the importance of boundary conditions and bond dimension for performance.

Findings

Born machine successfully captures quantum phases of XY model

Performance improves with matching boundary conditions

Effective near critical points despite long-range correlations

Abstract

Quantum phase transitions are ubiquitous in quantum many body systems. The quantum fluctuations that occur at very low temperatures are known to be responsible for driving the system across different phases as a function of an external control parameter. The XY Hamiltonian with a transverse field is a basic model that manifests two distinct quantum phase transitions, including spontaneous $Z_2$ symmetry breaking from an ordered to a disordered state. While programmable quantum devices have shown great success in investigating the various exotic quantum phases of matter, in parallel, the quest for harnessing machine learning tools in learning quantum phases of matter is ongoing. In this paper, we present a numerical study of the power of a quantum-inspired generative model known as the Born machine in learning quantum phases of matter. Data obtained from the system under open and periodic boundary conditions is considered. Our results indicate that a Born machine based on matrix product states can successfully capture the quantum state across various phases of the XY Hamiltonian and close to a critical point, despite the existence of long-range correlations. We further impose boundary conditions on the Born machine and show that matching the boundary condition of the Born machine and that of the training data improves performance when limited data is available and a small bond dimension is employed.