Quantum Phase Transition of Non-Hermitian Systems using Variational Quantum Techniques

TL;DR

This paper explores quantum algorithms, specifically variational techniques, to analyze phase transitions in non-Hermitian systems like the transverse Ising model with complex fields, advancing quantum simulation methods.

Contribution

It introduces a variational quantum algorithm tailored for non-Hermitian Hamiltonians, enabling the study of quantum phase transitions in such systems.

Findings

Successful application of the algorithm to the transverse Ising model with complex fields

Demonstrated ability to find eigenvalues and eigenvectors of non-Hermitian Hamiltonians

Provided insights into quantum phase transitions in non-Hermitian systems

Abstract

The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications to quantum phase transitions. We use a recently proposed variational algorithm. The systems studied are the transverse Ising model with both a purely real and a purely complex transverse field.