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

The motivation for studying non-Hermitian systems and the role of $\mathcal{P}\mathcal{T}$-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.