Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians

TL;DR

This paper develops algorithms to simulate non-Hermitian $PT$-symmetric quantum systems on standard quantum computers by transforming them into Hermitian equivalents, enabling practical quantum simulations of such exotic systems.

Contribution

It introduces two novel algorithms for simulating $PT$-symmetric systems using Hermitian transformations, including a hybrid classical-quantum approach and an ancilla-based reduction, validated on real quantum devices.

Findings

Algorithms successfully simulate $PT$-symmetric dynamics on quantum hardware.

Demonstrations validate the approach on noisy simulators and real devices.

Potential for scalable simulation of pseudo-Hermitian operators in quantum computing.

Abstract

Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the quantum dynamics of $PT$-symmetric systems on unitary-gate-based quantum computers by leveraging Hermitian equivalents through similarity transformations. We introduce two algorithms for simulating $PT$-symmetric systems near exceptional points where eigenvalues and eigenstates coalesce. The first is a hybrid classical-quantum algorithm and the second reduces the classical component by using an ancilla qubit. We then use perturbation theory to extend this method to consider the dynamics of two weakly interacting $PT$-symmetric systems. Demonstrations on a quantum device and noisy simulators validate the algorithm on current quantum devices, offering potential for scalable simulations of $PT$-symmetric systems and pseudo-Hermitian operators in quantum computation.