Quantum simulation of two-level <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> -symmetric systems using Hermitian Hamiltonians

Parity-time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>(</a:mo> <a:mi>P</a:mi> <a:mi>T</a:mi> <a:mo>)</a:mo> </a:mrow> </a:math> -symmetric Hamiltonians exhibit nonunitary 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>P</b:mi> <b:mi>T</b:mi> </b:mrow> </b:math> -symmetric systems on unitary-gate-based quantum computers by leveraging Hermitian equivalents through similarity transformations. We introduce two algorithms for simulating <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>P</c:mi> <c:mi>T</c:mi> </c:mrow> </c:math> -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 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>P</d:mi> <d:mi>T</d:mi> </d:mrow> </d:math> -symmetric systems. Demonstrations on a quantum device and noisy simulators validate the algorithm on current quantum devices, offering potential for scalable simulations of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>P</e:mi> <e:mi>T</e:mi> </e:mrow> </e:math> -symmetric systems and pseudo-Hermitian operators in quantum computation.