Quantum simulation of parity-time symmetric systems with diagonal operators

Quantum simulation of quantum systems stands as a pivotal application in the field of quantum computation. However, the accurate representation of real quantum systems poses a challenge, given that most are open systems undergoing non-unitary processes. To capture the dynamics of non-hermitian systems, we must employ innovative simulation methods. In this presentation, I will talk about the implementation of singular value decomposition of the evolution operator for a Parity-Time symmetric system. This method requires dilation of the Hilbert space of the desired quantum system with only one extra qubit. I will demonstrate the scalability of this technique by applying it to two-level and three-level non-Hermitian systems on a real quantum processor.