Simulating the non-Hermitian skin effect on a quantum computer

Non-Hermitian physics has gained considerable attention in the recent years, particularly for the non-Hermitian skin effect (NHSE). While the NHSE has been realized in various classical metamaterials and even ultracold atomic arrays, it has not been realized in full generality on a universal quantum processor. To realize the NHSE on a quantum computer, not only must the time evolution operator be non-unitary, it must also act over sufficiently many qubits to implement spatial non-reciprocity. In this talk, we describe how such non-unitary operations can be implemented by embedding them in a quantum circuit with ancilla qubits. We show how we use this approach to implement the paradigmatic non-Hermitian Su-Schrieffer-Heeger (nH-SSH) model on a noisy IBM quantum processor, with the main signature of the NHSE being asymmetric spatial propagation and attenuation. To minimize errors from inevitable noise, the evolution is performed in a trainable circuit using the variational quantum algorithm (VQA). Our study demonstrates a critical step forward in the quantum simulation of non-Hermitian lattices in present-day quantum computers and facilitates future research of non-Hermitian many-body physics.