Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer

Quantum computers have long been anticipated to excel in simulating quantum many-body physics. In this work, we demonstrate the power of variational quantum circuits for resource-efficient simulations of dynamical and equilibrium physics in non-Hermitian systems. Using a variational quantum compilation scheme for fermionic systems, we reduce gate count, save qubits, and eliminate the need for postselection, a major challenge in simulating non-Hermitian dynamics via standard Trotterization. On the Quantinuum H1 trapped-ion processor, we experimentally observed a supersonic mode on an n = 18 fermionic chain after a non-Hermitian, nearest-neighbor interacting quench, which would otherwise be forbidden in a Hermitian system. Additionally, we investigate sequential quantum circuits generated by tensor networks for ground-state preparation using a variance minimization scheme, accurately capturing correlation functions and energies across an exceptional point on a dissipative spin chain up to length n = 20 using only 3 qubits. On the other hand, we provide an analytical example demonstrating that simulating single-qubit non-Hermitian dynamics for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Θ</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mi>log</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mi>n</mml:mi></mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> time from certain initial states is exponentially hard on a quantum computer. Our work raises many intriguing questions about the intrinsic properties of non-Hermitian systems that permit efficient quantum simulation.