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

Abstract: Quantum computers have long been anticipated to excel in simulating quantum many-body physics. While most previous work has focused on Hermitian physics, we demonstrate the power of variational quantum circuits for resource-efficient simulations of dynamical and equilibrium physics in non-Hermitian systems, revealing new phenomena beyond standard Hermitian quantum machines. 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. Experimentally, we observed a supersonic mode in the connected density-density correlation function on an $ n = 18 $ fermionic chain after a non-Hermitian, locally interacting quench, which would otherwise be forbidden by the Lieb-Robinson bound in a Hermitian system. Additionally, we investigate sequential quantum circuits generated by tensor networks for ground state preparation, here defined as the eigenstate with the lowest real part eigenvalue, using a variance minimization scheme. Through a trapped-ion implementation on the Quantinuum H1 quantum processor, we accurately capture correlation functions and energies across an exceptional point on a dissipative spin chain up to length $ n = 20 $ using only 3 qubits. Motivated by these advancements, we provide an analytical example demonstrating that simulating single-qubit non-Hermitian dynamics for $\Theta(\log(n))$ time from certain initial states is exponentially hard on a quantum computer, offering insights into the opportunities and limitations of using quantum computation for simulating non-Hermitian physics.