Quantum trajectory simulation of two-dimensional non-equilibrium steady states with a trapped ion quantum processor

TL;DR

This paper demonstrates the use of a trapped-ion quantum computer to simulate two-dimensional non-equilibrium steady states, revealing complex physics and showcasing quantum computing capabilities and limitations.

Contribution

First experimental realization of quantum trajectories for 2D interacting particles on a trapped-ion quantum processor, studying non-equilibrium steady states with measurable effects.

Findings

Observed persistent currents in non-equilibrium steady states.

Particle statistics and magnetic fields affect steady state properties.

Showcased quantum computer's potential and current limitations for complex quantum simulations.

Abstract

Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by their classical counterparts. Capabilities including mid-circuit measurements and feedback allow for simulating the dynamics of interacting open quantum systems. Using the Quantinuum System Model H1 trapped-ion quantum computer, we experimentally realise quantum trajectories for a two-dimensional system of (interacting) particles-hard-core bosons or fermions-undergoing stochastic driving at a source and drain at opposite corners of a square lattice. We study the non-equilibrium steady state with persistent current resulting from the this in/out flow of particles. The particle statistics, presence of interactions, and introduction of a magnetic field produce measurable effects on the steady state. Our findings highlight the rich physics in this corner driven two-dimensional setup and showcases both the power and current limitations of quantum computers as a platform to study it.