Two Dimensional Non-Equilibrium Steady States under Corner Driving on a Trapped-Ion Quantum Computer

Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by classical computers. The architecture of trapped-ion quantum hardware is particularly suitable for simulating interacting open quantum systems, due to their all-to-all connectivity and ability to perform mid-circuit measurements and feedback.

Using Quantinuum’s System H1-1 trapped-ion quantum computer, we experimentally realise a two-dimensional system of interacting particles undergoing stochastic driving from the corners. This driving provides an in / out flow of particles in opposite corners, establishing a non-zero current in the non-equilibrium steady state (NESS).

We observe a striking difference in the NESS depending on the statistics of the particles. While hard-core bosons establish a density gradient from source to drain with currents spreading uniformly across the system, the density profile for fermions is flat and the current is localized along the shortest path between the corners. The difference is even more dramatic under the addition of a magnetic field, which can generate chiral edge currents in the presence of interactions, whereas hard-core bosons are insensitive.

Our findings provide direct visualization of how quantum statistics govern 2D non-equilibrium transport and establish quantum computers as a powerful platform for exploring rich non-equilibrium quantum dynamics in higher dimensions.