Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter—realized when discrete quantum gates approximate continuous time evolution—is susceptible to heating into chaotic, structureless states¹. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics^{2, 3, 4, 5, 6–7} can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviours observed in equilibrium systems, ranging from the non-trivial microscopic origins of thermalization itself⁸ to the stabilization of effective models hosting exotic emergent properties. Here we use Quantinuum’s H2 quantum computer^9,10 to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics owing to approximate energy conservation and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration^{11, 12–13}. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of 99.94(1)%) and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.