Digital Quantum Simulation of Spin Transport

Understanding transport phenomena in quantum spin systems has long intrigued physicists due to their potential applications in spintronic devices and spin qubits. Here, using a superconducting-qubit-based transmon device, we show that pre-fault-tolerant digital quantum simulation is reliable for studying transport phenomena via spin-current autocorrelation function (ACF). While quantum simulations of the spin-spin ACF have been used to probe spin transport, methods based on the spin-current ACF have yet to be demonstrated due to their high gate cost, despite offering more direct information relevant to the transport properties. Overcoming the resource constraints set by indirect measurement schemes like the Hadamard test, we showcase a direct measurement scheme that utilizes non-unitary operations, in particular mid-circuit measurements, to investigate spin transport for the 40-site 1D XXZ Heisenberg model in the near-ballistic, superdiffusive, and diffusive regimes. We successfully reproduce the expected power-law behavior in the superdiffusive regime and vanishing of the Drude weight in the diffusive regime.