Digital Quantum Simulation of Spin Transport

Transport phenomena in quantum spin systems have long intrigued physicists due to their potential applications in spintronic devices and spin qubits. Quantum simulations of the spin-spin autocorrelation function (ACF) have been used to probe spin transport, but 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 transport properties. 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 ACF. Overcoming the resource constraints of indirect measurement schemes like the Hadamard test, we showcase a direct measurement scheme using nonunitary operations, particularly midcircuit measurements, to investigate spin transport for the 40-site 1D XXZ Heisenberg model in the near-ballistic, superdiffusive, and diffusive regimes. We observe the power-law behavior consistent with the Kardar-Parisi-Zhang scaling in the superdiffusive regime and vanishing of the Drude weight in the diffusive regime.