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.

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• Measurement-based quantum computing
• Quantum simulation
• Spin diffusion
• Spin dynamics
• Transport phenomena
• Correlation function measurements