Quantum Simulation of Spin Transport on a Programmable Quantum Computer

Understanding transport phenomena in quantum spin systems is crucial for advancing spintronic devices and spin qubits. While quantum simulations based on the spin–spin autocorrelation function (ACF) have been used to probe spin transport, methods employing the spin-current ACF remain unexplored. The main reason is their higher gate cost, arising from the higher-weight Pauli operators, even though they can offer more direct insight into transport properties. In this study, we propose a simple framework to evaluate spin transport via the spin-current ACF. We illustrate a direct measurement scheme that incorporates mid-circuit measurements, providing greater computational efficiency than the traditional Hadamard test. We first validate our circuit design through 40-qubit experiments on quantum hardware, finding good agreement with matrix-product-state simulations. Furthermore, we demonstrate the applicability of our method for evaluating the two-time spin-current ACF. Finally, we perform 40-qubit transport experiments and observe a power-law scaling of the time-dependent diffusion coefficient in the superdiffusive regime, as well as a vanishing Drude weight in the diffusive regime. Our results demonstrate that pre-fault-tolerant digital quantum simulation provides a reliable approach for evaluating transport phenomena in many-body spin Hamiltonians via the spin-current ACF.