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arXiv:2507.22846 · Physical Review Letters

Digital Quantum Simulation of Spin Transport

Yi-Ting Lee, Bibek Pokharel, Jeffrey Cohn, André Schleife, Arnab Banerjee

Published Dec 24, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/mx9k-kdlj

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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.
Abstract Understanding how hydrodynamic behaviour emerges from the unitary evolution of the many-particle Schrödinger equation is a central goal of non-equilibrium statistical mechanics. In this work we implement a digital simulation of the discrete time quantum dynamics of a spin- 12\frac{1}{2}21​ 1 2 XXZ spin chain on a noisy near-term quantum device, and we extract the high temperature transport exponent at the isotropic point. We simulate the temporal decay of the relevant spin correlation function at high temperature using a pseudo-random state generated by a random circuit that is specifically tailored to the ibmq-montreal 27 qubit device. The resulting output is a spin excitation on a homogeneous background on a 21 qubit chain on the device. From the subsequent discrete time dynamics on the device we are able to extract an anomalous super-diffusive exponent consistent with the conjectured Kardar-Parisi-Zhang (KPZ) scaling at the isotropic point. Furthermore we simulate the restoration of spin diffusion with the application of an integrability breaking potential.
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Observing superdiffusive scaling in the spin transport of the integrable 1D Heisenberg model is one of the key discoveries in non-equilibrium quantum many-body physics. Despite this remarkable theoretical development and the subsequent experimental observation of the phenomena in KCuF3_33​, real materials are often imperfect and contain integrability breaking interactions. Understanding the effect of such terms on the superdiffusion is crucial in identifying connections to such materials. Current quantum hardware has already ascertained its utility in studying such non-equilibrium phenomena by simulating the superdiffusion of the 1D Heisenberg model. In this work, we perform a quantum simulation of the superdiffusion breakdown by generalizing the superdiffusive Floquet-type 1D Heisenberg model to a general 2D model. We comprehensively study the effect of different 2D interactions on the superdiffusion breakdown by tuning up their strength from zero, corresponding to the 1D Heisenberg chain, to finite nonzero values. We observe that certain 2D interactions are more resilient against superdiffusion breakdown than others and that the SU(2)SU(2)SU(2) preserving 2D interaction has the highest resilience among all the 2D interactions we study. Importantly, this observed resilience has direct implications for sustaining superdiffusive spin transport in two-dimensional lattices. We reason out the relative resilience against the superdiffusion breakdown through an analysis of the scattering coefficients off the 2D interaction in otherwise 1D chains. The relative resilience of different interaction types against superdiffusion breakdown was also captured in quantum hardware with remarkable accuracy, further establishing the current quantum hardware's applicability in simulating interesting non-equilibrium quantum many-body phenomena.
We construct a family of chaotic brickwork quantum circuits exhibiting superdiffusive transport with dynamical exponent z=3/2z=3/2z=3/2 in the full Kardar--Parisi--Zhang (KPZ) universality class. This is enabled by the equilibrium current associated with a inhomogeneous conserved density having a nontrivial dependence on the chemical potential. Using nonlinear fluctuating hydrodynamics, we derive the propagation velocity, broadening scale, and universal scaling form of the charge correlation function from microscopic equilibrium properties. Tensor-network simulations of a two-site spin-111 (qutrit) circuit reproduce these parameter-free predictions, including the full stationary KPZ profile. We further construct a three-site spin-12\frac1221​ (qubit) circuit, where transport varies from diffusive to superdiffusive with the chemical potential, while long-lived coherent quasiparticles delay the convergence of the profile to the KPZ scaling form. Our results establish that KPZ superdiffusion in quantum systems is not restricted to fine-tuned integrable models.