Simulating Infinite Temperature Energy Transport on Cloud-Accessible Quantum Hardware

The high-temperature transport of conserved quantities like spin and charge in strongly interacting quantum many-body systems is a topic of substantial recent theoretical investigation. One important open question is to understand the timescales for the emergence of hydrodynamic behavior, as quantified by the dynamical critical exponent z. The transport of energy, however, has been much less well studied, even though it is the most generic conserved quantity in Hamiltonian dynamics and is therefore of fundamental importance in studying such dynamics with local probes. We study the infinite-temperature transport of energy in the mixed-field Ising model using cloud-accessible superconducting quantum processors and classical simulation techniques. Instead of preparing Haar-random states to sample from the infinite-temperature distribution, which requires deep quantum circuits, we compute dynamics for a small ensemble of product states with zero energy expectation value. Using both generic and problem-tailored quantum error mitigation techniques, we obtain results for the dynamical exponent that are consistent with classical simulations.