Learning Hamiltonians from ergodic quantum dynamics in analog quantum simulators

Characterizing Hamiltonians in many-body quantum devices is a fundamental challenge for achieving accurate quantum simulation. Existing protocols often require a high level of control and are sensitive to experimental noise or spam errors. In this work, we present a scalable and robust approach to many-parameter Hamiltonian learning via the optimization of cross-entropy benchmarks (XEB). This approach is motivated by recent work showing the emergence of universal randomness driven by real-time Hamiltonian dynamics and its application to benchmarking in analog quantum simulators [1,2,3,4]. Specifically, starting from an initial model obtained from calibration of the underlying device physics, our procedure fine-tunes the Hamiltonian parameters by optimizing XEB scores with respect to experimental measurements. By applying the procedure to 20-qubit subsystems of a superconducting-qubit analog simulator, we achieve order-of-magnitude improvement in the estimated wavefunction fidelity. To demonstrate the scalability of our approach, we subsequently stitch together the parameters of the subsystems and benchmark the fidelity across a full-scale device. Our results provide insights into the universal randomness of real-time dynamics and open the door to ultra-precise characterization of strongly interacting quantum devices.

[1] Mark, Daniel K., et al. "Benchmarking quantum simulators using ergodic quantum dynamics." Physical Review Letters 131.11 (2023): 110601.

[2] Choi, Joonhee, et al. "Preparing random states and benchmarking with many-body quantum chaos." Nature 613.7944 (2023): 468-473.

[3] Shaw, Adam L., et al. "Benchmarking highly entangled states on a 60-atom analogue quantum simulator." Nature 628.8006 (2024): 71-77.

[4] Andersen, Trond I., et al. "Thermalization and criticality on an analogue–digital quantum simulator." Nature 638.8049 (2025): 79-85