Robustly learning the Hamiltonian dynamics of a superconducting quantum processor

The required precision to perform quantum simulations beyond the capabilitiesof classical computers imposes major experimental and theoretical challenges.The key to solving these issues are highly precise ways of characterizinganalog quantum sim ulators. Here, we robustly estimate the free Hamiltonianparameters of bosonic excitations in a superconducting-qubit analog quantumsimulator from measured time-series of single-mode canonical coordinates. Weachieve the required levels of precision in estimating the Hamiltonianparameters by maximally exploiting the model structure, making it robustagainst noise and state-preparation and measurement (SPAM) errors. Importantly,we are also able to obtain tomographic information about those SPAM errors fromthe same data, crucial for the experimental applicability of Hamiltonianlearning in dynamical quantum-quench experiments. Our learning algorithm ishighly scalable both in terms of the required amounts of data andpost-processing. To achieve this, we develop a new super-resolution techniquecoined tensorESPRIT for frequency extraction from matrix time-series. Thealgorithm then combines tensorESPRIT with constrained manifold optimization forthe eigenspace reconstruction with pre- and post-processing stages. For up to14 coupled superconducting qubits on two Sycamore processors, we identify theHamiltonian parameters - verifying the implementation on one of them up tosub-MHz precision - and construct a spatial implementation error map for a gridof 27 qubits. Our results constitute a fully characterized, highly accurateimplementation of an analog dynamical quantum simulation and introduce adiagnostic toolkit for understanding, calibrating, and improving analog quantumprocessors.