  The required precision to perform quantum simulations beyond the capabilities
of classical computers imposes major experimental and theoretical challenges.
The key to solving these issues are precise means of characterizing analog
quantum simulators. Here, we robustly estimate the free Hamiltonian parameters
of bosonic excitations in a superconducting-qubit analog quantum simulator from
measured time-series of single-mode canonical coordinates. We achieve high
levels of precision in estimating the Hamiltonian parameters by exploiting a
priori knowledge, making it robust against noise and state-preparation and
measurement (SPAM) errors. Importantly, we are also able to obtain tomographic
information about those SPAM errors from the same data, crucial for the
experimental applicability of Hamiltonian learning in dynamical quantum-quench
experiments. Our learning algorithm is scalable both in terms of the required
amounts of data and post-processing. To achieve this, we develop a new
super-resolution technique coined tensorESPRIT for frequency extraction from
matrix time-series. The algorithm then combines tensorESPRIT with constrained
manifold optimization for the eigenspace reconstruction with pre- and
post-processing stages. For up to 14 coupled superconducting qubits on two
Sycamore processors, we identify the Hamiltonian parameters -- verifying the
implementation on one of them up to sub-MHz precision -- and construct a
spatial implementation error map for a grid of 27 qubits. Our results
constitute an accurate implementation of a dynamical quantum simulation that is
characterized using a new diagnostic toolkit for understanding, calibrating,
and improving analog quantum processors.
