Precise Hamiltonian identification of a superconducting quantum processor (Part 1)

The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. Key to solving those issues are highly precise ways of characterizing and benchmarking analog quantum simulators. Here, we develop a characterization technique for identifying the Hamiltonian parameters of noninteracting particles from measured times series of the expectation values of single-mode canonical coordinates. To achieve the required levels of precision our approach uses denoising and explicitly incorporates the model structure, making it highly robust to incoherent errors during the evolution. On a technical level this is achieved using superresolution techniques for frequency extraction and constrained manifold optimization for eigenspace reconstruction. Importantly, in addition to precise estimates of the Hamiltonian parameters, we are able to obtain tomographic information about general state preparation errors and phase errors in the measurement. This additional information is crucial for the experimental applicability of Hamiltonian identification in dynamical quantum-quench experiments, where ramp phases are inevitable at the beginning and end of the time evolution phase of the experiment.