Automated precise multi-parameter estimation for quantum devices

Hardware built for quantum computing is designed with an ideal model in mind.  However, physically realised systems may have additional elements whose effects on the rest of the system are typically accounted for in effective models. In such cases, there is ambiguity in which model “correctly” describes the system - the effective model, or a more complete physical model that includes the dynamics in a larger Hilbert space. We present an efficient method for fitting Hamiltonian parameters using automated differentiation in a flexible graph representation for quantum models. Our approach works with noisy experimental data and is able to make statistical estimates of the parameter uncertainty. We demonstrate these approaches with an example where a coupling resonator is used to mediate multi-qubit gates between superconducting qubits.  We compare an effective model that eliminates the coupling resonator with a more fundamental model that retains the full dynamics and Hilbert space of the qubit-coupler-qubit system.  Using our model fitting techniques we are able to use information criteria to compare amongst models based on accuracy and predictive power, in the presence of noise and parameter uncertainty.  This has implications for hardware system identification and design cycles.