Hamiltonian and Lindbladian Parameter Estimation

Estimating the parameters governing the dynamics of a system is a prerequisite for its control. We present a simple but powerful new method to estimate the Hamiltonian (or Lindbladian) governing a quantum system of a few qubits. Our method makes efficient use of all measurements taken of the system and it saturates the information-theoretic limits for such an estimator. Importantly, it is inherently robust to state preparation and measurement errors. It is not limited to evaluating only a fixed set of possible gates, rather it estimates the complete Hamiltonian of the system. The estimator is applicable to any Hamiltonian that can be written as a piecewise-differentiable function and it can easily include estimators for the non-unitary parameters as well. At the heart of our approach is a stochastic gradient descent over the difference between experimental measurement and model prediction.