Description
Learning and certifying time-dependent quantum dynamics under realistic noise is key to trustworthy quantum simulation. I will present an efficient protocol that reconstructs the generators Hamiltonian and Markovian noise generators of multi-qubit devices from derivatives of expectation values of few-qubit observables via stable polynomial interpolation and semidefinite programming. To the best of our knowledge, this is the first scheme to efficiently learn local time-dependent Hamiltonians and Markovian noise at scale. The scheme is experimentally light, requiring only product-state preparation, single-qubit measurements, and post-processing polynomial in the qubit number, while the number of samples needed to identify all parameters grows only logarithmically with the qubit count. Our protocol thus enables a-posteriori certification of various crucial routines on quantum simulators such as adiabatic state preparation, and yield confidence guarantees for estimated expectation values along the schedule. Thus, together, these results provide a scalable route to diagnosing and certifying controlled time-dependent many-body dynamics. If time permits, we will also discuss recent experimental implementations of related protocols.
