Making the most of noise: Learning Hamiltonians and relaxation dynamics from thermal data

Jochen Rau

The ability to create and control ever more complicated quantum systems in the laboratory, and to implement logical gates for quantum computing, presupposes the ability to certify that systems are in the desired quantum state, and that quantum devices are working properly. Yet the pertinent experimental data are often incomplete and noisy. Reconstructing from such imperfect data a quantum state or process then becomes a nontrivial inference task, known as "tomography", which requires the use of advanced statistical estimation techniques. As for the reconstruction of a Hamiltonian, the conventional approach uses data about both input and time-evolved output states, as well as the time elapsed; it thus necessitates tight experimental control over all of these. I show that one can also do without tight control over input states and time, by inducing instead thermalization of the system at varying temperatures, certifying that thermalization has been complete, and then reconstructing the Hamiltonian from thermal data only. Furthermore, I show that if thermalization is partial, to a degree which varies between different runs of the experiment, these variations provide a handle for reconstructing the system's effective relaxation dynamics.