Agenda

Résumé : The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard; and only a few classes of states are currently known to be efficiently learnable. In this talk, I will present our new algorithm to learn fermionic states on n modes, prepared by any number of Gaussian (free-fermionic) and at most t non-Gaussian (interacting) gates. The algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, which is guaranteed to be accurate. I will show why the runtime of our algorithm — poly(n,2^t) — is essentially optimal for this task, under common assumptions from theory of cryptography. In addition to the outputs of quantum circuits, I will demonstrate how our tomography algorithm can be efficiently applied to learn target states which arise in the physics of impurity models. Beyond tomography, I would like to review an improved circuit compilation strategy, which is also enabled by our results. This talk is based on the work done in collaboration with Antonio Anna Mele (FU Berlin), which can be accessed at https://arxiv.org/abs/2402.18665