This Thursday, 13.01 at 11.00 am we will have a FH seminar where Tanmoy Pandit from the group of Dr. Raam Uzdin will give a lecture titled "Constraint on periodically driven quantum systems". See the details in the file attached.

Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics,
even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is
of interest to understand what constraints such dynamics must satisfy. We derive a set of
constraints for each number of cycles. For pure initial states, the observable being
constrained is the recurrence probability. We use our constraints for detecting undesired
coupling to unaccounted environments and drifts in the driving parameters. Our formalism is
based on the construction of positive operators in Liouville space. Using this approach we
explain previously observed features such as an exponential decay law in a perfectly isolated
system. To illustrate the relevance of these results for modern quantum systems we
demonstrate our findings experimentally on a trapped-ion quantum computer, and on various
IBM quantum computers. Specifically, we provide two experimental examples where these
constraints surpass fundamental bounds associated with known one-cycle constraints. This
scheme can potentially be used to detect the effect of the environment in quantum circuits
that cannot be classically simulated. Finally, we show that, in practice, testing an n-cycle
constraint requires executing only O[n^(1/2)] cycles, which makes the evaluation of
constraints associated with hundreds of cycles realistic.