Bounds on the recurrence probability in periodically-driven quantum systems

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. 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 (root n) cycles, which makes the evaluation of constraints associated with hundreds of cycles realistic.

Automated summary

Periodically-driven systems are common in the fields of science and technology, and understanding the constraints that govern the dynamics of such systems is of great interest. This study derives a set of constraints for each number of cycles in quantum dynamics and demonstrates experimentally the relevance of these constraints for modern quantum systems. Furthermore, it shows the potential of using these constraints to detect the effect of the environment in quantum circuits that cannot be simulated classically.