Bounds on the recurrence probability in periodically-driven quantum systems

Tanmoy Pandit1, Alaina M. Green2, C. Huerta Alderete2, Norbert M. Linke2, and Raam Uzdin1

1Fritz Haber Research Center for Molecular Dynamics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
2Joint Quantum Institute and Department of Physics, University of Maryland, College Park, MD 20742 USA

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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 $O(\sqrt{n})$ cycles, which makes the evaluation of constraints associated with hundreds of cycles realistic.

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Cited by

[1] Nikolay P. Tretyakov, "Fast driven quantum systems: interaction picture and boundary conditions", Physica Scripta 96 12, 125106 (2021).

[2] Raam Uzdin, "Methods for measuring noise, purity changes, and entanglement entropy in quantum devices and systems", arXiv:2112.00546.

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