aiqbench analysis
This is theoretical work on when periodically driven quantum many-body systems return exactly to their starting state, linking that recurrence to number-theoretic properties of the Floquet unitary. The most relevant takeaway for quantum computing readers is the proposed use of exact recurrences as a benchmarking tool, plus the observation that "magic," a resource for universal quantum computation, appears and revives periodically in a non-Clifford regime. The results are analytical and demonstrated on the kicked Ising chain, so their practical value for hardware depends on follow-up experimental and scaling studies.
Cyclotomic Structure and Exact Recurrences in Floquet Many-Body Quantum Dynamics
arXiv:2610.17137v1 Announce Type: new Abstract: Periodically driven quantum systems exhibit a wide range of complex dynamics, including chaos. Yet, at special parameter values, their evolution can recur exactly. Several quantum protocols have recently been proposed that exploit exact Floquet recurrences to demonstrate genuine quantum advantage. Such recurrences can be studied through the arithmetic structure of the Floquet unitary. In this work, we establish a necessary and sufficient arithmetic criterion for exact recurrence and determine the minimal recurrence period when one exists. Because recurrence is a global property of the unitary, it holds for every initial state. Applying our framework requires only knowledge of the number field associated with the Hamiltonian parameters. We demonstrate the method using the kicked Ising chain, establishing exact recurrences in both Clifford and non-Clifford regimes. We further show that, in the recurrent non-Clifford regime, magic--a resource for quantum computation--is generated at intermediate times and undergoes exact periodic revivals enforced by the recurrence of the full Floquet unitary. By connecting number theory, quantum many-body dynamics, and quantum information, our work shows that exact recurrence extends beyond Clifford circuits and opens new avenues for magic generation and quantum hardware benchmarking.
Abstract:Periodically driven quantum systems exhibit a wide range of complex dynamics, including chaos. Yet, at special parameter values, their evolution can recur exactly. Several quantum protocols have recently been proposed that exploit exact Floquet recurrences to demonstrate genuine quantum advantage. Such recurrences can be studied through the arithmetic structure of the Floquet unitary. In this work, we establish a necessary and sufficient arithmetic criterion for exact recurrence and determine the minimal recurrence period when one exists. Because recurrence is a global property of the unitary, it holds for every initial state. Applying our framework requires only knowledge of the number field associated with the Hamiltonian parameters. We demonstrate the method using the kicked Ising chain, establishing exact recurrences in both Clifford and non-Clifford regimes. We further show that, in the recurrent non-Clifford regime, magic--a resource for quantum computation--is generated at intermediate times and undergoes exact periodic revivals enforced by the recurrence of the full Floquet unitary. By connecting number theory, quantum many-body dynamics, and quantum information, our work shows that exact recurrence extends beyond Clifford circuits and opens new avenues for magic generation and quantum hardware benchmarking.
Quantum Physics (quant-ph); Number Theory (math.NT); Chaotic Dynamics (nlin.CD)
arXiv:2610.17137 [quant-ph]
(or arXiv:2610.17137v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.17137 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 287 words
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