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arXiv · 2111.08961

One bound to rule them all: from Adiabatic to Zeno

Daniel Burgarth·Paolo Facchi·Giovanni Gramegna·Kazuya Yuasa
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Abstract

We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions. We apply our result to provide explicit error bounds for the rotating-wave approximation and generalize it beyond the qubit case. We discuss the error of the rotating-wave approximation over long time and in the presence of time-dependent amplitude modulation. We also show how our universal bound can be used to derive and to generalize other known theorems such as the strong-coupling limit, the adiabatic theorem, and product formulas, which are relevant to quantum-control strategies including the Zeno control and the dynamical decoupling. Finally, we prove generalized versions of the Trotter product formula, extending its validity beyond the standard scaling assumption.

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Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, Kazuya Yuasa. 2022-06-06. One bound to rule them all: from Adiabatic to Zeno. https://doi.org/10.22331/q-2022-06-14-737

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