One bound to rule them all: from Adiabatic to Zeno
- URL: http://arxiv.org/abs/2111.08961v2
- Date: Mon, 6 Jun 2022 15:35:21 GMT
- Title: One bound to rule them all: from Adiabatic to Zeno
- Authors: Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, Kazuya Yuasa
- Abstract summary: We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians.
We discuss the error of the rotating-wave approximation over long time and in the presence of time-dependent amplitude modulation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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