One bound to rule them all: from Adiabatic to Zeno

Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, Kazuya Yuasa

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Article number737
Publication statusPublished - 2022

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'One bound to rule them all: from Adiabatic to Zeno'. Together they form a unique fingerprint.

Cite this