One bound to rule them all: from Adiabatic to Zeno
1Center for Engineered Quantum Systems, Macquarie University, 2109 NSW, Australia
2Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
3INFN, Sezione di Bari, I-70126 Bari, Italy
4Dipartimento di Fisica, Università di Trieste, I-34151 Trieste, Italy
5INFN, Sezione di Trieste, I-34151 Trieste, Italy
6Eberhard-Karls-Universität Tübingen, Institut für Theoretische Physik, 72076 Tübingen, Germany
7Department of Physics, Waseda University, Tokyo 169-8555, Japan
| Published: | 2022-06-14, volume 6, page 737 |
| Eprint: | arXiv:2111.08961v2 |
| Doi: | https://doi.org/10.22331/q-2022-06-14-737 |
| Citation: | Quantum 6, 737 (2022). |
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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.
Featured image: One bound to bring them all and in mathematics bind them.
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