Generalized product formulas and quantum control

Year: 2019

Authors: Burgarth D., Facchi P., Gramegna G., Pascazio S.

Autors Affiliation: Macquarie Univ, Dept Phys & Astron, N Ryde, NSW 2109, Australia;‎ Univ Bari, Dipartimento Fis, I-70126 Bari, Italy; Univ Bari, MECENAS, I-70126 Bari, Italy;‎ INFN, Sez Bari, I-70126 Bari, Italy; CNR, INO, I-50125 Florence, Italy

Abstract: We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of situations, both in physics (Feynman integral) and mathematics (product formulas). We focus on the case in which the two evolution times are scaled differently in the limit and generalize standard techniques and results.


Volume: 52 (43)      Pages from: 435301-1  to: 435301-22

More Information: We thank Kazuya Yuasa for discussions. PF, GG and SP are partially supported by Istituto Nazionale di Fisica Nucleare (INFN) through the project ´QUANTUM´. PF and GG are partially supported by the Italian National Group of Mathematical Physics (GNFM-INdAM).
KeyWords: product formulas; quantum control; quantum Zeno dynamics; adiabatic theorem
DOI: 10.1088/1751-8121/ab4403

Citations: 4
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