The roles of drift and control field constraints upon quantum control speed limits

Arenz, Christian; Russell, Benjamin; Burgarth, Daniel; Rabitz, Herschel

doi:10.1088/1367-2630/aa8242

Title: The roles of drift and control field constraints upon quantum control speed limits

Journal Article · 26 July 2017 · New Journal of Physics

DOI: https://doi.org/10.1088/1367-2630/aa8242 · OSTI ID:1507734

Arenz, Christian ^[1]; Russell, Benjamin ^[1]; Burgarth, Daniel ^[2]; Rabitz, Herschel ^[1]

Princeton Univ., NJ (United States)
Aberystwyth University (United Kingdom)

In this work we derive a lower bound for the minimum time required to implement a target unitary transformation through a classical time-dependent field in a closed quantum system. The bound depends on the target gate, the strength of the internal Hamiltonian and the highest permitted control field amplitude. These findings reveal some properties of the reachable set of operations, explicitly analyzed for a single qubit. Moreover, for fully controllable systems, we identify a lower bound for the time at which all unitary gates become reachable. We use numerical gate optimization in order to study the tightness of the obtained bounds. It is shown that in the single qubit case our analytical findings describe the relationship between the highest control field amplitude and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining tighter bounds for higher dimensional systems, offering a discussion about the mathematical form and the physical meaning of the bound.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-02ER15344

OSTI ID:: 1507734

Journal Information:: New Journal of Physics, Vol. 19, Issue 10; ISSN 1367-2630

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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