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

Author(s): Arenz, Christian; Russell, Benjamin M.; Burgarth, Daniel Klaus; Rabitz, Herschel A.

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Abstract: © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. 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.
Publication Date: Oct-2017
Electronic Publication Date: 20-Oct-2017
Citation: Arenz, C., Russell, B., Burgarth, D., Rabitz, H. (2017). The roles of drift and control field constraints upon quantum control speed limits. New Journal of Physics, 19 (10), 10.1088/1367-2630/aa8242
DOI: doi:10.1088/1367-2630/aa8242
ISSN: 1367-2630
Pages: 19.10:103015-1 -103015-11
Type of Material: Journal Article
Journal/Proceeding Title: New Journal of Physics
Version: Final published version. This is an open access article.
Notes: New Journal of Physics. Volume 19, Issue 10, 20 October 2017, Article number 103015.

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