The roles of drift and control field constraints upon quantum control speed limits
Abstract
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.
- Authors:
-
- Princeton Univ., NJ (United States)
- Aberystwyth University (United Kingdom)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1507734
- Grant/Contract Number:
- FG02-02ER15344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 10; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Arenz, Christian, Russell, Benjamin, Burgarth, Daniel, and Rabitz, Herschel. The roles of drift and control field constraints upon quantum control speed limits. United States: N. p., 2017.
Web. doi:10.1088/1367-2630/aa8242.
Arenz, Christian, Russell, Benjamin, Burgarth, Daniel, & Rabitz, Herschel. The roles of drift and control field constraints upon quantum control speed limits. United States. https://doi.org/10.1088/1367-2630/aa8242
Arenz, Christian, Russell, Benjamin, Burgarth, Daniel, and Rabitz, Herschel. Wed .
"The roles of drift and control field constraints upon quantum control speed limits". United States. https://doi.org/10.1088/1367-2630/aa8242. https://www.osti.gov/servlets/purl/1507734.
@article{osti_1507734,
title = {The roles of drift and control field constraints upon quantum control speed limits},
author = {Arenz, Christian and Russell, Benjamin and Burgarth, Daniel and Rabitz, Herschel},
abstractNote = {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.},
doi = {10.1088/1367-2630/aa8242},
journal = {New Journal of Physics},
number = 10,
volume = 19,
place = {United States},
year = {Wed Jul 26 00:00:00 EDT 2017},
month = {Wed Jul 26 00:00:00 EDT 2017}
}
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Cited by: 20 works
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Figures / Tables:
Figure 1.: Characterization of the gates that proveably cannot be reached for a single qubit described by the control system. Based on (11), (a) shows the set of states that cannot be reached (gray area) from an initial eigenstate of $\sigma_z$ for an evolution time T=0.52 and $\Omega$ = $f_{max}$more »
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Works referencing / citing this record:
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