Dependence of the quantum speed limit on system size and control complexity
Abstract
We extend the work in 2017 New J. Phys. 19 103015 by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. Here, it is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1440380
- Alternate Identifier(s):
- OSTI ID: 1500091
- Grant/Contract Number:
- FG02-02ER15344
- Resource Type:
- Published Article
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Name: New Journal of Physics Journal Volume: 20 Journal Issue: 6; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum control; quantum speed limit; quantum computation
Citation Formats
Lee, Juneseo, Arenz, Christian, Rabitz, Herschel, and Russell, Benjamin. Dependence of the quantum speed limit on system size and control complexity. United Kingdom: N. p., 2018.
Web. doi:10.1088/1367-2630/aac6f3.
Lee, Juneseo, Arenz, Christian, Rabitz, Herschel, & Russell, Benjamin. Dependence of the quantum speed limit on system size and control complexity. United Kingdom. https://doi.org/10.1088/1367-2630/aac6f3
Lee, Juneseo, Arenz, Christian, Rabitz, Herschel, and Russell, Benjamin. Fri .
"Dependence of the quantum speed limit on system size and control complexity". United Kingdom. https://doi.org/10.1088/1367-2630/aac6f3.
@article{osti_1440380,
title = {Dependence of the quantum speed limit on system size and control complexity},
author = {Lee, Juneseo and Arenz, Christian and Rabitz, Herschel and Russell, Benjamin},
abstractNote = {We extend the work in 2017 New J. Phys. 19 103015 by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. Here, it is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.},
doi = {10.1088/1367-2630/aac6f3},
journal = {New Journal of Physics},
number = 6,
volume = 20,
place = {United Kingdom},
year = {Fri Jun 01 00:00:00 EDT 2018},
month = {Fri Jun 01 00:00:00 EDT 2018}
}
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https://doi.org/10.1088/1367-2630/aac6f3
https://doi.org/10.1088/1367-2630/aac6f3
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Cited by: 11 works
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Figures / Tables:
Figure 1: Comparison of the obtained bound (8) with the minimum gate time obtained from numerical gate optimization of the gate error (14) using GRAPE for the N-level system (9) (with coupling strength J = 1) with a SWAP operation (10) as the goal. The solid surface plot represents themore »
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