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Title: 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.

Authors:
; ; ORCiD logo; ORCiD logo
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. https://doi.org/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 = {2018},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1088/1367-2630/aac6f3

Citation Metrics:
Cited by: 1 work
Citation information provided by
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Figures / Tables:

Figure 1 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 » bound and the transparent surface plot represents the GRAPE data, both as a function of the number of levels N ϵ [2, 15] and the number of controls M ϵ [1, 14]. The inset plot show the same data for a fixed number of controls M = 1 (a), and a fixed number of levels N = 15 (b), wherein the solid gray line represents the bound and the solid black line the minimum gate time obtained from GRAPE.« less

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Geometric derivation of the quantum speed limit
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Time-Optimal Quantum Evolution
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Speed limits for quantum gates in multiqubit systems
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Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework
journal, August 2011


Global controllability with a single local actuator
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Driven Quantum Dynamics: Will It Blend?
journal, October 2017

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    Works referencing / citing this record:

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      Figures / Tables found in this record:

        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.