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Cited by 72Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum Mechanics and Applications

Zermelo navigation and a speed limit to quantum information processing

Open access
Russell, Benjamin, Stepney, Susan·2014·Physical Review A
DOI 10.1103/physreva.90.012303
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Abstract

We use a specific geometric method to determine speed limits for the implementation of quantum gates in controlled quantum systems that have a specific class of constrained control functions. We achieve this by applying a recent theorem of Shen, which provides a connection between time optimal navigation on Riemannian manifolds and the geodesics of a certain Finsler metric of Randers type. We use the lengths of these geodesics to derive the optimal implementation times (under the assumption of constant control fields) for an arbitrary quantum operation (on a finite dimensional Hilbert space), and explicitly calculate the result for the case of a controlled single spin system in a magnetic field and a swap gate in a Heisenberg spin chain.

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  • Deffner and Lutz extended the ML bound to open quantum systems using a geometric approach with the Bures angle, introduced a new bound tighter than both ML and MT, and showed that non-Markovianity can speed up quantum evolution.

    “Then, Deffner and Lutz [33] extended the ML bound to open quantum systems by adopting again a geometric approach using the Bures angle.These authors have also introduced a new sort of bound, which is tighter than both the ML and MT ones, and shown that non-Markovianity can speed up the quantum evolution.”

    From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [33]

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Research works printed but not linked: 33

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Cited by

Sorted by citations

Authors
Russell, B., & Stepney, S.
Affiliations
University of York (GB)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2014-07-02
Volume
90
Issue
1
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.90.012303
OpenAlex
W1968557587
Cited by
72
References
6
Citations by year
2025: 1 · 2024: 6 · 2023: 5 · 2022: 7 · 2021: 5 · 2020: 5 · 2019: 6 · 2018: 5 · 2017: 9 · 2016: 8 · 2015: 13 · 2014: 2
FWCI
10.63
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (submittedVersion)
  • arXiv (Cornell University)
Funders
Engineering and Physical Sciences Research Council
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum speed limit, quantum gate implementation, time-optimal control, Riemannian manifolds, Finsler metrics, Randers metrics, geodesics, quantum operations, SWAP gate, Heisenberg spin chain, quantum information processing

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