CoChat
Sign Up
Cited by 164Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum Mechanics and Applications

Robustness of quantum gates in the presence of noise

Open access
Harrow, Aram W., Nielsen, Michael A.·2003·Physical Review A
DOI 10.1103/physreva.68.012308
Open this paper in CoChat — free accountOpen PDF

Abstract

We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all bipartite unitary quantum gates, and it is found that the controlled-NOT gate is the most robust two-qubit quantum gate, in the sense that it is the quantum gate which can tolerate the most depolarizing noise and still generate entanglement. Our results enable us to place several analytic upper bounds on the value of the threshold for quantum computation, with the best bound in the most pessimistic error model being ${p}_{\mathrm{th}}<~0.5.$

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physreva.68.012308

Cites

23 of 23 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • At criticality, the von Neumann entropy of a subregion of size l scales as c/6 log(L/π sin(lπ/L)) + A.

    “At criticality, this entropy scales as c/ 6 log( L/π sin( lπ/L ))+ A [188-190].”

    From Can one trust quantum simulators? (2012) · cites this paper as [190]

  • For systems with open boundary conditions, a fit to c/6 log(L/π sin(lπ/L))+A (excluding small l) yields the effective central charge c.

    “For systems with open boundary conditions, a fit to c/ 6 log( L/π sin( lπ/L ))+ A (excluding small values of l ) yields the effective central charge c [188-190].”

    From Can one trust quantum simulators? (2012) · cites this paper as [190]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 13

  1. E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59 , 1070 (1999), arXiv:quant-ph/9804053. · arXiv
  2. [20]J. I. Cirac, W. D¨ ur, B. Kraus, and M. Lewenstein, Phys. Rev. Lett. 86 , 544 (2001), arXiv:quant-ph/0007057. · arXiv
  3. [21]M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 60 , 1888 (1999), arXiv:quant-ph/9807091. · arXiv
  4. [22]A. C. Yao, Proc. of the 34th Ann. IEEE Symp. on Foundations of Computer Science pp. 352-361 (1993).
  5. [23]R. T. Rockafeller, Convex Analysis (Princeton University Press, Princeton, 1970).
  6. [24]R. Jozsa and N. Linden, arXiv:quant-ph/0201143 (2002). · arXiv
  7. [25]S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. 83 , 1054 (1999), arXiv:quant-ph/9811018. · arXiv
  8. [26]N. C. Menicucci and C. M. Caves, Phys. Rev. Lett. 88 , 167901 (2002), arXiv:quant-ph/0111152. · arXiv
  9. [27]N. Linden and S. Popescu, Phys. Rev. Lett. 87 , 047901 (2001), arXiv:quant-ph/9906008. · arXiv
  10. [28]A. Peres, Phys. Rev. Lett. 77 , 1413 (1996), arXiv:quant-ph/9604005. · arXiv
  11. [30]M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, arXiv:quant-ph/0207072 (2002). · arXiv
  12. [31]I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44 , 2455 (1997), arXiv:quant-ph/9610001. · arXiv
  13. [34]R. K. Brylinski and G. Chen, eds., Mathematics of Quantum Computation , Computational Mathematics (Chapman &amp; Hall / CRC Press, 2002).

Cited by

Sorted by citations

Related

Authors
Harrow, A. W., & Nielsen, M. A.
Affiliations
The University of Queensland (AU)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2003-07-11
Volume
68
Issue
1
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.68.012308
OpenAlex
W1545271014
Cited by
164
References
23
Citations by year
2026: 10 · 2025: 13 · 2024: 10 · 2023: 10 · 2022: 9 · 2021: 10 · 2020: 6 · 2019: 10 · 2018: 5 · 2017: 4 · 2016: 2 · 2015: 3 · 2014: 5 · 2013: 3 · 2012: 3
FWCI
7.07
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)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
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
depolarizing noise, CNOT gate, two-qubit gates, entanglement generation, noise immunity

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review