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Cited by 128Random Matrices and ApplicationsQuantum chaos and dynamical systemsSpectral Theory in Mathematical Physics

Composed ensembles of random unitary matrices

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Pozniak, Marcin, Zyczkowski, Karol, Kus, Marek·1998·Journal of Physics A: Mathematical and General
DOI 10.1088/0305-4470/31/3/016
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Abstract

Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance. We also discuss the methods of generating random matrices distributed according to invariant Haar measure on the orthogonal and unitary group.

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Crossref · 10.1088/0305-4470/31/3/016

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26 of 26 references verified0 citation errors · 0 not checkable

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  • Choosing the target transformation U randomly from the Haar measure leads to a universal form of the gate fidelity depending only on the intrinsic strength of the cumulative noise.

    “The key idea is to choose the target transformation U randomly from the Haar measure [12]. This will earn us the advantage of the concentration of measure in large Hilbert spaces, as described further below, and leads to a universal form of the gate fidelity depending only on the intrinsic strength of the cumulative noise.”

    From Scalable noise estimation with random unitary operators (2005) · cites this paper as [12]

  • The only inefficiency of the protocol is the requirement of experimentally implementing a Haar-random unitary, whose decomposition into elementary one- and two-qubit gates requires an exponentially long gate sequence.

    “The only inefficiency of our protocol is the requirement of experimentally implementing a Haar-random unitary: the decomposition into elementary one and two qubit gates requires an exponentially long gate sequence [12].”

    From Scalable noise estimation with random unitary operators (2005) · cites this paper as [12]

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Research works printed but not linked: 4

  1. [3]C. W. J. Beenakker, preprint cont-mat/9612179 and to appear in Rev. Mod. Phys. 1997 .
  2. [6]M. L. Mehta, Random Matrices , II ed. Academic Press, New York, 1991.
  3. [19]F. Izrailev, Phys. Rep. 129, 299 (1990).
  4. [24]K. ˙ Zyczkowski, Phys. Rev. E, 1997, in press

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Related

Authors
Pozniak, M., Zyczkowski, K., & Kus, M.
Affiliations
Jagiellonian University (PL)
Venue
Journal of Physics A: Mathematical and General
Publisher
IOP Publishing
Published
1998-01-23
Volume
31
Issue
3
Pages
1059-1071
ISSN
  • 0305-4470 (ISSN-L)
  • 1361-6447
DOI
10.1088/0305-4470/31/3/016
OpenAlex
W1993950005
Cited by
128
References
26
Citations by year
2025: 3 · 2024: 4 · 2023: 4 · 2022: 1 · 2021: 2 · 2020: 4 · 2019: 1 · 2018: 5 · 2017: 2 · 2016: 3 · 2015: 6 · 2014: 5 · 2013: 6 · 2012: 2
FWCI
8.51
Type
journal article
Language
en
Open access
Locations
  • Journal of Physics A Mathematical and General (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
Keywords
random unitary matrices, matrix products, eigenvalue statistics, Haar measure, unitary groups, orthogonal group, random matrix theory

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