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Composed ensembles of random unitary matrices
Open accessAbstract
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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“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]
In the citing paper
“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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Citations
Cites
Random-matrix theory of quantum transport
Beenakker, C. W. J. (1997) · Reviews of Modern Physics · doi:10.1103/revmodphys.69.731 · Cited by 2,551
Statistical Theory of the Energy Levels of Complex Systems. I
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703773 · Cited by 2,215
Haake, F. (2010) · Springer series in synergetics · doi:10.1007/978-3-642-05428-0 · Cited by 2,072
Simple models of quantum chaos: Spectrum and eigenfunctions
Izrailev, F. M. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90067-c · Cited by 888
Statistical Theory of the Energy Levels of Complex Systems. III
Dyson, F. J. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703775 · Cited by 600
Semiclassical level spacings when regular and chaotic orbits coexist
Berry, M., & Robnik, M. (1984) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/17/12/013 · Cited by 594
Quantum dynamics of a nonintegrable system
Grempel, D. R., Prange, R. E., & Fishman, S. (1984) · Physical Review A · doi:10.1103/physreva.29.1639 · Cited by 496
Classical and quantum chaos for a kicked top
Haake, F., Kuś, M., & Scharf, R. (1987) · The European Physical Journal B · doi:10.1007/bf01303727 · Cited by 399
Classical irregular scattering and its quantum-mechanical implications
Blümel, R., & Smilansky, U. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.477 · Cited by 318
Życzkowski, K., & Kuś, M. (1994) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/27/12/028 · Cited by 279
Research works printed but not linked: 2
- Zyczkowski K, 1993, Acta Phys. Pol., 24, 967
- Hurwitz A, 1897, Nachr. Ges. Wiss. Gött. Math.-Phys., Kl, 71
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Metadata
- 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
- 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
- green
- arxiv.org
- 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
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 ›
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