Graphical description of the action of local Clifford transformations on graph states
Open accessAbstract
We translate the action of local Clifford operations on graph states into transformations on their associated graphs, i.e., we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the evolution of graph states under local Clifford operations. As we will show, there is essentially one basic rule, successive application of which generates the orbit of any graph state under local unitary operations within the Clifford group.
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The state |Φ̂θ〉△ is obtained via local complementation on qubit 2 of |Φ̂θ〉⊂.
“The state | Φ ˆ θ 〉 △ is obtained via local complementation [44] on qubit 2 of | Φ ˆ θ 〉 ⊂ .”
From Demonstration of Blind Quantum Computing (2012) · cites this paper as [44]
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- Authors
- Van den Nest, M., Dehaene, J., & De Moor, B.
- Affiliations
- KU Leuven (BE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2004-02-24
- Volume
- 69
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2165148883
- Cited by
- 335
- References
- 8
- Citations by year
- 2026: 14 · 2025: 34 · 2024: 25 · 2023: 21 · 2022: 19 · 2021: 22 · 2020: 16 · 2019: 15 · 2018: 11 · 2017: 8 · 2016: 13 · 2015: 6 · 2014: 8 · 2013: 9 · 2012: 12
- FWCI
- 14.54
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- graph states, Clifford group, local unitary operations, graph transformation, quantum error correction, graph 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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