The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
Open accessAbstract
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a $(2n+1)\ifmmode\times\else\texttimes\fi{}(2n+1)$ binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.
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“To prove Eq. (5.4) using the semidefinite program in [49] first note that Φ = E 1 -E 2 has action,”
From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [49]
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Citations
Cites
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
The Heisenberg Representation of Quantum Computers
Gottesman, D. (1998) · University of North Texas Digital Library (University of North Texas) · Cited by 385
Local permutations of products of Bell states and entanglement distillation
Dehaene, J., den Nest, M. V., Moor, B. D., & Verstraete, F. (2003) · Physical Review A · doi:10.1103/physreva.67.022310 · Cited by 84
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Cited by
Sorted by citations
Improved simulation of stabilizer circuits
Aaronson, S., & Gottesman, D. (2004) · Physical Review A · doi:10.1103/physreva.70.052328 · Cited by 1,515
Characterizing quantum gates via randomized benchmarking
Magesan, E., Gambetta, J. M., & Emerson, J. (2012) · Physical Review A · doi:10.1103/physreva.85.042311 · Cited by 464
A Universal Operator Growth Hypothesis
Parker, D. E., Cao, X., Avdoshkin, A., Scaffidi, T., & Altman, E. (2019) · Physical Review X · doi:10.1103/physrevx.9.041017 · Cited by 588
“[105] Jeroen Dehaene and Bart De Moor, “Clifford group, stabilizer states, and linear and quadratic operations over gf(2),” Phys.”
BackgroundHudson’s theorem for finite-dimensional quantum systems
Gross, D. (2006) · Journal of Mathematical Physics · doi:10.1063/1.2393152 · Cited by 366
Trading Classical and Quantum Computational Resources
Bravyi, S. B., Smith, G., & Smolin, J. A. (2016) · Physical Review X · doi:10.1103/physrevx.6.021043 · Cited by 415
Metadata
- Authors
- Dehaene, J., & De Moor, B.
- Affiliations
- KU Leuven (BE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2003-10-20
- Volume
- 68
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2009169733
- Cited by
- 183
- References
- 3
- Citations by year
- 2026: 16 · 2025: 21 · 2024: 14 · 2023: 14 · 2022: 16 · 2021: 10 · 2020: 13 · 2019: 9 · 2018: 6 · 2017: 6 · 2016: 7 · 2015: 6 · 2014: 7 · 2013: 2 · 2012: 5
- FWCI
- 5.32
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Lirias (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Clifford group, stabilizer states, binary quadratic forms, binary vector spaces, GF(2), group isomorphism, quantum error correction, entanglement distillation
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