The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Topological quantum computation
Open accessAbstract
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possibility for the realization of quantum computers. The chief advantage of anyonic computation would be physical error correction: An error rate scaling like e−αℓ, where ℓ is a length scale, and α is some positive constant. In contrast, the “presumptive" qubit-model of quantum computation, which repairs errors combinatorically, requires a fantastically low initial error rate (about 10−4) before computation can be stabilized.
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Citations
Cites
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758
Quantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Quantum Mechanics Helps in Searching for a Needle in a Haystack
Grover, L. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.325 · Cited by 4,306 · cited 1×
“In this context, there are three areas where remarkable algorithms have been found: searching a data base [15], abelian groups (factoring and discrete logarithm) [19], [27], and simulating physical systems [5], [21].”
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088 · cited 2×
“In this context, there are three areas where remarkable algorithms have been found: searching a data base [15], abelian groups (factoring and discrete logarithm) [19], [27], and simulating physical systems [5], [ 21 ].”
Fidelity for Mixed Quantum States
Jozsa, R. (1994) · Journal of Modern Optics · doi:10.1080/09500349414552171 · Cited by 1,911
Feynman, R. P. (1986) · Foundations of Physics · doi:10.1007/bf01886518 · Cited by 1,770
Quantum computations: algorithms and error correction
Kitaev, A. Y. (1997) · Russian Mathematical Surveys · doi:10.1070/rm1997v052n06abeh002155 · Cited by 1,424
Self-citation
Cited by
Non-Abelian anyons and topological quantum computation
Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1083 · Cited by 6,861
Self-citationColloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Non-Abelian statistics and topological quantum information processing in 1D wire networks
Alicea, J., Oreg, Y., Refael, G., von Oppen, F., & Fisher, M. P. A. (2011) · Nature Physics · doi:10.1038/nphys1915 · Cited by 1,636
Universal quantum computation with ideal Clifford gates and noisy ancillas
Bravyi, S., & Kitaev, A. (2005) · Physical Review A · doi:10.1103/physreva.71.022316 · Cited by 1,525
Self-citationMatrix product states and projected entangled pair states: Concepts, symmetries, theorems
Cirac, J. I., Pérez-García, D., Schuch, N., & Verstraete, F. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.045003 · Cited by 769
Metadata
- Authors
- Freedman, M., Kitaev, A., Larsen, M., & Wang, Z.
- Venue
- Bulletin of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 2002-10-10
- Volume
- 40
- Issue
- 1
- Pages
- 31-38
- ISSN
- 0002-9904 (ISSN-L)
- 0273-0979
- 1088-9485
- OpenAlex
- W2949110438
- Cited by
- 669
- References
- 12
- FWCI
- 8.03
- Type
- journal article
- Language
- en
- Open access
- diamond
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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