zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fault-tolerant quantum computation by anyons. (English) Zbl 1012.81006
Summary: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.

81P68Quantum computation
81R10Infinite-dimensional groups and algebras motivated by physics
Full Text: DOI
[1] Shor, P.: Proceedings of the 35th annual symposium on fundamentals of computer science. 124-134 (1994)
[2] Shor, P.: Proceedings of the symposium on the foundations of computer science. (1996)
[3] E. Knill, R. Laflamme, Concatenated quantum codes, 1996 (e-print quant-ph/9608012)
[4] E. Knill, R. Laflamme, W. Zurek, Accuracy threshold for quantum computation, 1996 (e-print quant-ph/9610011)
[5] D. Aharonov, M. Ben-Or, Fault-tolerant quantum computation with constant error, 1996 (e-print quant-ph/9611025)
[6] Kitaev, A. Yu.: Quantum computation: algorithms and error correction. Russian math. Surveys 52, No. 6, 1191 (1997)
[7] C. Zalka, Threshold estimate for fault-tolerant quantum computing, 1996 (e-print quant-ph/9612028)
[8] Kitaev, A. Yu.: O.hirotaa.s.holevoc.m.cavesquantum communication, computing and measurement. Quantum communication, computing and measurement (1997)
[9] Wilczek, F.: Fractional statistics and anyon superconductivity. (1990) · Zbl 0709.62735
[10] Dijkgraaf, R.; Pasquier, V.; Roche, P.: Nucl. phys. B (Proc. Suppl.). 18B (1990)
[11] Bais, F. A.; Van Driel, P.; De Wild Propitius, M.: Phys. lett. B. 280, 63 (1992)
[12] F.A. Bais, M. de Wild Propitius, Discrete gauge theories, 1995 (e-print hep-th/9511201)
[13] Lo, H. K.; Preskill, J.: Phys. rev. D. 48, 4821 (1993)
[14] Castagnoli, G.; Rasetti, M.: Int. J. Mod. phys.. 32, 2335 (1993)
[15] Gottesman, D.: Phys. rev. A. 54, 1862 (1996)
[16] Calderbank, A. R.; Rains, E. M.; Shor, P. M.; Sloane, N. J. A.: Phys. rev. Lett.. 78, 405 (1997)
[17] A.R. Calderbank, P.W. Shor, Good quantum error-correcting codes exist, 1995 (e-print quant-ph/9512032)
[18] Arovas, D.; Schrieffer, J. R.; Wilczek, F.: Phys. rev. Lett.. 53, 722-723 (1984)
[19] Einarsson, T.: Phys. rev. Lett.. 64, 1995-1998 (1984)
[20] Drinfeld, V. G.: Proc. int. Cong. math. (Berkley, 1986). 798-820 (1987)
[21] Sweedler, M.: Hopf algebras. (1969) · Zbl 0194.32901
[22] Majid, S.: Int. J. Mod. phys. A. 5, 1-91 (1990)
[23] Kassel, C.: Quantum groups. (1995) · Zbl 0808.17003
[24] A.Yu. Kitaev, Quantum measurements and Abelian stabilizer problem, 1995 (e-print quant-ph/9511026)
[25] T’hooft, G.: Nucl. phys. B. 138, 1 (1978)