×

zbMATH — the first resource for mathematics

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.

MSC:
81P68 Quantum computation
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Shor, P., (), 124-134
[2] Shor, P., (), e-print quant-ph/9605011
[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, 6, 1191, (1997) · Zbl 0917.68063
[7] C. Zalka, Threshold estimate for fault-tolerant quantum computing, 1996 (e-print quant-ph/9612028)
[8] Kitaev, A.Yu., ()
[9] Wilczek, F., Fractional statistics and anyon superconductivity, (1990), World Scientific Singapore · 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., (), 798-820
[21] Sweedler, M., Hopf algebras, (1969), W.A. Benjamin New York · Zbl 0194.32901
[22] Majid, S., Int. J. mod. phys. A, 5, 1-91, (1990)
[23] Kassel, C., Quantum groups, (1995), Springer-Verlag New York · 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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.