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Știința și tehnologia calculatoarelor. Calculatoare. Procesarea datelor (4156) |
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SM ISO690:2012 KANTSER, Valeriu. Some Aspects of Mathematical and Physical
Approaches for Topological Quantum
Computation. In: Computer Science Journal of Moldova, 2011, nr. 2(56), pp. 206-216. ISSN 1561-4042. |
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Computer Science Journal of Moldova | ||||||
Numărul 2(56) / 2011 / ISSN 1561-4042 /ISSNe 2587-4330 | ||||||
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CZU: 004:[519.712+530.145] | ||||||
Pag. 206-216 | ||||||
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Rezumat | ||||||
A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of
knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin
braid group - the mathematical basis of topological quantum
computation (TQC). Vector spaces of TQC correspond to associated strings of particle interactions, and TQC operates its
calculations on braided strings of special physical quasiparticles
- anyons - with non-Abelian statistics. The physical platform of
TQC is to use the topological quantum numbers of such small
groups of anyons as qubits and to perform operations on these
qubits by exchanging the anyons, both within the groups that
form the qubits and, for multi-qubit gates, between groups. By
braiding two or more anyons, they acquire up a topological phase
or Berry phase similar to that found in the Aharonov-Bohm effect. Topological matter such as fractional quantum Hall systems and novel discovered topological insulators open the way to
form system of anyons - Majorana fermions - with the unique
property of encoding and processing quantum information in a
naturally fault-tolerant way. In the topological insulators, due to
its fundamental attribute of topological surface state occurrence
of the bound, Majorana fermions are generated at its heterocontact with superconductors. One of the key operations of TQC - braiding of non-Abelian anyons: it is illustrated how it can be implemented in one-dimensional topological isolator wire networks. |
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Cuvinte-cheie topological computation, braided strings, anyons, topological phase, braiding |
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