期刊
NUCLEAR PHYSICS B
卷 926, 期 -, 页码 491-508出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.nuclphysb.2017.11.016
关键词
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资金
- Brazilian Ministry of Education
- RFBR grants [16-01-00291, 15-01-05990, 16-02-01021, 17-01-00585, 17-51-50051-YaF, 15-51-52031-NSC-a, 16-51-53034-GFEN, 16-51-45029-IND-a]
- [16-32-60047-Mol-a-dk]
Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms. (C) 2017 The Authors. Published by Elsevier B.V.
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