TY - JOUR

T1 - Towards topological quantum computer

AU - Melnikov, D.

AU - Mironov, A.

AU - Mironov, S.

AU - Morozov, A.

AU - Morozov, An

N1 - Publisher Copyright:
© 2017 The Authors

PY - 2018/1

Y1 - 2018/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85037656515&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2017.11.016

DO - 10.1016/j.nuclphysb.2017.11.016

M3 - 文章

AN - SCOPUS:85037656515

VL - 926

SP - 491

EP - 508

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -