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AN EXACT ENTANGLING GATE USING FIBONACCI ANYONS

Part of: Categories with structure Low-dimensional topology

Published online by Cambridge University Press:  12 November 2018

STEPHEN BIGELOW Open the ORCID record for STEPHEN BIGELOW [Opens in a new window]  and
CLAIRE LEVAILLANT Open the ORCID record for CLAIRE LEVAILLANT [Opens in a new window]
STEPHEN BIGELOW*
Affiliation:
Department of Mathematics, South Hall Room 6607, University of California, Santa Barbara, CA 93106, USA email bigelow@math.ucsb.edu
CLAIRE LEVAILLANT
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA email clairelevaillant@yahoo.fr
*
✉bigelow@math.ucsb.edu
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Abstract

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Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However, there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known ‘leakage-free’ entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.

Keywords

quantum computationFibonacci anyonsknot invariants

MSC classification

Primary: 81P68: Quantum computation
Secondary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 57M27: Invariants of knots and 3-manifolds

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 319 - 326
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Bonderson, P., Freedman, M. and Nayak, C., ‘Measurement-only topological quantum computation’, Phys. Rev. Lett. 101(1) (2008), 010501, 4 pages.Google Scholar
Carnahan, C., Zeuch, D. and Bonesteel, N. E., ‘Systematically generated two-qubit anyon braids’, Phys. Rev. A (3) 93 (2016), 052328, 9 pages.Google Scholar
Dodd, J. L., Nielsen, M. A., Bremner, M. J. and Thew, R. T., ‘Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries’, Phys. Rev. A (3) 65(4, part A) (2002), 040301, 4 pages.Google Scholar
Freedman, M. H., Larsen, M. and Wang, Z., ‘A modular functor which is universal for quantum computation’, Comm. Math. Phys. 227(3) (2002), 605–622.Google Scholar
Wang, Z., Topological Quantum Computation, CBMS Regional Conference Series in Mathematics, 112 (American Mathematical Society, Providence, RI, 2010).Google Scholar
Kitaev, A. Yu., ‘Fault-tolerant quantum computation by anyons’, Ann. Physics 303(1) (2003), 2–30.Google Scholar