The idea of topological quantum computation via the Chern-Simons theory of anyons (e.g. in the quantum Hall effect) is due to:
Alexei Kitaev, Fault-tolerant quantum computation by anyons, Annals Phys. 303 (2003) 2-30 (arXiv:quant-ph/9707021, doi:10.1016/S0003-4916(02)00018-0)
Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang, Topological quantum computation, Bull. Amer. Math. Soc. 40 (2003), 31-38 (arXiv:quant-ph/0101025, doi:10.1090/S0273-0979-02-00964-3, pdf)
Michael Freedman, Michael Larsen, Zhenghan Wang, A modular functor which is universal for quantum computation, Communications in Mathematical Physics. 2002, Vol 227, Num 3, pp 605-622 (arXiv:quant-ph/0001108)
(specifically via su(2)-anyons)
D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov, Towards topological quantum computer, Nucl. Phys. B926 (2018) 491-508 (arXiv:1703.00431, doi:10.1016/j.nuclphysb.2017.11.016)
Textbook accounts:
Zhenghan Wang, Topological Quantum Computation, CBMS Regional Conference Series in Mathematics 112, AMS 2010 (ISBN-13: 978-0-8218-4930-9, pdf)
Jiannis K. Pachos, Introduction to Topological Quantum Computation, Cambridge University Press (2012) doi:10.1017/CBO9780511792908
Tudor D. Stanescu, Part IV of: Introduction to Topological Quantum Matter & Quantum Computation, CRC Press 2020 (ISBN:9780367574116)
Steven H. Simon, Topological Quantum, 2021 pdf, webpage
Review:
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys. 80 1083 (2008) arXiv:0707.1888, doi:10.1103/RevModPhys.80.1083
Ady Stern, Netanel H. Lindner, Topological Quantum Computation – From Basic Concepts to First Experiments, Science 339 6124 (2013) 1179-1184 (doi:10.1126/science.1231473)
Eric C. Rowell, An Invitation to the Mathematics of Topological Quantum Computation, J. Phys.: Conf. Ser. 698 (2016) 012012 (doi:10.1088/1742-6596/698/1/012012)
Ville Lahtinen, Jiannis K. Pachos, A Short Introduction to Topological Quantum Computation, SciPost Phys. 3 021 (2017) (arXiv:1705.04103)
Eric C. Rowell, Zhenghan Wang, Mathematics of Topological Quantum Computing, Bull. Amer. Math. Soc. 55 (2018), 183-238 (arXiv:1705.06206, doi:10.1090/bull/1605)
Bernard Field, Tapio Simula, Introduction to topological quantum computation with non-Abelian anyons, Quantum Science and Technology 3 (2018) 045004 (arXiv:1802.06176, doi:10.1088/2058-9565/aacad2)
Focus on abelian anyons:
Jiannis K. Pachos, Quantum computation with abelian anyons on the honeycomb lattice, International Journal of Quantum Information 4 6 (2006) 947-954 (arXiv:quant-ph/0511273)
James Robin Wootton, Dissecting Topological Quantum Computation, 2010 (pdf, pdf)
“non-Abelian anyons are usually assumed to be better suited to the task. Here we challenge this view, demonstrating that Abelian anyon models have as much potential as some simple non-Abelian models.”
Wade Bloomquist, Zhenghan Wang, On Topological Quantum Computing With Mapping Class Group Representations, J. Phys. A: Math. Theor. 52 (2019) 015301 (arXiv:1805.04622, doi:10.1088/1751-8121/aaeea1)
Seth Lloyd, Quantum computation with abelian anyons, Quantum Information Processing 1 1/2 (2002) (arXiv:quant-ph/0004010, doi:10.1023/A:1019649101654)
Realization in experiment:
Daniel Nigg, Markus Mueller, Esteban A. Martinez, Philipp Schindler, Markus Hennrich, Thomas Monz, Miguel A. Martin-Delgado, Rainer Blatt,
Experimental Quantum Computations on a Topologically Encoded Qubit, Science 18 Jul 2014: Vol. 345, Issue 6194, pp. 302-305 (arXiv:1403.5426, doi:10.1126/science.1253742)
(for quantum error correction)
On linear representations of braid groups (see also at braid group statistics and interpretation as quantum gates in topological quantum computation):
Review:
Camilo Arias Abad, Introduction to representations of braid groups, Rev. colomb. mat. vol.49 no.1 (2015) (arXiv:1404.0724, doi:10.15446/recolma.v49n1.54160)
Toshitake Kohno, Introduction to representation theory of braid groups, Peking 2018 (pdf, pdf)
in relation to modular tensor categories:
Braid representations seen inside the topological K-theory of the braid group‘s classifying space:
Alejandro Adem, Daniel C. Cohen, Frederick R. Cohen, On representations and K-theory of the braid groups, Math. Ann. 326 (2003) 515-542 (arXiv:math/0110138, doi:10.1007/s00208-003-0435-8)
Frederick R. Cohen, Section 3 of: On braid groups, homotopy groups, and modular forms, in: J.M. Bryden (ed.), Advances in Topological Quantum Field Theory, Kluwer 2004, 275–288 (pdf)
See also:
As quantum gates for topological quantum computation with anyons:
Louis H. Kauffman, Samuel J. Lomonaco, Braiding Operators are Universal Quantum Gates, New Journal of Physics, Volume 6, January 2004 (arXiv:quant-ph/0401090, doi:10.1088/1367-2630/6/1/134)
Samuel J. Lomonaco, Louis Kauffman, Topological Quantum Computing and the Jones Polynomial, Proc. SPIE 6244, Quantum Information and Computation IV, 62440Z (2006) (arXiv:quant-ph/0605004)
(braid group representation serving as a topological quantum gate to compute the Jones polynomial)
Louis H. Kauffman, Samuel J. Lomonaco, Topological quantum computing and braid group representations, Proceedings Volume 6976, Quantum Information and Computation VI; 69760M (2008) (doi:10.1117/12.778068, rg:228451452)
C.-L. Ho, A.I. Solomon, C.-H.Oh, Quantum entanglement, unitary braid representation and Temperley-Lieb algebra, EPL 92 (2010) 30002 (arXiv:1011.6229)
Louis H. Kauffman, Majorana Fermions and Representations of the Braid Group, International Journal of Modern Physics AVol. 33, No. 23, 1830023 (2018) (arXiv:1710.04650, doi:10.1142/S0217751X18300235)
Introduction and review:
Approximating all topological quantum gates by just the weaves among all braids:
Steven H. Simon, Nick E. Bonesteel, Michael H. Freedman, N. Petrovic, Layla Hormozi, Topological Quantum Computing with Only One Mobile Quasiparticle, Phys. Rev. Lett. 96 (2006) 070503 (arXiv:quant-ph/0509175, doi:10.1103/PhysRevLett.96.070503)
Layla Hormozi, Georgios Zikos, Nick E. Bonesteel, Steven H. Simon, Topological quantum compiling, Phys. Rev. B 75, 165310 (doi:10.1103/PhysRevB.75.165310, arXiv:quant-ph/0610111)
Mohamed Taha Rouabah, Compiling single-qubit braiding gate for Fibonacci anyons topological quantum computation (arXiv:2008.03542)
Last revised on June 11, 2022 at 12:05:03. See the history of this page for a list of all contributions to it.