publication . Part of book or chapter of book . Preprint . 2013

QUANTUM COMPUTING: A QUANTUM GROUP APPROACH

Wang, Zhenghan;
Open Access
  • Published: 14 Aug 2013
  • Publisher: WORLD SCIENTIFIC
Abstract
Comment: To appear in the proceedings of the 2012 Nankai international conference group methods in physics
Subjects
free text keywords: Mathematics - Quantum Algebra, Quantum Physics
Related Organizations
Funded by
NSF| Collaborative Research: Topological Phases of Matter and Their Application to Quantum Computing
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1108736
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
23 references, page 1 of 2

[1] Bennett, C.H. and Brassard,G. (1984) Quantum Cryptography: Public key distribution and coin tossing, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, p. 175 (1984).

[2] B. Bakalov and A. Kirillov, Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series 21, Amer. Math. Soc., 2001.

[3] S. Bravyi and A. Kitaev, Universal Quantum Computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005), arXiv:quantph/0403025. [OpenAIRE]

[4] P. Bruillard, S. Ng, E. Rowell, and Z. Wang, On modular categories, in preparation.

[5] P. Etingof, D. Nikshych, and V. Ostrik, On fusion categories, Ann. of Math. (2) 162, 2 (2005), 581-642, arXiv:math/0203060.

[6] M. Freedman, P/NP, and the quantum field computer, Proc. Natl. Acad. Sci. USA 95, 1 (1998), 98-101.

[7] Z.-G. Gu, Z. Wang, X.-G. Wen, A classification of 2D fermionic and bosonic topological orders, arXiv:1010.1517.

[8] Hastings, M.B. (2009), Superadditivity of communication capacity using entangled inputs, Nature Physics 5, 255 - 257 (2009).

[9] M.B. Hastings, C. Nayak, and Z. Wang, Metaplectic Anyons, Majorana Zero Modes, and their Computational Power, arXiv:1210.5477.

[10] H.C. Jiang, L. Balents, and Z. Wang, Identifying topological order by entanglement entropy, Nature Physics 8, 902-905(2012), doi:10.1038/nphys2465, arXiv:1205.4289.

[11] V. Jones, Braid groups, Hecke algebras and type II1 factors, in Geometric Methods in Operator Algebras (Kyoto, 1983), Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech., Harlow, 1986, 242-273. Harlow, 1986.

[12] K. Walker and Z. Wang, (3+1)-TQFTs and Topological Insulators, Front. Phys., 2012, 7(2): 150-159, arXiv:1104.2632.

[13] A. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Physics 303, 1 (2003), 2-30, arXiv:quant-ph/9707021.

[14] A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Physics 321, 1 (2006), 2-111, arXiv:cond-mat/0506438.

[15] M. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases, Phys. Rev. B 71, 4 (2005), 045110, arXiv:cond-mat/0404617.

23 references, page 1 of 2
Abstract
Comment: To appear in the proceedings of the 2012 Nankai international conference group methods in physics
Subjects
free text keywords: Mathematics - Quantum Algebra, Quantum Physics
Related Organizations
Funded by
NSF| Collaborative Research: Topological Phases of Matter and Their Application to Quantum Computing
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1108736
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
23 references, page 1 of 2

[1] Bennett, C.H. and Brassard,G. (1984) Quantum Cryptography: Public key distribution and coin tossing, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, p. 175 (1984).

[2] B. Bakalov and A. Kirillov, Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series 21, Amer. Math. Soc., 2001.

[3] S. Bravyi and A. Kitaev, Universal Quantum Computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005), arXiv:quantph/0403025. [OpenAIRE]

[4] P. Bruillard, S. Ng, E. Rowell, and Z. Wang, On modular categories, in preparation.

[5] P. Etingof, D. Nikshych, and V. Ostrik, On fusion categories, Ann. of Math. (2) 162, 2 (2005), 581-642, arXiv:math/0203060.

[6] M. Freedman, P/NP, and the quantum field computer, Proc. Natl. Acad. Sci. USA 95, 1 (1998), 98-101.

[7] Z.-G. Gu, Z. Wang, X.-G. Wen, A classification of 2D fermionic and bosonic topological orders, arXiv:1010.1517.

[8] Hastings, M.B. (2009), Superadditivity of communication capacity using entangled inputs, Nature Physics 5, 255 - 257 (2009).

[9] M.B. Hastings, C. Nayak, and Z. Wang, Metaplectic Anyons, Majorana Zero Modes, and their Computational Power, arXiv:1210.5477.

[10] H.C. Jiang, L. Balents, and Z. Wang, Identifying topological order by entanglement entropy, Nature Physics 8, 902-905(2012), doi:10.1038/nphys2465, arXiv:1205.4289.

[11] V. Jones, Braid groups, Hecke algebras and type II1 factors, in Geometric Methods in Operator Algebras (Kyoto, 1983), Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech., Harlow, 1986, 242-273. Harlow, 1986.

[12] K. Walker and Z. Wang, (3+1)-TQFTs and Topological Insulators, Front. Phys., 2012, 7(2): 150-159, arXiv:1104.2632.

[13] A. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Physics 303, 1 (2003), 2-30, arXiv:quant-ph/9707021.

[14] A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Physics 321, 1 (2006), 2-111, arXiv:cond-mat/0506438.

[15] M. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases, Phys. Rev. B 71, 4 (2005), 045110, arXiv:cond-mat/0404617.

23 references, page 1 of 2
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