### Quantum computing

[1] article : “P/NP, and the quantum field computer,” Proc. Natl. Acad. Sci. USA 95 : 1 (1998), pp. 98–101. MR 1612425 Zbl 0895.68053

[2] incollection : “Topological views on computational complexity,” pp. 453–464 in Proceedings of the International Congress of Mathematicians (Berlin, 1998), published as Doc. Math. Extra II. Fakultät für Mathematik, Universität Bielefeld (Bielefeld), 1998. MR 1648095 Zbl 0967.68520

[3]
incollection
:
“__\( K \)__-sat on groups and undecidability,”
pp. 572–576
in
Proceedings of the thirtieth annual ACM symposium on theory of computing
(Dallas, TX, May 23–26, 1998).
Edited by Association for Computing Machinery.
Association for Computing Machinery (New York),
1998.
MR
1715605
Zbl
1028.68068

[4] article : “Projective plane and planar quantum codes,” Found. Comput. Math. 1 : 3 (2001), pp. 325–332. MR 1838758 Zbl 0995.94037 ArXiv quant-ph/9810055

[5] article : “Quantum computation and the localization of modular functors,” Found. Comput. Math. 1 : 2 (2001), pp. 183–204. MR 1830035 Zbl 1004.57026 ArXiv quant-ph/0003128

[6] article : “The two-eigenvalue problem and density of Jones representation of braid groups,” Comm. Math. Phys. 228 : 1 (2002), pp. 177–199. MR 1911253 Zbl 1045.20027

[7] article : “A modular functor which is universal for quantum computation,” Comm. Math. Phys. 227 : 3 (2002), pp. 605–622. MR 1910833 Zbl 1012.81007 ArXiv quant-ph/0001108

[8] article : “Simulation of topological field theories by quantum computers,” Comm. Math. Phys. 227 : 3 (2002), pp. 587–603. MR 1910832 Zbl 1014.81006 ArXiv quant-ph/0001071

[9] article : “Poly-locality in quantum computing,” Found. Comput. Math. 2 : 2 (2002), pp. 145–154. MR 1894373 Zbl 1075.81507 ArXiv quant-ph/0001077

[10]
incollection
:
“__\( Z_2 \)__-systolic freedom and quantum codes,”
pp. 287–320
in
Mathematics of quantum computation.
Edited by R. K. Brylinski and G. Chen.
Computational Mathematics 3.
Chapman & Hall/CRC (Boca Raton, FL),
2002.
MR
2007952
Zbl
1075.81508

[11] article : “A magnetic model with a possible Chern–Simons phase,” Comm. Math. Phys. 234 : 1 (2003), pp. 129–183. With an appendix by F. Goodman and H. Wenzl. MR 1961959 Zbl 1060.81054 ArXiv quant-ph/0110060

[12] article : “Topological quantum computation,” Bull. Amer. Math. Soc. (N.S.) 40 : 1 (2003), pp. 31–38. MR 1943131 Zbl 1019.81008 ArXiv quant-ph/0101025

[13] techreport : Non-Abelian topological phases in an extended Hubbard model. Preprint, September 2003. ArXiv cond-mat/0309120

[14]
article
:
“A class of __\( P,T \)__-invariant topological phases of interacting electrons,”
Ann. Physics
310 : 2
(2004),
pp. 428–492.
MR
2044743
Zbl
1057.81053

[15] article : “Approximate counting and quantum computation,” Combin. Probab. Comput. 14 : 5–6 (2005), pp. 737–754. MR 2174653 Zbl 1089.68040

[16] : “Line of critical points in \( 2+1 \) dimensions: Quantum critical loop gases and non-abelian gauge theory,” Phys. Rev. Lett. 94 : 14 (2005), pp. 147205.

[17] article : “Topologically-protected qubits from a possible non-abelian fractional quantum Hall state,” Phys. Rev. Lett. 94 : 6 (2005), pp. 166802. ArXiv cond-mat/0412343

[18] : “An extended Hubbard model with ring exchange: A route to a non-abelian topological phase,” Phys. Rev. Lett. 94 : 6 (2005), pp. 066401.

[19] techreport : Tilted interferometry realizes universal quantum computation in the Ising TQFT without overpasses. Preprint, December 2005. ArXiv cond-mat/0512072

[20] : “Towards universal topological quantum computation in the \( \nu=5/2 \) fractional quantum Hall state,” Phys. Rev. B 73 : 24 (2006), pp. 245307.

[21] : “Topological quantum computation,” Physics Today 59 : 7 (July 2006), pp. 32–38.

[22] article : “Topological quantum computing with only one mobile quasiparticle,” Phys. Rev. Lett. 96 : 7 (2006), pp. 070503. MR 2205654 ArXiv quant-ph/0509175

[23] article : “Interacting anyons in topological quantum liquids: The golden chain,” Phys. Rev. Lett. 98 (2007), pp. 160409. ArXiv cond-mat/0612341

[24] article : “Large quantum Fourier transforms are never exactly realized by braiding conformal blocks,” Phys. Rev. A (3) 75 : 3 (2007), pp. 032322. MR 2312110 ArXiv cond-mat/0609411

[25] article : “Measurement-only topological quantum computation,” Phys. Rev. Lett. 101 : 1 (2008), pp. 010501. MR 2429542 Zbl 1228.81121 ArXiv 0802.0279

[26] article : “Non-abelian anyons and topological quantum computation,” Rev. Modern Phys. 80 : 3 (2008), pp. 1083–1159. MR 2443722 Zbl 1205.81062 ArXiv 0707.1889

[27] : “Lieb–Schultz–Mattis theorem for quasitopological systems,” Phys. Rev. B 78 (2008), pp. 174411.

[28]
incollection
:
“On picture __\( (2+1) \)__-TQFTs,”
pp. 19–106
in
Topology and physics
(Tianjin, China, 27–31 July 2007).
Edited by K. Lin, Z. Weng, and W. Zhang.
Nankai Tracts in Mathematics 12.
World Scientific (Hackensack, NJ),
2008.
MR
2503392
Zbl
1168.81024
ArXiv
0806.1926

[29] techreport : A topological phase in a quantum gravity model. Preprint, December 2008. A talk at Solvay conference, October 2008. ArXiv 0812.2278

[30] article : “Measurement-only topological quantum computation via anyonic interferometry,” Ann. Physics 324 : 4 (2009), pp. 787–826. MR 2508474 Zbl 1171.81004 ArXiv 0808.1933

[31] article : “From string nets to nonabelions,” Comm. Math. Phys. 287 : 3 (2009), pp. 805–827. MR 2486662 Zbl 1196.82072 ArXiv cond-mat/0610583

[32] techreport : A blueprint for a topologically fault-tolerant quantum computer. Preprint, March 2010. ArXiv 1003.2856

[33] article : “Topological phases: An expedition off lattice,” Ann. Physics 326 : 8 (2011), pp. 2108–2137. MR 2812881 Zbl 1221.81219 ArXiv 1102.0270

[34] techreport : 3D non-abelian anyons: Degeneracy splitting and detection by adiabatic cooling. Preprint, February 2011. ArXiv 1102.5742

[35] article : “Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions,” Phys. Rev. B 83 : 11 (2011), pp. 115132. ArXiv 1005.0583