\begin{thebibliography}{100}
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi

\bibitem{Lestel05}
D.~Lestel, C.~Herzfeld, Topological apes: Knots tying and untying and the
  origins of mathematics, in: P.~Grialou, G.~Longo, M.~Okada (Eds.), Image and
  Reasoning, Vol.~1, Tokyo: University of Keio Press, 2005, pp. 147--162.

\bibitem{Herzfeld05}
C.~Herzfeld, D.~Lestel, Knot tying in great apes: etho-ethnology of an unusual
  tool behavior, Social Science Information 44 (2005) 621--653.

\bibitem{Newton1687}
I.~Newton, {P}hilosophi{\ae} {N}aturalis {P}rincipia {M}athematica, London,
  1687.

\bibitem{Ehrenfest1917}
P.~Ehrenfest, Proc. Amsterdam Acad. 20 (1917) 200.

\bibitem{Ehrenfest1920}
P.~Ehrenfest, {W}elche {R}olle spielt die {D}reidimensionalit\"{a}t des
  {R}aumes in den {G}rundgesetzen der {P}hysik?, Ann. Physik 61 (1920) 440.

\bibitem{Tangherlini63}
F.~R. Tangherlini, Schwarzschild field in {$n$} dimensions and the
  dimensionality of space problem, Nuovo Cimento (10) 27 (1963) 636--651.

\bibitem{Buchel63}
W.~B\"{u}chel, {W}arum hat der {R}aum drei {D}imensionen?, Physikalische
  Bl\"{a}tter 19 (1963) 547--549, {E}nglish translation in~\cite{Freeman69}.

\bibitem{Bose1924}
S.~N. Bose, {P}lancks {G}esetz und {L}ichtquantenhypothese, Zeits. f. Physik 26
  (1924) 178--181.

\bibitem{Einstein1924}
A.~Einstein, {Q}uantentheorie des einatomigen idealen {G}ases, in: Sitzungsber.
  Kgl. Preuss. Akad. Wiss., 1924, pp. 261--267.

\bibitem{Fermi1926}
E.~Fermi, Zur {Q}uantelung des idealen einatomigen {G}ases, Zeits. f. Physik 36
  (1926) 902.

\bibitem{Dirac1926}
P.~A.~M. Dirac, On the theory of quantum mechanics, Proc. Roy. Soc. A112 (1926)
  661--677.

\bibitem{Born1926}
M.~Born, Zur {Q}uantenmechanik der {S}to{\ss}vorg\"{a}nge, Zeits. f. Physik 37
  (1926) 863--867.

\bibitem{Fadell62}
E.~Fadell, L.~Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111--118.

\bibitem{Feynman48}
R.~P. Feynman, Space-time approach to non-relativistic quantum mechanics, Rev.
  Mod. Phys. 20 (1948) 367--387.

\bibitem{Laidlaw71}
M.~G.~G. Laidlaw, C.~M. DeWitt, Feynman functional integrals for systems of
  indistinguishable particles, Phys. Rev. D 3 (1971) 1375--1378.

\bibitem{Green53}
H.~S. Green, A generalized method of field quantization, Phys. Rev. 90 (1953)
  270--273.

\bibitem{Druhl70}
K.~Dr\"{u}hl, R.~Haag, J.~E. Roberts, On parastatistics, Commun. Math. Phys. 18
  (1970) 204--226.

\bibitem{Leinaas77}
J.~M. Leinaas, J.~Myrheim, On the theory of identical particles, Nuovo Cimento
  B 37B (1977) 1.

\bibitem{Artin1926}
E.~Artin, {T}heorie der {Z}\"{o}pfe, Abh. math. Sem. Hamburg 4 (1926) 47--72.

\bibitem{Wilczek82a}
F.~Wilczek, Magnetic flux, angular momentum, and statistics, Phys. Rev. Lett.
  48 (1982) 1144--1146.

\bibitem{Wilczek82b}
F.~Wilczek, Quantum mechanics of fractional-spin particles, Phys. Rev. Lett. 49
  (1982) 957--959.

\bibitem{Goldin85}
G.~A. Goldin, R.~Menikoff, D.~H. Sharp, Comments on ``{G}eneral {T}heory for
  {Q}uantum {S}tatistics in {T}wo {D}imensions'', Phys. Rev. Lett. 54 (1985)
  603.

\bibitem{Imbo90}
T.~D. Imbo, J.~March-Russell, Exotic statistics on surfaces, Phys. Lett. B 252
  (1990) 84--90.

\bibitem{Moore88}
G.~Moore, N.~Seiberg, Polynomial equations for rational conformal field
  theories, Phys. Lett. B 212 (1988) 451--460.

\bibitem{Moore89b}
G.~Moore, N.~Seiberg, Classical and quantum conformal field theory, Commun.
  Math. Phys. 123 (1989) 177--254.

\bibitem{Witten89}
E.~Witten, Quantum field theory and the {J}ones polynomial, Comm. Math. Phys.
  121 (1989) 351--399.

\bibitem{Fredenhagen89}
K.~Fredenhagen, K.~H. Rehren, B.~Schroer, Superselection sectors with braid
  group statistics and exchange algebras, Commun. Math. Phys. 125 (1989)
  201--226.

\bibitem{Froehlich90}
J.~Fr\"{o}hlich, F.~Gabbiani, Braid statistics in local quantum theory, Rev.
  Math. Phys. 2 (1990) 251--353.

\bibitem{Turaev94}
V.~G. Turaev, Quantum Invariants of Knots and 3-Manifolds, Walter de Gruyter,
  Berlin, New York, 1994.

\bibitem{Kassel95}
C.~Kassel, Quantum Groups, Springer-Verlag, New York, Berlin, Heidelberg, 1995.

\bibitem{Bakalov01}
B.~Bakalov, A.~Kirillov, Lectures on Tensor Categories and Modular Functors,
  Vol.~21 of University Lecture Series, American Mathematical Society, 2001.

\bibitem{Prange87}
R.~Prange, S.~M. Girvin (Eds.), The Quantum {H}all effect, Springer-Verlag, New
  York, 1987.

\bibitem{Karlhede92}
A.~Karlhede, S.~A. Kivelson, S.~L. Sondhi, The quantum {H}all effect: The
  article, in: V.~J. Emery (Ed.), Correlated Electron Systems, World
  Scientific, Singapore, 1992, lectures presented at the 9th Jerusalem Winter
  School for Theoretical Physics.

\bibitem{DasSarma97}
S.~Das~Sarma, A.~Pinczek, Perspectives in quantum {H}all effects: Novel quantum
  liquids in low-dimensional semiconductor structures, Wiley, New York, 1997.

\bibitem{Ezawa00}
Z.~Ezawa (Ed.), Quantum {H}all effects, field theoretical approach and related
  topics, World Scientific, Singapore, 2000.

\bibitem{Eisenstein90}
J.~P. Eisenstein, H.~L. Stormer, The fractional quantum {H}all effect, Science
  248 (1990) 1510--1516.

\bibitem{Stormer99}
H.~L. Stormer, D.~C. Tsui, A.~C. Gossard, The fractional quantum {H}all effect,
  Rev. Mod. Phys. 71 (1999) S298--S305.

\bibitem{von_Klitzing80}
K.~von Klitzing, G.~Dorda, M.~Pepper, New method for high-accuracy
  determination of the fine-structure constant based on quantized {H}all
  resistance, Phys. Rev. Lett. 45 (1980) 494--497.

\bibitem{Tsui82}
D.~C. Tsui, H.~L. Stormer, A.~C. Gossard, Two-dimensional magnetotransport in
  the extreme quantum limit, Phys. Rev. Lett. 48 (1982) 1559--62.

\bibitem{Goldman95}
V.~J. Goldman, B.~Su, Resonant tunneling in the quantum {H}all regime:
  Measurement of fractional charge, Science 267 (1995) 1010--1012.

\bibitem{Goldman05a}
V.~J. Goldman, J.~Liu, A.~Zaslavsky, Fractional statistics of {L}aughlin
  quasiparticles in quantum antidots, Phys. Rev. B 71 (2005) 153303.

\bibitem{Camino05a}
F.~E. Camino, W.~Zhou, V.~J. Goldman, Realization of a {L}aughlin quasiparticle
  interferometer: Observation of fractional statistics, Phys. Rev. B 72 (2005)
  075342, cond-mat/0502406.

\bibitem{Camino05b}
F.~E. Camino, W.~Zhou, V.~J. Goldman, {A}haronov--{B}ohm superperiod in a
  {L}aughlin quasiparticle interferometer, Phys. Rev. Lett. 95 (2005) 246802,
  cond-mat/0504341.

\bibitem{Camino06a}
F.~E. Camino, W.~Zhou, V.~J. Goldman, Transport in the {L}aughlin quasiparticle
  interferometer: Evidence for topological protection in an anyonic qubit,
  Phys. Rev. B 74 (2006) 115301, cond-mat/0606742.

\bibitem{Camino07a}
F.~E. Camino, W.~Zhou, V.~J. Goldman, $e/3$ {L}aughlin quasiparticle
  primary-filling $\nu=1/3$ interferometer, Phys. Rev. Lett. 98 (2007) 076805,
  cond-mat/0610751.

\bibitem{Camino07b}
F.~E. Camino, W.~Zhou, V.~J. Goldman, Experimental realization of a
  primary-filling e/3 quasiparticle interferometer (2006), cond-mat/0611443.

\bibitem{Moore91}
G.~Moore, N.~Read, Nonabelions in the fractional quantum {H}all effect, Nucl.
  Phys. B 360 (1991) 362--396.

\bibitem{Laughlin83}
R.~B. Laughlin, Anomalous quantum {H}all effect: an incompressible quantum
  fluid with fractionally charged excitations, Phys. Rev. Lett. 50 (1983)
  1395--8.

\bibitem{Willett87}
R.~Willett, J.~P. Eisenstein, H.~L. Stormer, D.~C. Tsui, A.~C. Gossard, J.~H.
  English, Observation of an even-denominator quantum number in the fractional
  quantum {H}all effect, Phys. Rev. Lett. 59 (1987) 1776--9.

\bibitem{Pan99}
W.~Pan, J.-S. Xia, V.~Shvarts, D.~E. Adams, H.~L. Stormer, D.~C. Tsui, L.~N.
  Pfeiffer, K.~W. Baldwin, K.~W. West, Exact quantization of the
  even-denominator fractional quantum {H}all state at $\nu=5/2$ {L}andau level
  filling factor, Phys. Rev. Lett. 83 (1999) 3530--3, cond-mat/9907356.

\bibitem{Eisenstein02}
J.~P. Eisenstein, K.~B. Cooper, L.~N. Pfeiffer, K.~W. West, Insulating and
  fractional quantum {H}all states in the first excited {L}andau level, Phys.
  Rev. Lett. 88 (2002) 076801, cond-mat/0110477.

\bibitem{Xia04}
J.~S. Xia, W.~Pan, C.~L. Vicente, E.~D. Adams, N.~S. Sullivan, H.~L. Stormer,
  D.~C. Tsui, L.~N. Pfeiffer, K.~W. Baldwin, K.~W. West, Electron correlation
  in the second {L}andau level: A competition between many nearly degenerate
  quantum phases, Phys. Rev. Lett. 93 (2004) 176809, cond-mat/0406724.

\bibitem{Read99}
N.~Read, E.~Rezayi, Beyond paired quantum {H}all states: Parafermions and
  incompressible states in the first excited {L}andau level, Phys. Rev. B 59
  (1999) 8084--–8092, cond-mat/9809384.

\bibitem{Morf98}
R.~H. Morf, Transition from quantum {H}all to compressible states in the second
  {L}andau level: new light on the $\nu=5/2$ enigma, Phys. Rev. Lett. 80 (1998)
  1505--8, cond-mat/9809024.

\bibitem{Rezayi00}
E.~H. Rezayi, F.~D.~M. Haldane, Incompressible paired {H}all state, stripe
  order, and the composite fermion liquid phase in half-filled {L}andau levels,
  Phys. Rev. Lett. 84 (2000) 4685--4688, cond-mat/9906137.

\bibitem{Nayak96c}
C.~Nayak, F.~Wilczek, $2n$-quasihole states realize $2^{n-1}$-dimensional
  spinor braiding statistics in paired quantum {H}all states, Nucl. Phys. B 479
  (1996) 529--53, cond-mat/9605145.

\bibitem{Slingerland01}
J.~K. Slingerland, F.~A. Bais, Quantum groups and nonabelian braiding in
  quantum {H}all systems, Nucl. Phys. B 612 (2001) 229--290, cond-mat/0104035.

\bibitem{Read00}
N.~Read, D.~Green, Paired states of fermions in two dimensions with breaking of
  parity and time-reversal symmetries and the fractional quantum {H}all effect,
  Phys. Rev. B 61 (2000) 10267--10297, cond-mat/9906453.

\bibitem{Ivanov01}
D.~A. Ivanov, Non-{A}belian statistics of half-quantum vortices in p-wave
  superconductors, Phys. Rev. Lett. 86 (2001) 268--271, cond-mat/0005069.

\bibitem{Stern04}
A.~Stern, F.~von Oppen, E.~Mariani, Geometric phases and quantum entanglement
  as building blocks for non-{A}belian quasiparticle statistics, Phys. Rev. B
  70 (2004) 205338, cond-mat/0310273.

\bibitem{Ardonne99}
E.~Ardonne, K.~Schoutens, A new class of non-{A}belian spin-singlet quantum
  {H}all states, Phys. Rev. Lett. 82~(25) (1999) 5096--5099, cond-mat/9811352.

\bibitem{Kitaev97}
A.~Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303
  (2003) 2, quant-ph/9707021.

\bibitem{Kitaev06a}
A.~Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321 (2006)
  2--111, cond-mat/0506438.

\bibitem{Freedman03}
M.~H. Freedman, A magnetic model with a possible {C}hern-{S}imons phase,
  Commun. Math. Phys. 234 (2003) 129--183, quant-ph/0110060.

\bibitem{Freedman04a}
M.~Freedman, C.~Nayak, K.~Shtengel, K.~Walker, Z.~Wang, A class of
  ${P,T}$-invariant topological phases of interacting electrons, Ann. Phys. 310
  (2004) 428--492, cond-mat/0307511.

\bibitem{Freedman05a}
M.~Freedman, C.~Nayak, K.~Shtengel, Extended {H}ubbard model with ring
  exchange: A route to a non-{A}belian topological phase, Phys. Rev. Lett. 94
  (2005) 066401, cond-mat/0312273.

\bibitem{Freedman05b}
M.~Freedman, C.~Nayak, K.~Shtengel, Line of critical points in $2+1$
  dimensions: Quantum critical loop gases and non-{A}belian gauge theory, Phys.
  Rev. Lett. 94 (2005) 147205, cond-mat/0408257.

\bibitem{Turaev92}
V.~G. Turaev, O.~Y. Viro, State sum invariants of 3-manifolds and quantum
  6j-symbols, Topology 31 (1992) 865--902.

\bibitem{Levin05a}
M.~A. Levin, X.-G. Wen, String-net condensation: A physical mechanism for
  topological phases, Phys. Rev. B 71 (2005) 045110, cond-mat/0404617.

\bibitem{Fendley05a}
P.~Fendley, E.~Fradkin, Realizing non-{A}belian statistics in
  time-reversal-invariant systems, Phys. Rev. B 72 (2005) 024412,
  cond-mat/0502071.

\bibitem{Fidkowski07a}
L.~Fidkowski, From string nets to nonabelions (2006), cond-mat/0610583.

\bibitem{Doucot04}
B.~Dou\c{c}ot, L.~B. Ioffe, J.~Vidal, Discrete non-{A}belian gauge theories in
  {J}osephson-junction arrays and quantum computation, Phys. Rev. B 69 (2004)
  214501, cond-mat/0302104.

\bibitem{DasSarma06a}
S.~D. Sarma, C.~Nayak, S.~Tewari, Proposal to stabilize and detect half-quantum
  vortices in strontium ruthenate thin films: Non-{A}belian braiding statistics
  of vortices in a $p_ x + ip_y$ superconductor, Phys. Rev. B 73 (2006) 220502,
  cond-mat/0510553.

\bibitem{Tewari07a}
S.~Tewari, S.~D. Sarma, C.~Nayak, C.~Zhang, P.~Zoller, Quantum computation
  using vortices and majorana zero modes of a $p_x + ip_y$ superfluid of
  fermionic cold atoms, Phys. Rev. Lett. 98 (2007) 010506, quant-ph/0606101.

\bibitem{Gurarie05a}
V.~Gurarie, L.~Radzihovsky, A.~V. Andreev, Quantum phase transitions across a
  $p$-wave {F}eshbach resonance, Phys. Rev. Lett. 94 (2005) 230403,
  cond-mat/0410620.

\bibitem{Cooper01a}
N.~R. Cooper, N.~K. Wilkin, J.~M.~F. Gunn, Quantum phases of vortices in
  rotating {B}ose--{E}instein condensates, Phys. Rev. Lett. 87 (2001) 120405,
  cond-mat/0107005.

\bibitem{Cooper04a}
N.~R. Cooper, Exact ground states of rotating {B}ose gases close to a
  {F}eshbach resonance, Physical Review Letters 92 (2004) 220405,
  cond-mat/0107005.

\bibitem{Rezayi05}
E.~H. Rezayi, N.~Read, N.~R. Cooper, Incompressible liquid state of rapidly
  rotating bosons at filling factor 3/2, Phys. Rev. Lett. 95 (2005) 160404,
  cond-mat/0507064.

\bibitem{Preskill98}
J.~Preskill, Fault-tolerant quantum computation, in: H.-K. Lo, S.~Popescu,
  T.~P. Spiller (Eds.), Introduction to Quantum Computation, World Scientific,
  1998.

\bibitem{Ogburn99}
R.~W. Ogburn, J.~Preskill, Topological quantum computation, Lect. Notes in
  Comp. Sci. 1509 (1999) 341--356.

\bibitem{Freedman01}
M.~H. Freedman, Quantum computation and the localization of modular functors,
  Found. Comput. Math. 1 (2001) 183--204, quant-ph/0003128.

\bibitem{Freedman02a}
M.~H. Freedman, M.~J. Larsen, Z.~Wang, A modular functor which is universal for
  quantum computation, Commun. Math. Phys. 227 (2002) 605--622,
  quant-ph/0001108.

\bibitem{FKLW}
M.~Freedman, A.~Kitaev, M.~Larsen, Z.~Wang, Topological quantum computation,
  quant-ph/0101025 (2001).

\bibitem{Mochon03}
C.~Mochon, Anyons from nonsolvable finite groups are sufficient for universal
  quantum computation, Phys. Rev. A 67 (2003) 022315, quant-ph/0206128.

\bibitem{Mochon04}
C.~Mochon, Anyon computers with smaller groups, Phys. Rev. A 69 (2004) 032306,
  quant-ph/0306063.

\bibitem{DasSarma05}
S.~Das~Sarma, M.~Freedman, C.~Nayak, Topologically protected qubits from a
  possible non-{A}belian fractional quantum {H}all state, Phys. Rev. Lett. 94
  (2005) 166802, cond-mat/0412343.

\bibitem{FNW05a}
M.~Freedman, C.~Nayak, K.~Walker, Towards universal topological quantum
  computation in the $\nu=5/2$ fractional quantum {H}all state (2005),
  cond-mat/0512066.

\bibitem{FNW05b}
M.~Freedman, C.~Nayak, K.~Walker, Tilted interferometry realizes universal
  quantum computation in the {I}sing {TQFT} without overpasses (2005),
  cond-mat/0512072.

\bibitem{Bravyi06}
S.~Bravyi, Universal quantum computation with the $\nu=5/2$ fractional quantum
  {H}all state, Phys. Rev. A 73 (2006) 042313, quant-ph/0511178.

\bibitem{Bonesteel05}
N.~E. Bonesteel, L.~Hormozi, G.~Zikos, S.~H. Simon, Braid topologies for
  quantum computation, Phys. Rev. Lett. 95 (2005) 140503, quant-ph/0505065.

\bibitem{Simon06a}
S.~H. Simon, N.~E. Bonesteel, M.~H. Freedman, N.~Petrovic, L.~Hormozi,
  Topological quantum computing with only one mobile quasiparticle, Phys. Rev.
  Lett. 96 (2006) 070503, quant-ph/0509175.

\bibitem{Hormozi07a}
L.~Hormozi, G.~Zikos, N.~E. Bonesteel, S.~H. Simon, Topological quantum
  compiling, Phys. Rev. B 75 (2007) 165310, quant-ph/0610111.

\bibitem{Aharonov59}
Y.~Aharonov, D.~Bohm, Significance of electromagnetic potentials in the quantum
  theory, Phys. Rev. 115 (1959) 485--491.

\bibitem{Braginsky75}
V.~B. Braginsky, Y.~I. Vorontsov, Usp. Fiz. Nauk 41--62 (1974) 114, [Sov. Phys.
  Uspekhi 17, 644 (1975)].

\bibitem{Preskill-lectures}
J.~Preskill, Topological quantum computation, lecture notes (2004).
\newline\urlprefix\url{http://www.theory.caltech.edu/~preskill/ph219/topologic%
al.ps}

\bibitem{MacLane98}
S.~Mac~Lane, {C}ategories for the {W}orking {M}athematician, 2nd Edition,
  {G}raduate {T}exts in {M}athematics, Springer-Verlag, New York, 1998.

\bibitem{Buchberger65}
B.~Buchberger, Ein {A}lgorithmus zum {A}uffinden der {B}asiselemente des
  {R}estklassenringes nach einem nulldimensionalen {P}olynomideal, Ph.D.
  thesis, {E}nglish translation in~\cite{Buchberger06} (1965).

\bibitem{Buchberger70}
B.~Buchberger, Ein algorithmisches {K}riterium f\"{u}r die {L}\"{o}sbarkeit
  eines algebraischen {G}leichungssystems, Aequationes mathematicae 4 (1970)
  374--383, {E}nglish translation in~\cite{Buchberger98}.

\bibitem{Etingof05}
P.~Etingof, D.~Mikshych, V.~Ostrik, On fusion categories, Ann. Math. 162 (2005)
  581--642.

\bibitem{Zehnder1891}
L.~Zehnder, Ein neuer interferenzrefractor, Zeitschr. f. Instrkde. 11 (1891)
  275--285.

\bibitem{Mach1892}
L.~Mach, \"{U}ber einer interferenzrefractor, Zeitschr. f. Instrkde. 12 (1892)
  89--93.

\bibitem{Bonderson07a}
P.~Bonderson, K.~Shtengel, J.~K. Slingerland, Decoherence of anyonic charge in
  interferometry measurements, Phys. Rev. Lett. 98 (2007) 070401,
  quant-ph/0608119.

\bibitem{Overbosch01}
B.~J. Overbosch, F.~A. Bais, Inequivalent classes of interference experiments
  with non-{A}belian anyons, Phys. Rev. A 64 (2001) 062107, quant-ph/0105015.

\bibitem{Zeilinger81}
A.~Zeilinger, General properties of lossless beam splitters in interferometry,
  Am. J. Phys. 49 (1981) 882--883.

\bibitem{Bonderson06b}
P.~Bonderson, K.~Shtengel, J.~K. Slingerland, Probing non-{A}belian statistics
  with quasiparticle interferometry, Phys. Rev. Lett. 97 (2006) 016401,
  cond-mat/0601242.

\bibitem{Ji03}
Y.~Ji, Y.~Chung, D.~Sprinzak, M.~Heiblum, D.~Mahalu, H.~Shtrikman, An
  electronic {M}ach--{Z}ehnder interferometer, Nature 422 (2003) 415--418,
  cond-mat/0303553.

\bibitem{Neder05}
I.~Neder, M.~Heiblum, Y.~Levinson, D.~Mahalu, V.~Umansky, Coherence and phase
  in an electronic {M}ach--{Z}ehnder interferometer: An unexpected behavior of
  interfering electrons (2005), cond-mat/0508024.

\bibitem{Neder06}
I.~Neder, M.~Heiblum, Y.~Levinson, D.~Mahalu, V.~Umansky, Unexpected behavior
  in a two-path electron interferometer, Phys. Rev. Lett. 96 (2006) 016804.

\bibitem{Kane03}
C.~L. Kane, Telegraph noise and fractional statistics in the quantum {H}all
  effect, Phys. Rev. Lett. 90 (2003) 226802, cond-mat/0210621.

\bibitem{Jonckheere05}
T.~Jonckheere, P.~Devillard, A.~Crepieux, T.~Martin, Electronic
  {Mach}--{Z}ehnder interferometer in the fractional quantum {H}all effect,
  Phys. Rev. B 72 (2005) 201305(R), cond-mat/0503617.

\bibitem{Law06}
K.~T. Law, D.~E. Feldman, Y.~Gefen, Electronic {M}ach-{Z}ehnder interferometer
  as a tool to probe fractional statistics, Phys. Rev. B 74 (2006) 045319,
  cond-mat/0506302.

\bibitem{Feldman06}
D.~E. Feldman, A.~Kitaev, Detecting non-{A}belian statistics with an electronic
  {M}ach--{Z}ehnder interferometer, Phys. Rev. Lett. 97 (2006) 186803,
  cond-mat/0607541.

\bibitem{Fabry1897}
C.~Fabry, A.~P\'{e}rot, Sur les franges des lames minces argente\'{e}s et leur
  application \`{a} la mesure de petites \'{e}paisseurs d{'}air, Ann. Chim.
  Phys. 12 (1897) 459--501.

\bibitem{Chamon97}
C.~de~C.~Chamon, D.~E. Freed, S.~A. Kivelson, S.~L. Sondhi, X.~G. Wen, Two
  point-contact interferometer for quantum {H}all systems, Phys. Rev. B 55
  (1997) 2331--43, cond-mat/9607195.

\bibitem{Fradkin98}
E.~Fradkin, C.~Nayak, A.~Tsvelik, F.~Wilczek, A {C}hern-{S}imons effective
  field theory for the {P}faffian quantum {H}all state, Nucl. Phys. B 516
  (1998) 704--18, cond-mat/9711087.

\bibitem{Stern06a}
A.~Stern, B.~I. Halperin, Proposed experiments to probe the non-abelian
  $\nu=5/2$ quantum {H}all state, Phys. Rev. Lett. 96 (2006) 016802,
  cond-mat/0508447.

\bibitem{Bonderson06a}
P.~Bonderson, A.~Kitaev, K.~Shtengel, Detecting non-{A}belian statistics in the
  $\nu=5/2$ fractional quantum {H}all state, Phys. Rev. Lett. 96 (2006) 016803,
  cond-mat/0508616.

\bibitem{Grosfeld06b}
E.~Grosfeld, S.~H. Simon, A.~Stern, Switching noise as a probe of statistics in
  the fractional quantum {H}all effect, Phys. Rev. Lett. 96 (2006) 226803,
  cond-mat/0602634.

\bibitem{Hou06}
C.-Y. Hou, C.~Chamon, ``{W}ormhole'' geometry for entrapping topologically
  protected qubits in non-{A}belian quantum {H}all states and probing them with
  voltage and noise measurements, Phys. Rev. Lett. 97 (2006) 146802,
  cond-mat/0603142.

\bibitem{Fendley06a}
P.~Fendley, M.~P. Fisher, C.~Nayak, Dynamical disentanglement across a point
  contact in a non-{A}belian quantum {H}all state, Phys. Rev. Lett. 97 (2006)
  036801, cond-mat/0604064.

\bibitem{Fendley07a}
P.~Fendley, M.~P. Fisher, C.~Nayak, Edge states and tunneling of non-{A}belian
  quasiparticles in the $\nu=5/2$ quantum {H}all state and p+ip
  superconductors, Phys. Rev. B 75 (2007) 045317, cond-mat/0607431.

\bibitem{Chung06}
S.~B. Chung, M.~Stone, Proposal for reading out anyon qubits in non-{A}belian
  $\nu = 12/5$ quantum {H}all state, Phys. Rev. B 73 (2006) 245311,
  cond-mat/0601594.

\bibitem{Fidkowski07c}
L.~Fidkowski, Double point contact in the k=3 {R}ead--{R}ezayi state (2007),
  arXiv:0704.3291.

\bibitem{Kim06e}
E.-A. Kim, Aharanov-bohm interference and fractional statistics in a quantum
  hall interferometer, Phys. Rev. Lett. 97 (2006) 216404, cond-mat/0604359.

\bibitem{Rosenow07a}
B.~Rosenow, B.~I. Halperin, Influence of interactions on flux and back-gate
  period of quantum {H}all interferometers, Phys. Rev. Lett. 98 (2007) 106801,
  cond-mat/0611101.

\bibitem{Gefen91}
D.~J. Thouless, Y.~Gefen, Fractional quantum {H}all effect and multiple
  {A}haronov--{B}ohm periods, Phys. Rev. Lett. 66 (1991) 806--809.

\bibitem{Wen92b}
X.~G. Wen, Theory of the edge states in fractional quantum {H}all effects,
  Intl. J. Mod. Phys. B 6 (1992) 1711--62.

\bibitem{Miller07a}
J.~B. Miller, I.~P. Radu, D.~M. Zumbuhl, E.~M. Levenson-Falk, M.~A. Kastner,
  C.~M. Marcus, L.~N. Pfeiffer, K.~W. West, Fractional quantum {H}all effect in
  a quantum point contact at filling fraction 5/2 (2007), cond-mat/0703161.

\bibitem{Dijkgraaf89}
R.~Dijkgraaf, C.~Vafa, E.~Verlinde, H.~Verlinde, The operator algebra of
  orbifold models, Commun. Math. Phys. 123 (1989) 485--526.

\bibitem{Dijkgraaf90a}
R.~Dijkgraaf, V.~Pasquier, P.~Roche, Quasi {H}opf algebras, group cohomology
  and orbifold models, Nucl. Phys. B (Proc. Suppl.) 18B (1990) 60--72.

\bibitem{Bais92}
F.~A. Bais, P.~van Driel, M.~de~Wild~Propitius, Quantum symmetries in discrete
  gauge theories, Phys. Lett. B 280 (1992) 63--70, hep-th/9203046.

\bibitem{Wess71}
J.~Wess, B.~Zumino, Consequences of anomalous {W}ard identities, Phys. Lett. B
  37 (1971) 95.

\bibitem{Witten83}
E.~Witten, Global aspects of current algebra, Nucl. Phys. B 223 (1983)
  422--432.

\bibitem{Jones85}
V.~F.~R. Jones, A polynomial invariant for knots via von {N}eumann algebras,
  Bull. Am. Math. Soc. 12 (1985) 103--111.

\bibitem{KuperbergU}
G.~Kuperberg, unpublished.

\bibitem{Freedman02b}
M.~H. Freedman, M.~J. Larsen, Z.~Wang, The two-eigenvalue problem and density
  of jones representation of braid groups, Commun. Math. Phys. 228 (2002)
  177--199.

\bibitem{Moore89c}
G.~Moore, N.~Seiberg, Taming the conformal zoo, Phys. Lett. B 220 (1989)
  422--430.

\bibitem{Gepner89}
D.~Gepner, Field identification in coset conformal field theories, Phys. Lett.
  B 222~(2) (1989) 207--212.

\bibitem{Zamolodchikov85}
A.~B. Zamolodchikov, V.~Fateev, Nonlocal (parafermion) currents in
  two-dimensional conformal quantum field theory and self-dual critical points
  in $z_{N}$-symmetric statistical systems, Soviet Physics - JETP 62 (1985)
  215--225.

\bibitem{Gepner87}
D.~Gepner, Z.~Qiu, Modular invariant partition functions for parafermionic
  field theories, Nucl. Phys. B 285 (1987) 423--453.

\bibitem{BondersonWIP}
P.~Bonderson, J.~K. Slingerland, in preparation.

\bibitem{Schwarz78}
A.~S. Schwarz, The partition function of degenerate quadratic functional and
  {R}ay-{S}inger invariants, Lett. Math. Phys. 2 (1978) 247--252.

\bibitem{Schonfeld80}
J.~F. Schonfeld, A mass term for three-dimensional gauge fields, Nucl. Phys. B
  185 (1981) 157.

\bibitem{Deser81}
S.~Deser, R.~Jackiw, S.~Templeton, Topologically massive gauge theories, Ann.
  Phys. 140 (1982) 372--411.

\bibitem{Dijkgraaf90}
R.~Dijkgraaf, E.~Witten, Topological gauge theories and group cohomology,
  Commun. Math. Phys. 129 (1990) 393--429.

\bibitem{Wen92a}
X.~G. Wen, A.~Zee, Classification of {A}belian quantum {H}all states and matrix
  formulation of topological fluids, Phys. Rev. B 46 (1992) 2290--301.

\bibitem{Haldane83}
F.~D.~M. Haldane, Fractional quantization of the {H}all effect: A hierarchy of
  incompressible quantum fluid states, Phys. Rev. Lett. 51 (1983) 605--608.

\bibitem{Halperin84}
B.~I. Halperin, Statistics of quasiparticles and the hierarchy of fractional
  quantized {H}all states, Phys. Rev. Lett. 52 (1984) 1583--6.

\bibitem{Jain89}
J.~K. Jain, Composite fermion approach for the fractional quantum {H}all
  effect, Phys. Rev. Lett. 63 (1989) 199--202.

\bibitem{Gepner87b}
D.~Gepner, New conformal field theories associated with {L}ie algebras and
  their partition functions, Nucl. Phys. B 290 (1987) 10.

\bibitem{Wang06}
Z.~Wang, Classification of {TQFT}s, talk at the {KITP} conference on
  {T}opological {P}hases and {Q}uantum {C}omputation, {S}anta {B}arbara (2006).
\newline\urlprefix\url{http://online.itp.ucsb.edu/online/qubit\_c06/}

\bibitem{Gepner94}
D.~Gepner, A.~Kapustin, On the classification of fusion rings, Phys. Lett. B
  349 (1995) 71--75, hep-th/9410089.

\bibitem{Freeman69}
I.~M. Freeman, Why is space three-dimensional?, Am. J. Phys. 37~(12) (1969)
  1222--1224, based on {W. B\"{u}chel: ``Warum hat der Raum drei
  Dimensionen?,'' Physikalische Bl\"{a}tter 19, 12, pp. 547--549 (December
  1963)}.

\bibitem{Buchberger06}
B.~Buchberger, An algorithm for finding the basis elements in the residue class
  ring modulo a zero dimensional polynomial ideal, Ph.D. thesis (2006).

\bibitem{Buchberger98}
B.~Buchberger, An algorithmic criterion for the solvability of algebraic
  systems of equations 251 (1998) 535--545.

\end{thebibliography}
