Universal quantum computation with the {nu}=5/2 fractional quantum Hall state
Abstract
We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landaulevel filling fraction {nu}=5/2. Since the braid group representation describing the statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy nontopological operations such as direct shortrange interactions between anyons to simulate a universal set of gates. Assuming that all TQC operations are implemented perfectly, we prove that the threshold error rate for nontopological operations is above 14%. The total number of nontopological computational elements that one needs to simulate a quantum circuit with L gates scales as L(ln L){sup 3}.
 Authors:
 IBM Watson Research Center, Yorktown Heights, New York 10598, USA and Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)
 Publication Date:
 OSTI Identifier:
 20787086
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.73.042313; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ANYONS; ENERGY LEVELS; ERRORS; HALL EFFECT; INFORMATION THEORY; INTERACTION RANGE; NOISE; QUANTUM COMPUTERS; QUANTUM MECHANICS; STATISTICS; TOPOLOGY
Citation Formats
Bravyi, Sergey. Universal quantum computation with the {nu}=5/2 fractional quantum Hall state. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.
Bravyi, Sergey. Universal quantum computation with the {nu}=5/2 fractional quantum Hall state. United States. doi:10.1103/PHYSREVA.73.0.
Bravyi, Sergey. Sat .
"Universal quantum computation with the {nu}=5/2 fractional quantum Hall state". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20787086,
title = {Universal quantum computation with the {nu}=5/2 fractional quantum Hall state},
author = {Bravyi, Sergey},
abstractNote = {We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landaulevel filling fraction {nu}=5/2. Since the braid group representation describing the statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy nontopological operations such as direct shortrange interactions between anyons to simulate a universal set of gates. Assuming that all TQC operations are implemented perfectly, we prove that the threshold error rate for nontopological operations is above 14%. The total number of nontopological computational elements that one needs to simulate a quantum circuit with L gates scales as L(ln L){sup 3}.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 4,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}

We report ultralow temperature experiments on the obscure fractional quantum Hall effect at Landau level filling factor {nu}=5/2 in a very highmobility specimen of {mu}=1.7{times}10{sup 7} cm {sup 2}/Vthinsp s . We achieve an electron temperature as low as {approximately}4 mK , where we observe vanishing R{sub xx} and, for the first time, a quantized Hall resistance, R{sub xy}=h/(5/2)e{sup 2} to within 2thinspthinspppm. R{sub xy} at the neighboring odddenominator states {nu}=7/3 and 8/3 is also quantized. The temperature dependences of the R{sub xx} minima at these fractional fillings yield activation energy gaps {Delta}{sub 5/2}=0.11 , {Delta}{sub 7/3}=0.10 , and {Delta}{submore »
