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Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall
State
Sergey Bravyi
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 Landau level filling fraction nu=5/2. Since the braid group representation
describing statistics of these anyons is not computationally universal, one
cannot directly apply the standard TQC technique. We propose to use very noisy
non-topological operations such as direct short-range interaction 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
non-topological operations is above 14%. The total number of non-topological
computational elements that one needs to simulate a quantum circuit with $L$
gates scales as $L(\log L)^3$.
- oai_identifier:
- oai:arXiv.org:quant-ph/0511178
- categories:
- quant-ph
- comments:
- 17 pages, 12 eps figures
- doi:
- 10.1103/PhysRevA.73.042313
- arxiv_id:
- quant-ph/0511178
- journal_ref:
- Phys. Rev. A 73, 042313 (2006)
- created:
- 2005-11-17
Full article ▸
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