# 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 Landau-level 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 short-range 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 Landau-level 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 short-range 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}

}