Exploiting geometric degrees of freedom in topological quantum computing
Abstract
In a topological quantum computer, braids of non-Abelian anyons in a (2+1) -dimensional space time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to create and exploit redundant geometric degrees of freedom to improve the theoretical accuracy of topological single- and two-qubit quantum gates. We demonstrate the power of the idea using explicit constructions in the Fibonacci model. We compare its efficiency with that of the Solovay-Kitaev algorithm and explain its connection to the leakage errors reduction in an earlier construction [H. Xu and X. Wan, Phys. Rev. A 78, 042325 (2008)].
- Publication:
-
Physical Review A
- Pub Date:
- July 2009
- DOI:
- 10.1103/PhysRevA.80.012306
- arXiv:
- arXiv:0812.2414
- Bibcode:
- 2009PhRvA..80a2306X
- Keywords:
-
- 03.67.Lx;
- 03.65.Vf;
- 03.67.Pp;
- 73.43.-f;
- Quantum computation;
- Phases: geometric;
- dynamic or topological;
- Quantum error correction and other methods for protection against decoherence;
- Quantum Hall effects;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Strongly Correlated Electrons;
- Quantum Physics
- E-Print:
- 5 pages, 2 figures, accepted for publication in Phys. Rev. A