Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle
Abstract
A topological quantum computer should allow intrinsically faulttolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. It is known that topological quantum computation can be implemented with limited quasiparticle braiding capabilities, in fact using only a single mobile quasiparticle, if the system can be properly initialized by measurements. It is also known that measurements alone suffice without any braiding, provided that the measurement devices can be dynamically created and modified. We study a model in which both measurement and braiding capabilities are limited. Given the ability to pull nontrivial Fibonacci anyon pairs from the vacuum with a certain success probability, we show how to simulate universal quantum computation by braiding one quasiparticle and with only one measurement, to read out the result. The difficulty lies in initializing the system. We give a systematic construction of a family of braid sequences that initialize to arbitrary accuracy nontrivial composite anyons. Instead of using the SolovayKitaev theorem, the sequences are based on a quantum algorithm for convergent search.
 Publication:

arXiv eprints
 Pub Date:
 June 2012
 DOI:
 10.48550/arXiv.1206.0330
 arXiv:
 arXiv:1206.0330
 Bibcode:
 2012arXiv1206.0330R
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 18 pages, 4 figures