# Topological quantum computing with only one mobile quasiparticle.

@article{Simon2006TopologicalQC, title={Topological quantum computing with only one mobile quasiparticle.}, author={Steven H. Simon and N. E. Bonesteel and Michael H. Freedman and N Petrovic and Layla Hormozi}, journal={Physical review letters}, year={2006}, volume={96 7}, pages={ 070503 } }

In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2 + 1 dimensional space-time. In this Letter we show that any such quantum computation that can be done by braiding n identical quasiparticles can also be done by moving a single quasiparticle around n - 1 other identical quasiparticles whose positions remain fixed.

#### 29 Citations

QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

- Physics
- 2007

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging… Expand

Non-Abelian Anyons and Topological Quantum Computation

- Physics
- 2008

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of… Expand

BRAIDING AND ENTANGLEMENT IN NONABELIAN QUANTUM HALL STATES

- Physics
- 2009

Certain fractional quantum Hall states, including the experimentally observed ν = 5/2 state, and, possibly, the ν = 12/5 state, may have a sufficiently rich form of topological order (i.e. they may… Expand

Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

- Physics
- 2008

Abstract We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read–Rezayi state whose effective theory is the… Expand

Introduction to topological quantum computation with non-Abelian anyons

- Computer Science, Physics
- Quantum Science and Technology
- 2018

This work aims to provide a pedagogical, self-contained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations. Expand

Non-Abelian Anyons: Statistical Repulsion and Topological Quantum Computation

- Physics
- 2017

As opposed to classical mechanics, quantum mechanical particles can be truly identical and lead to new and interesting phenomena. Identical particles can be of different types, determined by their ...

Classical Structures in Topological Quantum Computing

- Physics
- 2013

Classical structures are a mathematical tool for describing quantum algorithms and protocols at a more abstract level than that of individual qubits. This approach is similar to using high-level… Expand

Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle

- Physics, Computer Science
- Quantum Inf. Comput.
- 2012

It is shown how to simulate universal quantum computation by braiding one quasiparticle and with only one measurement, to read out the result. Expand

Braid matrices and quantum gates for Ising anyons
topological quantum computation

- Physics
- 2010

Abstract
We study various aspects of the topological quantum computation scheme based on the non-Abelian anyons corresponding to fractional quantum hall effect states at filling fraction 5/2 using… Expand

Braiding, Majorana fermions, Fibonacci particles and topological quantum computing

- Physics, Computer Science
- Quantum Inf. Process.
- 2018

The remarkable unitary braid group representations associated with Majorana fermions are studied to study the relationships between topology, quantum computing, and the properties of Fermions. Expand

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