Topological Quantum Computing with Only One Mobile Quasiparticle

Abstract

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 paper 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.

4 pages, 5 figures

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• Topological Quantum Computing with Read-Rezayi States
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Quantum hashing with the icosahedral group
• Systematically generated two-qubit anyon braids
• Anyonic Quantum Walks
• Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
• $q$ - Deformed Spin Networks, Knot Polynomials and Anyonic Topological Quantum Computation
• Topological Quantum Gate Construction by Iterative Pseudogroup Hashing
• Composite anyon coding and the initialization of a topological quantum computer
• Majorana Fermions and Representations of the Braid Group
• Topological Insulating Phases of Non-Abelian Anyonic Chains
• Detecting topological order from modular transformations of ground states on the torus
• Braiding Majorana Fermions
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Topological quantum compilation of two-qubit gates
• Topological Quantum Computation on Supersymmetric Spin Chains
• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
• Density and unitarity of the Burau representation from a non-semisimple TQFT
• Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory