Braid Topologies for Quantum Computation

Abstract

In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum gates depend only on the topology of the braids formed by these world-lines. We show how to find braids that yield a universal set of quantum gates for qubits encoded using a specific kind of quasiparticle which is particularly promising for experimental realization.

4 pages, 4 figures, minor revisions

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• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• A Short Introduction to Topological Quantum Computation
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Bipartite entanglement entropy in fractional quantum Hall states
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• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
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• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Wavefunctions for topological quantum registers
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• Non-Abelian anyons: when Ising meets Fibonacci
• Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure
• Landau level mixing in the nu=5/2 fractional quantum Hall state
• Mapping the braiding properties of the Moore-Read state
• Quantum Circuits for Measuring Levin-Wen Operators
• Entanglement between particle partitions in itinerant many-particle states
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Fibonacci anyons versus Majorana fermions
• Quantum hashing with the icosahedral group
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Proposal for reading out anyon qubits in non-abelian $\nu =12/5$ quantum Hall state
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• Quons: A 3D Language for Quantum Information
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• Engineering Yang-Lee anyons via Majorana bound states
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• Simple analog of the black-hole information paradox in quantum Hall interfaces
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• Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
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• Genetic braid optimization: A heuristic approach to compute quasiparticle braids
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• Identifying non-Abelian anyons with upstream noise
• Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Measuring Topological Order
• Do Rydberg chains yield Fibonacci anyons?
• Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level
• Composite anyon coding and the initialization of a topological quantum computer
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Deterministic quantum one-time pad via Fibonacci anyons
• Majorana Fermions and Representations of the Braid Group
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
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• 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
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Experimental implementation of Hardy-like quantum pigeonhole paradoxes
• Topological Quantum Computation on Supersymmetric Spin Chains
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• Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms
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• A probabilistic evolutionary optimization approach to compute quasiparticle braids
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• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
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