Why should anyone care about computing with anyons?

Abstract

In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behavior, and we establish their relation to quantum computation. Possible directions for the physical realization of topological systems and the detection of anyonic behavior are elaborated.

22 pages, 13 figures. Some changes to existing sections, several references added, and a new section on criteria for TQO and TQC in lattice systems

References in corpus (33)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Persistent entanglement in arrays of interacting particles
• String-net condensation: A physical mechanism for topological phases
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Quantum orders in an exact soluble model
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• A symmetry principle for Topological Quantum Order
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Topological Computation without Braiding
• Quantum groups and nonabelian braiding in quantum Hall systems
• Influence of Interactions on Flux and Back-gate Period of Quantum Hall Interferometers
• Fault-Tolerant Quantum Computation with Local Gates
• Probing Non-Abelian Statistics with QuasiParticle Interferometry
• Realizing non-Abelian statistics
• Manipulation of Single Neutral Atoms in Optical Lattices
• Qudit surface codes and gauge theory with finite cyclic groups
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
• The Wavefunction of an Anyon
• Proposed Measurement of an Effective Flux Quantum in the Fractional Quantum Hall Effect
• Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer
• Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

Cited by in corpus (44)

• Non-Abelian Anyons and Topological Quantum Computation
• Surface code quantum computing by lattice surgery
• A symmetry principle for Topological Quantum Order
• Quantum memories at finite temperature
• Interacting Fibonacci anyons in a Rydberg gas
• Introduction to topological quantum computation with non-Abelian anyons
• Anyonic interferometry and protected memories in atomic spin lattices
• High threshold error correction for the surface code
• Fault tolerant architectures for superconducting qubits
• Simulations of quantum double models
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Testing an astronomically-based decadal-scale empirical harmonic climate model versus the IPCC (2007) general circulation climate models
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Manifestations of topological effects in graphene
• Decoding non-Abelian topological quantum memories
• Universal fault-tolerant measurement-based quantum computation
• Experimental simulation of anyonic fractional statistics with an NMR quantum information processor
• Quantum control of the hyperfine-coupled electron and nuclear spins in alkali atoms
• Quantum picturalism for topological cluster-state computing
• Quantum memories and error correction
• Topological phase transitions driven by gauge fields in an exactly solvable model
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Quantum hashing with the icosahedral group
• Non-abelian statistics from an abelian model
• Erasure tolerant quantum memory and the quantum null energy condition in holographic systems
• Majorana Fermions in a Box
• Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
• Anyonic Quantum Walks
• Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
• Topological Quantum Gates in Homotopy Type Theory
• Topological Quantum Gate Construction by Iterative Pseudogroup Hashing
• Chern-Simons theory encoded on a spin chain
• Scalable quantum control and non-abelian anyon creation in the Kitaev honeycomb model
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Quantum Control of d-Dimensional Quantum Systems with Application to Alkali Atomic Spins
• Towards unambiguous calculation of the topological entropy for mixed states
• Creation and manipulation of surface code defects with quantum optimal control
• A witness for topological order and stable quantum memories in abelian anyonic systems
• Suppressing decoherence in quantum state transfer with unitary operations
• Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator
• Universal Quantum Computation with Abelian Anyon Models
• On the Scattering Aharonov-Bohm effect
• Hawking radiation of anyons
• Superradiance of anyons