Anyon computers with smaller groups

Abstract

Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons based on finite groups that are solvable but not nilpotent are capable of universal quantum computation. This extends previously published results to groups that are smaller, and therefore more practical. Additionally, a new universal gate-set is built out of an operation called a probabilistic projection, and a quasi-universal leakage correction scheme is discussed.

28 pages, REVTeX 4 (minor corrections in v2)

References in corpus (7)

• Fault-tolerant quantum computation by anyons
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Fault-tolerant quantum computation
• Anyons from non-solvable finite groups are sufficient for universal quantum computation
• Quantum symmetries in discrete gauge theories
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• Discrete gauge theories

Cited by in corpus (65)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
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• Condensate induced transitions between topologically ordered phases
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Braid Topologies for Quantum Computation
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Interferometry of non-Abelian Anyons
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Long-range entanglement from measuring symmetry-protected topological phases
• Quantum accuracy threshold for concatenated distance-3 codes
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• A hierarchy of topological tensor network states
• Topological Quantum Computing with Only One Mobile Quasiparticle
• Universal quantum computation with weakly integral anyons
• Deep neural decoders for near term fault-tolerant experiments
• Simulations of quantum double models
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Decoding non-Abelian topological quantum memories
• A proposal to demonstrate non-abelian anyons on a NISQ device
• Level Reduction and the Quantum Threshold Theorem
• Quantum memories and error correction
• Haag duality for Kitaev's quantum double model for abelian groups
• Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons
• Handling Leakage with Subsystem Codes
• Generalized Cluster States Based on Finite Groups
• Subspace Confinement: How good is your qubit?
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Braiding and fusion of non-Abelian vortex anyons
• Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation
• Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime
• Kitaev's quantum double model from a local quantum physics point of view
• Local Hamiltonians in Quantum Computation
• Universal quantum computation in the surface code using non-Abelian islands
• Creating anyons from photons using a nonlinear resonator lattice subject to dynamic modulation
• From orbifolding conformal field theories to gauging topological phases
• Towards Large-Scale Quantum Computation
• Non-Abelian Chern-Simons models with discrete gauge groups on a lattice
• Finite temperature quantum simulation of stabilizer Hamiltonians
• Qutrit Toric Code and Parafermions in Trapped Ions
• Generalized Color Codes Supporting Non-Abelian Anyons
• Experimentally Realizable C-NOT Gate in a Flux Qubit/Resonator System
• Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
• Stability and Loop Models from Decohering Non-Abelian Topological Order
• Topological Quantum Gates in Homotopy Type Theory
• Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups
• Measuring Topological Order
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Simulation of non-Abelian Anyons using ribbon operators connected to a common base site
• A Universal Circuit Set Using the $S_3$ Quantum Double
• Quasitriangular Hopf algebras, braid groups and quantum entanglement
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Dihedral twist liquid models from emergent Majorana fermions
• Twofold twist defect chains at criticality
• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Error Channels and the Threshold for Fault-tolerant Quantum Computation
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Universal Quantum Computation with Abelian Anyon Models
• Simplifying quantum double Hamiltonians using perturbative gadgets
• Topological Properties and Characterizations
• Universal Gates from Braiding and Fusing Anyons on Quantum Hardware