Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices

Abstract

Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged. This can be used to perform quantum computations [A. Yu. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003)]. We show how to simulate the creation and manipulation of Abelian and non- Abelian anyons in topological lattice models using trapped atoms in optical lattices. Our proposal, feasible with present technology, requires an ancilla particle which can undergo single-particle gates, be moved close to each constituent of the lattice and undergo a simple quantum gate, and be detected.

8 pages, 4 pdf figures; v2: reference added, typos fixed; v3: matches published version (title changed), contains appendix not there

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• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Criticality, the area law, and the computational power of PEPS
• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• Coherence properties and quantum state transportation in an optical conveyor belt
• Anyonic interferometry and protected memories in atomic spin lattices
• Creation and Manipulation of Anyons in the Kitaev Model
• Minimum instances of topological matter in an optical plaquette
• Anyonic Braiding in Optical Lattices
• Theoretical analysis of the implementation of a quantum phase gate with neutral atoms on atom chips
• Physical implementation of topologically decoherence-protected superconducting qubits
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Cited by in corpus (54)

• Digital lattice gauge theories
• Measurement as a shortcut to long-range entangled quantum matter
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Anyonic interferometry and protected memories in atomic spin lattices
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Long-range entanglement from measuring symmetry-protected topological phases
• Interface Between Topological and Superconducting Qubits
• Preparation of matrix product states with log-depth quantum circuits
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Simulations of quantum double models
• Intrinsic Mixed-state Topological Order
• Junctions of anyonic Luttinger wires
• Methods for simulating string-net states and anyons on a digital quantum computer
• Mixed-state long-range order and criticality from measurement and feedback
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Symmetry protected topological phases under decoherence
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Separability transitions in topological states induced by local decoherence
• A proposal to demonstrate non-abelian anyons on a NISQ device
• Symmetry-enforced many-body separability transitions
• Quantum spin systems for measurement-based quantum computation
• Implementing topological quantum manipulation with superconducting circuits
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• Engineered Open Systems and Quantum Simulations with Atoms and Ions
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Non-locality of non-Abelian anyons
• Characterizing MPS and PEPS Preparable via Measurement and Feedback
• Minimal instances for toric code ground states
• Inhomogeneous hard-core bosonic mixture with checkerboard supersolid phase: Quantum and thermal phase diagram
• Periodic driving induced helical Floquet channels with ultracold atoms in momentum space
• Playing nonlocal games across a topological phase transition on a quantum computer
• An analog of topological entanglement entropy for mixed states
• Simulation of anyonic fractional statistics of Kitaev's toric model in circuit QED
• Stabilizer Scars
• Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
• Quasimomentum distribution and expansion of an anyonic gas
• An anyon model in a toric honeycomb lattice
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• General scheme for preparation of different topological states on the cluster states
• On the locality of qubit encodings of local fermionic modes
• Variational LOCC-assisted quantum circuits for long-range entangled states
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Non-Abelian Anyons with Rydberg Atoms
• Subsystem Complexity and Measurements in Holography
• Post-measurement Quantum Monte Carlo
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Topological Properties and Characterizations