Linear-optical dynamics of one-dimensional anyons (original) (raw)

Quantum computation from fermionic anyons on a one-dimensional lattice

Physical Review A, 2019

Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear optical model which allows for universal quantum computation.

Quantum computation from fermionic anyons on a 1D lattice

2020

Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear optical model which allows for universal quantum computation.

Creation, Manipulation, and Detection of Abelian and Non-Abelian Anyons in Optical Lattices

Physical Review Letters, 2008

Anyons are particle-like excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wavefunction, generalizing Bose and Fermi statistics, when two of them are interchanged. This can be used to perform quantum computations . 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.

Creation, manipulation and detection of anyons in optical lattices

2008

Anyons are particle-like excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wavefunction, generalizing Bose and Fermi statistics, when two of them are interchanged. This can be used to perform quantum computations . 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.

Ground-state properties of hard-core anyons in one-dimensional optical lattices

Physical Review A, 2009

We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit (χ = 1) and Fermi limit (χ = 0) the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviors from the Bose limit to the Fermi limit.

Universal quantum computation with continuous-variable Abelian anyons

Physical Review A, 2012

We describe a generalization of the cluster-state model of quantum computation to continuousvariable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multi-mode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.

A categorical presentation of quantum computation with anyons

2011

In nature one observes that in three space dimensions particles are either symmetric under interchange (bosons) or antisymmetric (fermions). These phases give rise to the two possible “statistics” that one observes. In two dimensions, however, a whole continuum of phases is possible.“Anyon” is a term coined in by Frank Wilczek to describe particles in 2 dimensions that can acquire “any” phase when two or more of them are interchanged.

Topological Quantum Computation using Abelian Anyons

Topological quantum computation using abelian anyons in Kitaev model is studied. We initially discuss the basics of quantum computation and then present a brief description of topological quantum computation using anyons. The exact solution of the 2D Kitaev model and the emergence of abelian anyons is also described. We also discuss quantum error correction and error tolerant quantum memory using Kitaev’s toric code. Abelian anyonic quantum computation, though not completely fault-tolerant, the universal gates can be realized by including some non topological operations with the topological operations. We verify an already proposed model to realize the universal gates in 2D Kitaev lattice by explicitly investigating the theoretical implementation. We find that the adiabatic transport of anyons for braiding cannot be directly represented by some loop operator if they are to be used for a controlled gate operation.

Anyons and transmutation of statistics via a vacuum-induced Berry phase

Physical Review A, 2004

We show that bosonic fields may present anyonic behavior when interacting with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished via the interaction of a two-level system with two quantized modes of a harmonic oscillator; under suitable conditions, the system acquires a fractional geometric phase. A crucial role is played by the entanglement of the system eigenstates, which provides a twodimensional confinement in the effective evolution of the system, leading to the anyonic behavior. For a particular choice of parameters, we show that it is possible to transmute the statistics of the system continually from fermions to bosons. We also present an experimental proposal, in an ion-trap setup, in which fractional statistical features can be generated, controlled, and measured.