Related papers: Braiding Interactions in Anyonic Quantum Walks

We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous time quantum walks in a one-dimensional ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is…

Traditional anyons in two dimensions have generalized exchange statistics governed by the braid group. By analyzing the topology of configuration space, we discover that an alternate generalization of the symmetric group governs particle…

We clarify the relations between the mathematical structures that enable fashioning quantum walks on regular graphs and their realizations in anyonic systems. Our protagonist is association schemes that may be synthesized from type-II…

Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…

Correlations of partitioned particles carry essential information about their quantumness. Partitioning full beams of charged particles leads to current fluctuations, with their autocorrelation (namely, shot noise) revealing the particle'…

Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon…

We consider a two-dimensional spin system that exhibits abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically the model…

We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For…

Anyons are exotic quasiparticles obeying fractional statistics,whose behavior can be emulated in artificially designed spin systems.Here we present an experimental emulation of creating anyonic excitations in a superconducting circuit that…

Qubits in topological quantum computation are built from non-Abelian anyons. Adiabatic braiding of anyons is exploited as topologically protected logical gate operations. Thus, the adiabaticity upon which the notion of quantum statistics is…

Studies of free particles in low-dimensional quantum systems such as two-leg ladders provide insight into the influence of statistics on collective behaviour. The behaviours of bosons and fermions are well understood, but two-dimensional…

We report on a numerical experiment in which we use time-dependent potentials to braid non-abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where $\nu$, the ratio of…

Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We…

I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…

Adiabatically exchanging anyons gives rise to topologically protected operations on the quantum state of the system, but the desired result is only achieved if the anyons are well separated, which requires a sufficiently large area. Being…

It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this…

We study how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of entanglement spectrum statistics. In particular, we focus on the degree of scrambling, defined as the randomness produced by…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…

In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with a trapping potential or, for larger systems, from the linear combination of the edge Jack…