Related papers: Non-abelian statistics from an abelian model
The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by…
Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather…
I define quantum loop models whose degrees of freedom are Ising spins on the square lattice as in the toric code, but where the excitations should have non-abelian statistics. The inner product is topological, allowing a direct…
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…
We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain $\mathbf{Z}_n$…
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here we go beyond…
Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between…
We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian…
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…
I propose that non-Abelian topological order can emerge from the organization of quantum particles into identical indistinguishable copies of the same quantum many-body state. Quantum indistinguishability (symmetrization) of the…
Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the…
Non-Abelian topological orders offer an intriguing path towards fault-tolerant quantum computation, where information can be encoded and manipulated in a topologically protected manner immune to arbitrary local noises and perturbations.…
Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as…
We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work…
Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically…
Anyons are particles obeying statistics of neither bosons nor fermions. Non-Abelian anyons, whose exchanges are described by a non-Abelian group acting on a set of wave functions, are attracting a great attention because of possible…