Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the nonabelian Berry phase. We show that these errors can be eliminated by suitably designed counterdiabatic correction terms in the Hamiltonian. We implement the result...

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the C-topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic group of finite index or a...

A skew-morphism of a finite group G is permutation σ on fixing the identity element such that product 〈 〉 with left regular representation forms . This called skew-product The was introduced as an algebraic tool to investigate Cayley maps. In this paper, we characterize skew-products skew-morphisms nonabelian characteristically simple groups (see Theorem 1.2 ) and corresponding maps 1.6 ).

Abstract. Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V (KG)be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V (KG) commute with each other if and only if G is isomorphic to one of the groups on this list. In particular, this property depends only on G and not ...

Error-correcting encoding is a mathematical manipulation of the information against transmission errors over noisy communications channels. One class of error-correcting codes is the so-called group codes. Presently, there are many good binary group codes which are abelian. A group code is a family of bi-infinite sequences produced by a finite state machine FSM homomorphic encoder defined on th...

The axion particle may or not exist, but the field can be used, as shown here, in an explicitly local formulation of a chiral U(1) gauge theory with both classical and quantum invariance. Nonabelian analogues fields, which have recently been introduced, together their special symmetries, similar construction nonabelian theories. As known cases, symmetry is broken boson acquires mass by swallowi...

A Cayley graph Cay(G, S) of a group G is called a CI-graph if whenever T is another subset of G for which Cay(G, S) ∼= Cay(G, T ), there exists an automorphism σ of G such that Sσ = T . For a positive integer m, the group G is said to have the m-CI property if all Cayley graphs of G of valency m are CI-graphs; further, if G has the k-CI property for all k ≤ m, then G is called an m-CI-group, an...

We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show arbitrary partition of the conjugacy classes or irreducible characters can be refined coarsest that belongs theory. Our constructions emphasize duality between superclasses and supercharacters. An algorithm presented all on given table. The used compute number some no...

If the countable group G has a nonabelian free subgroup, then there exists a standard Borel G-space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.