This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. The paper discusses these results in the context ...

Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. Thes...

The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra A having a λ-cocommutative infinitesimal braiding for some regular element λ 6= 0 in the base field, then the infinitesimal braiding of A is of Hecke-type of mark...

We develop an approach to realizing a topological phase transition and non-Abelian braiding statistics with dynamically induced Floquet Majorana fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasienergy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space w...

We demonstrate that non-Abelian rotations within the degenerate ground-state manifold of a set of Majorana fermions can be realized by the addition or removal of single electrons, and propose an implementation using Coulomb blockaded quantum dots. The exchange of electrons generates rotations similar to braiding, though not in real space. Unlike braiding operations, rotations by a continuum of ...

This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a unitary representation of the braid group. We discuss the evaluation of the polynomial as a generalized quantum amplitude and show how the braiding part of the eva...

We investigate the self-correcting properties of a network of Majorana wires, in the form of a trijunction, in contact with a parity-preserving thermal environment. As opposed to the case where Majorana bound states are immobile, braiding Majorana bound states within a trijunction introduces dangerous error processes that we identify. Such errors prevent the lifetime of the memory from increasi...