Related papers: Spin Networks and Anyonic Topological Computing
We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network…
We construct a braiding operator in terms of the quantum dilogarithm function based on the quantum cluster algebra. We show that it is a q-deformation of the R-operator for which hyperbolic octrahedron is assigned. Also shown is that, by…
It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…
We present a method for network-capable quantum computing that relies on holographic spin-wave excitations stored collectively in ensembles of qubits. We construct an orthogonal basis of spin waves in a one-dimensional array and show that…
We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum…
Treating the infinite-dimensional Hilbert space of non-abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming…
The connection between braided Hopf algebra structure and the quantum group covariance of deformed oscillators is constructed explicitly. In this context we provide deformations of the Hopf algebra of functions on SU(1,1). Quantum subgroups…
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…
When a quantum hyperboloid is realized, as a three - parameter algebra $\ahqc$, in the usual manner, the following problem arises: what is a ``representation theory'' of this algebra? We construct the series of all spin representations of…
We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed…
The properties of the deformed bosonic oscillator, and the quantum groups ${\cal U}_q(SL(2))$ and $GL_q(2)$ in the limit as their deformation parameter $q$ goes to a root of unity are investigated and interpreted physically. These…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
Representations of small quantum groups $u_q({\mathfrak{g}})$ at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig…
We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models are based on the representation theory of two copies of U_q(su(2)) at a root of…
We adapt some of the methods of quantum Teichm\"uller theory to construct a family of representations of the pure braid group of the sphere.
We propose a general setting for a universal representation of the quantum structure on which quantum information stands, whose dynamical evolution (information manipulation) is based on angular momentum recoupling theory. Such scheme…