Related papers: Quantizing Braids and Other Mathematical Objects: …
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…
Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
Braid theories are applied to quantum computation processes, where to each crossing in the Braid diagram a unitary Yang-Baxter operator R is associated, representing either a Braiding matrix or a universal quantum gate. By operating with…
In the paper we give a survey on braid groups and subjects connected with them. We start with the initial definition, then we give several interpretations as well as several presentations of these groups. Burau presentation for the pure…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
We propose a new non-commutative generalization of the representation variety and the character variety of a knot group. Our strategy is to reformulate the construction of the algebra of functions on the space of representations in terms of…
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…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…
It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it…
A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
We provide a comprehensive systematic method for the numerical computation of elementary braid operations in topological quantum computation (TQC). This {procedure} is systematically applicable to all anyon models, including $SU(2)_k$.…