Related papers: Two paradigms for topological quantum computation
Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…
We study the construction of both universal quantum computation and multi-partite entangled states in the topological diagrammatical approach to quantum teleportation. Our results show that the teleportation-based quantum circuit model…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet…
These lecture notes offer a pedagogical yet concise introduction to topological quantum computing. The material focuses on topological superconductors and Majorana qubits. It concludes with a discussion of more general braiding phenomena.…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
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…
We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley--Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual…
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much…
We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We review the q-deformed spin network approact to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. These methods produce a concise proof…
Existing and near-term quantum computers can only perform two-qubit gates between physically connected qubits. Research has been done on compilers to rewrite quantum programs to match hardware constraints. However, the quantum processor…
This contribution, to be published in Imagine Math 8 to celebrate Michele Emmer's 75th birthday, can be seen as the second part of my previous considerations on the relationships between topology and physics (Mouchet, 2018). Nevertheless,…
This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators"…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials,…