Related papers: Quantum Statistics and Spacetime Topology: Quantum…
Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…
Kauffman and Lomonaco explored the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G.…
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…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco…
Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial,…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum…
This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the…
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…
We connect topological changes that can occur in $3$-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
Braiding operators corresponding to the third Reidemeister move in the theory of knots and links are realized in terms of parametrized unitary matrices for all dimensions. Two distinct classes are considered. Their (non-local) unitary…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…
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…
We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
In this paper we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used \textquotedblleft knotted\textquotedblright{} quantum states of topological phases…