Related papers: Quantum Theory in Design
A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators…
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…
Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics (QCD). In order to fulfill that promise, phenomenology and theory must reach a new level, limiting and overcoming…
These lectures on QCD stress the theoretical elements that underlie a wide range of phenomenological studies, particularly gauge invariance, renormalization, factorization and infrared safety. The three parts cover the basics of QCD, QCD at…
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that…
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
These lectures on QCD stress the theoretical elements that underlie a wide range of phenomenological studies, particularly gauge invariance, renormalization, factorization and infrared safety. The three parts cover the basics of QCD, QCD at…
The optical properties of solids are governed not only by their energy band dispersions but also by the quantum geometry of Bloch states. While the role of energy bands in determining the perceived optical appearance of materials, such as…
Double-bosonisation associates to a braided group in the category of modules of a quantum group, a new quantum group. We announce the semiclassical version of this inductive construction.
We briefly discuss the current state, and future computational implications, of quantum type theory.
We introduce a representation theory of q-Lie algebras defined earlier in \cite{DG1}, \cite{DG2}, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in…
We prove direct quantum coding theorem for random quantum codes. The problem is separated into two parts: proof of distinguishability of codewords by receiver, and that of indistinguishability of codewords by environment (privacy). For a…
Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light…
We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
Nonequilibrium quantum field theory is often used to derive an approximation for the evolution of number densities and asymmetries in astroparticle models when a more precise treatment of quantum thermal effects is required. This work…
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…