Related papers: Knot Based Large Scale Structure Code (complete pa…
We extend the QCD Parton Model analysis by employing a factorized nuclear structure model that explicitly accounts for both individual nucleons and correlated nucleon pairs. This novel framework establishes a paradigm that directly links…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other…
A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…
We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc…
Following two recent papers [Phys. Chem. Chem. Phys. 2015, \textbf{17}, 3196; Mol. Phys. 2015, \textbf{113}, 1843], we perform a larger-scale study of chemical structure in one dimension (1D). We identify a wide, and occasionally…
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…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the…
We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Could one start from scratch, ignore relativity theory and quantum theory, create and expand our 3-D universe with no singularities, have the mathematical model predict correctly all of the cosmological parameters, provide the origins and…
We propose a quantum computer structure based on coupled asymmetric single-electron quantum dots. Adjacent dots are strongly coupled by means of electric dipole-dipole interactions enabling rapid computation rates. Further, the asymmetric…
I start with a scenario where the universe is an abstract space $\mathcal{M}$ having $d$ dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $\mathcal{M}$ that has a field theory…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…
A ribbon is, intuitively, a smooth mapping of an annulus $S^1 \times I$ in 3-space having constant width $\varepsilon$. This can be formalized as a triple $(x,\varepsilon, \mathbf{u})$ where $x$ is smooth curve in 3-space and $\mathbf{u}$…
A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…
In the first part of the talk, I explain what empirical evidence points to the need for having an effective grand unification-like symmetry possessing the symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive theory…
This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More…