Related papers: Knot Morphing Algorithm for Quantum `Fragile Topol…
This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting codes starting from the colorings of a knot, describing…
We discuss the basic problem of signal transmission in quantum mechanics in terms of topological theories. Using the analogy between knot diagrams and quantum amplitudes we calculate the transmission coefficients of the concept topological…
The goal of this paper is to discuss the possibility of finding an algorithm that can give all distinct knots up to a desired complexity. Two such algorithms are presented, one based on projections on a plane, the other on closed…
Using the cubic honeycomb (cubic tessellation) of Euclidean 3-space, we define a quantum system whose states, called quantum knots, represent a closed knotted piece of rope, i.e., represent the particular spatial configuration of a knot…
Quantum mechanics is a successful theory that describes the behavior of photons, electrons, and other atomic- and molecular-scale objects. However, it is far from being well understood. In this paper, a new theory - knot physics for…
A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is…
In this paper, we investigate the use of variational quantum algorithms for simulating the thermodynamic properties of dinuclear metal complexes. Our study highlights the potential of quantum computing to transform advanced simulations and…
In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this…
Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales,…
While there is a general consensus about the structure of one qubit operations in topological quantum computer, two qubits are as usual a more difficult and complex story of different attempts with varying approaches, problems and…
Sequential Monte Carlo algorithms, or particle filters, are widely used for approximating intractable integrals, particularly those arising in Bayesian inference and state-space models. We introduce a new variance reduction technique, the…
There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or…
Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the…
This paper visualizes a knot reduction algorithm
This project explores the mathematical study of knots and links in topology, focusing on differentiating between the two-component Unlink and the Hopf Link using a computational tool named LINKAGE. LINKAGE employs the linking number,…
We use categories of representations of finite dimensional quantum groupoids (weak Hopf algebras) to construct ribbon and modular categories that give rise to invariants of knots and 3-manifolds.
Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter,…
Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…
We propose a new classification scheme for quantum entanglement based on topological links. This is done by identifying a non-rigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the…
The probability of a random polygon (or a ring polymer) having a knot type $K$ should depend on the complexity of the knot $K$. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially…