Related papers: Knot theory and quantum computing
This is a series of lecture notes explaining topos theory and its application in physics.
Quantum computing is poised to redefine the algorithmic foundations of communication systems. While quantum superposition and entanglement enable quadratic or exponential speedups for specific problems, identifying use cases where these…
Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that…
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 computers are becoming real, and they have the inherent potential to significantly impact many application domains. We sketch the basics about programming quantum computers, showing that quantum programs are typically hybrid…
It is considered an interdependence of the theory of quantum computing and some perspective information technologies. A couple of illustrative and useful examples are discussed. The reversible computing from very beginning had the serious…
Quantum networking is an emerging area with the potential to transform information processing and communications. In this paper, we present a brief introduction to quantum network control, an area in quantum networking dedicated to…
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…
This is an expository article of our work on analogies between knot theory and algebraic number theory. We shall discuss foundational analogies between knots and primes, 3-manifolds and number rings mainly from the group-theoretic point of…
The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of…
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…
This paper gives a criterion for detecting the entanglement of a quantum state, and uses it to study the relationship between topological and quantum entanglement. It is fundamental to view topological entanglements such as braids as…
In this paper we constructed new model of plastic deformation. The knot theory was used to classify the plastic state.
Artificial neural networks have been proposed as potential algorithms that could benefit from being implemented and run on quantum computers. In particular, they hold promise to greatly enhance Artificial Intelligence tasks, such as image…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In…
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum…