Related papers: The Computational Complexity of Classical Knot Rec…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
Knot theory is the Mathematical study of knots. In this paper we have studied the Composition of two knots. Knot theory belongs to Mathematical field of Topology, where the topological concepts such as topological spaces, homeomorphisms,…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended…
The expectations arising from the latest achievements in the quantum computing field are causing that researchers coming from classical artificial intelligence to be fascinated by this new paradigm. In turn, quantum computing, on the road…
In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical…
Quantum machine learning is receiving significant attention currently, but its usefulness in comparison to classical machine learning techniques for practical applications remains unclear. However, there are indications that certain quantum…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
We analyze different aspects of neural network predictions of knot invariants. First, we investigate the impact of different knot representations on the prediction of invariants and find that braid representations work in general the best.…
We study the complexity of the Virtual Network Embedding Problem (VNE), which is the combinatorial core of several telecommunication problems related to the implementation of virtualization technologies, such as Network Slicing. VNE is to…
In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a…
In this paper we use artificial neural networks to predict and help compute the values of certain knot invariants. In particular, we show that neural networks are able to predict when a knot is quasipositive with a high degree of accuracy.…
A polynomial knot is a smooth embedding $\kappa: \real \to \real^n$ whose components are polynomials. The case $n = 3$ is of particular interest. It is both an object of real algebraic geometry as well as being an open ended topological…
While many quantum computing techniques for machine learning have been proposed, their performance on real-world datasets remains to be studied. In this paper, we explore how a variational quantum circuit could be integrated into a…
A virtual knot that has a homologically trivial representative $\mathscr{K}$ in a thickened surface $\Sigma \times [0,1]$ is said to be an almost classical (AC) knot. $\mathscr{K}$ then bounds a Seifert surface $F\subset \Sigma \times…
We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial $\Delta_0$ (as defined by Silver and Williams) of these virtual twist knots. These results are applied…
Object detection is a fundamental task in computer vision and image understanding, with the goal of identifying and localizing objects of interest within an image while assigning them corresponding class labels. Traditional methods, which…
In our works with Stoimenow, Vdovina and with Byberi, we introduced the virtual canonical genus $g_{vc}(K)$ and the virtual bridge number $vb(K)$ invariants of virtual knots. One can see from the definitions that for an classical knot $K$…