Related papers: Complex Quantum Network Manifolds in Dimension $d>…
An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new…
Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new…
The algebras obtained as fixed points of the action of the cyclic group $Z_N$ on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following…
Quantum computing enables quantum neural networks (QNNs) to have great potentials to surpass artificial neural networks (ANNs). The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Quantum neural networks (QNNs) represent a pioneering intersection of quantum computing and deep learning. In this study, we unveil a fundamental convolution property inherent to QNNs, stemming from the natural parallelism of quantum gate…
Dynamical systems with a network structure can display anomalous bifurcations as a generic phenomenon. As an explanation for this it has been noted that homogeneous networks can be realized as quotient networks of so-called fundamental…
The rapid development of quantum computer hardware has laid the hardware foundation for the realization of QNN. Due to quantum properties, QNN shows higher storage capacity and computational efficiency compared to its classical…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to…
Continuous-variable (CV) quantum computing offers a promising framework for scalable quantum machine learning, leveraging optical systems with infinite-dimensional Hilbert spaces. While discrete-variable (DV) quantum neural networks have…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We present a new implementation of quantum computation that treats quantum computers as a special type of Bayesian Network called a QuDot Net. QuDot Nets allow for the efficient representation of some qubit systems. Single qubit quantum…
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi…
In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework…
The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…
The unprecedented pace of evolution in nanoscale architectures for cavity quantum electrodynamics (cQED) has posed crucial challenges for theory, where the quantum dynamics arising from the non-perturbative dressing of matter by cavity…