Related papers: Quantum statistics on graphs
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…
In quantum information theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper,…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
Quantum computation offers exciting new possibilities for statistics. This paper explores the use of the D-Wave machine, a specialized type of quantum computer, which performs quantum annealing. A general description of quantum annealing…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…
Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…