Related papers: Graph Theory Data for Topological Quantum Chemistr…
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…
We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically,…
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories…
Bloch theory describes the electronic states in crystals whose energies are distributed as bands over the Brillouin zone. The electronic states corresponding to a (few) isolated energy band(s) thus constitute a vector bundle. The…
We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time…
Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
Graph Theory and Topological Data Analytics, while powerful, have many drawbacks related to their sensitivity and consistency with TDA & Graph Network Analytics. In this paper, we aim to propose a novel approach for encoding vectorized…
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…
Analyzing the geometry of correlation sets constrained by general causal structures is of paramount importance for foundational and quantum technology research. Addressing this task is generally challenging, prompting the development of…
We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges, and subgraphs, our metric graph kernels are purely based on…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
We consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between…
This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…