Related papers: Synthesising Graphical Theories
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…
There exist several graphical languages for quantum information processing, like quantum circuits, ZX-Calculus, ZW-Calculus, etc. Each of these languages forms a dagger-symmetric monoidal category (dagger-SMC) and comes with an…
As the field of quantum physics evolves, researchers naturally form subgroups focusing on specialized problems. While this encourages in-depth exploration, it can limit the exchange of ideas across structurally similar problems in different…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…
As the use and diversity of diagrams across many disciplines grows, there is an increasing interest in the diagrams research community concerning how such diversity might be documented and explained. In this article, we argue that one way…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…
Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances…
We introduce a general diagrammatic theory of digital circuits, based on connections between monoidal categories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntactically and…
The most efficient automated way to construct a large class of quantum photonic experiments is via abstract representation of graphs with certain properties. While new directions were explored using Artificial intelligence and SAT solvers…
The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Conceptual Graphs (CGs) are a formalism to represent knowledge. However producing a CG database is complex. To the best of our knowledge, existing methods do not fully use the expressivity of CGs. It is particularly troublesome as it is…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles and combinatorics.
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much…
In this paper we attempt to consider quantum superpositions from the perspective of the logos categorical approach presented in [26]. We will argue that our approach allows us not only to better visualize the structural features of quantum…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…