Related papers: A Superposition-Based Calculus for Quantum Diagram…
We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be…
The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…
In this article, we establish a mathematical framework that utilizes concepts from graph theory to formalize the parity transformation, an encoding strategy for compiling optimization problems on quantum devices. We introduce the…
We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…
We use a labelled deduction system ( LND$_{ED-}$TRS ) based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type, which allowed us to carry out in homotopic theory an approach using…
We introduce a novel scheme of quantum recursive programming, in which large unitary transformations, i.e. quantum gates, can be recursively defined using quantum case statements, which are quantum counterparts of conditionals and case…
The concept of diagrammatic combinatorial Hopf algebras in the form introduced for describing the Heisenberg-Weyl algebra in~\cite{blasiak2010combinatorial} is extended to the case of so-called rule diagrams that present graph rewriting…
A method for selecting solution constructors in narrowing is presented. The method is based on a sort discipline that describes regular sets of ground constructor terms as sorts. It is extended to cope with regular sets of ground…
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax…
Kelly's lemma is a basic result on graph reconstruction. It states that given the deck of a graph $G$ on $n$ vertices, and a graph $F$ on fewer than $n$ vertices, we can count the number of subgraphs of $G$ that are isomorphic to $F$.…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…