Related papers: A unified framework for graph algebras and quantum…
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…
We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces…
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group $G$. A classical construction of Gross and Tucker associates to every voltage graph with vertex set $V$ a so-called derived graph with vertex…
Starting from the canonical symmetroid $\mathcal{S}(G)$ associated with a groupoid $G$, the issue of describing dynamical maps in the groupoidal approach to Quantum Mechanics is addressed. After inducing a Haar measure on the canonical…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
We define a notion of quantum automorphism group of Graph C*-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of underlying…
We construct a colored operad whose category of algebras is the category of algebraic quantum field theories. This is achieved by a construction that depends on the choice of a category, whose objects provide the operad colors, equipped…
Categorical quantum mechanics (CQM) and the theory of quantum groups rely heavily on the use of structures that have both an algebraic and co-algebraic component, making them well-suited for manipulation using diagrammatic techniques.…
There has been intensive work on the parameterized complexity of the typically NP-hard task to edit undirected graphs into graphs fulfilling certain given vertex degree constraints. In this work, we lift the investigations to the case of…
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…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
We investigate the computational power and unified resource use of hybrid quantum-classical computations, such as teleportation and measurement-based computing. We introduce a physically causal and local graphical calculus for quantum…
We develop the viewpoint that the opposite of the category of W*-algebras and unital normal *-homomorphisms is analogous to the category of sets and functions. For each pair of W*-algebras, we construct their free exponential, which in the…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…