Related papers: Span(Graph): a Canonical Feedback Algebra of Open …
Let $\fS$ be an analytic free semigroup algebra. In this paper, we explore richer structures of $\fS$ and its predual $\fS_*$. We prove that $\fS$ and $\fS_*$ both are Hopf algebras. Moreover, the structures of $\fS$ and $\fS_*$ are closely…
We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie…
Solving algebra problems (APs) continues to attract significant research interest as evidenced by the large number of algorithms and theories proposed over the past decade. Despite these important research contributions, however, the body…
Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind…
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
We establish comparison maps between the classical algebraic $K$-theory of algebras over a field and its analogue $K^c$, an algebraic $K$-theory for coalgebras over a field. The comparison maps are compatible with the Hattori--Stallings…
We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our…
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
Span program is a linear-algebraic model of computation which can be used to design quantum algorithms. For any Boolean function there exists a span program that leads to a quantum algorithm with optimal quantum query complexity. In…
Here we investigate the single-layer linearized perceptron near the SAT-UNSAT transition point as a prototypical model of the convex continuous satisfaction problems. The simplicity of the model allows us to take into account the effects of…
For any tracial non-commutative probability space $(\mathcal{A}, \varphi)$, C\'{e}bron, Dahlqvist, and Male showed that one can always construct an enveloping traffic space $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$ that extends the trace.…
The recently presented quantum antibrackets are generalized to quantum Sp(2)-antibrackets. For the class of commuting operators there are true quantum versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a…
Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…
In a recent article, we gave a definition of partition C*-algebras. These are universal C*-algebras based on algebraic relations which are induced from partitions of sets. In this follow up article, we show that often we can associate a…
Tabular and textual question answering requires systems to perform reasoning over heterogeneous information, considering table structure, and the connections among table and text. In this paper, we propose a ChAin-centric Reasoning and…
We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global…