Related papers: Quantale Modules, with Applications to Logic and I…
We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…
We determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms {of these algebras.} In the case where $q$ is {an arbitrary} root of unity, this further…
We present a new framework for imaging and sensing based on utilizing a quantum computer to coherently process quantum information in an electromagnetic field. We describe the framework, its potential to provide improvements in imaging and…
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
Various applications of quantum algebraic techniques in nuclear structure physics and molecular physics are briefly reviewed. Contains 81 references.
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Use is made of a relativistic kinematic modulation effect to compliment imagery from Stochastic Electrodynamics to provide intuitive paradigms for Quantum Mechanics. Based on these paradigms, resolutions for epistemological problems vexing…
We introduce an abstract machine architecture for classical/quantum computations---including compilation---along with a quantum instruction language called Quil for explicitly writing these computations. With this formalism, we discuss…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The…
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
We define a convenient $\infty$-operad parametrizing modules over commutative algebras in $\infty$-categories.
We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…