Related papers: Quantum algebra in R: the weyl package
At the interception between quantum computing and machine learning, Quantum Reinforcement Learning (QRL) has emerged as a promising research field. Due to its novelty, a standardized and comprehensive collection for QRL algorithms has not…
Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…
In this work we introduce Qumin, a novel quantum programming language with a focus on providing an easy to use, minimalist, high-level, and easily extensible platform for quantum programming. Qumin's design concentrates on encompassing the…
Suppose q is a complex number of modulus one and different from 1,-1. Let O(R^2_q) be the *-algebra with two hermitean generators x and y satisfying the relation xy=qyx. Using operator representations of the *-algebra O(R^2_q) on Hilbert…
Polymer representations of the Weyl algebra of linear systems provide the simplest analogues of the representation used in loop quantum gravity. The construction of these representations is algebraic, based on the Gelfand-Naimark-Segal…
We introduce a new version $kk^{\rm alg}$ of bivariant $K$-theory that is defined on the category of all locally convex algebras. A motivating example is the Weyl algebra $W$, i.e. the algebra generated by two elements satisfying the…
Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages…
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
We describe a quantum Lie algebra based on the Cremmer-Gervais R-matrix. The algebra arises upon a restriction of an infinite-dimensional quantum Lie algebra.
We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and…
Even though in recent years the scale of statistical analysis problems has increased tremendously, many statistical software tools are still limited to single-node computations. However, statistical analyses are largely based on dense…
Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules of the quantized enveloping algebras. On them the quantum Lie…
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine…
Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative…
The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment. This enables the R user…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
In this article a new formulation of the Weyl C*-algebra, which has been invented by Fleischhack, in terms of C*-dynamical systems is presented. The quantum configuration variables are given by the holonomies along paths in a graph.…