Related papers: Quantum Trigonometric B\'ezier Curves
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
According to the Hall algebras of quivers with automorphisms under Lusztig's construction, the polynominal forms of several structure coefficients for quantum groups of all finite types are presented in this note. We first provide a…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
In this paper, a new analogue of blossom based on post quantum calculus is introduced. The post quantum blossom has been adapted for developing identities and algorithms for Bernstein bases and B$\acute{e}$zier curves. By applying the post…
We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere - which, with additional structures, we identify with the quantum projective line.…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
The approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case of Bernstein-Bezoutian matrices constructed when the polynomials are given in…
We study real and integral structures in the space of solutions to the quantum differential equations. First we show that, under mild conditions, any real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Matrix weighted rational B\'{e}zier curves can represent complex curve shapes using small numbers of control points and clear geometric definitions of matrix weights. Explicit formulae are derived to convert matrix weighted rational…
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are expressed in terms of Bernstein polynomials and augment the…
We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…