2 citations · 5 across the 13 of their papers we have counts for
13 papers
Quantum Computing Algebra (QCA), the theory and implementation
Jaroslav Hrdina, Dietmar Hildenbrand, Oliver Rettig
We present a real geometric algebra framework designed for the direct translation of the Dirac formalism into geometric algebra representations. Unlike previous approaches based on…
Quantization of Two- and Three-player Cooperative Games Based on QRA
Ivan Eryganov, Jaroslav Hrdina, Aleš Návrat
In this paper, a novel quantization scheme for cooperative games is proposed. The considered circuit is inspired by the Eisert-Wilkens-Lewenstein protocol modified to represent coo…
Quantum Register Algebra: the mathematical language for quantum computing
Jaroslav Hrdina, Dietmar Hildenbrand, Aleš Návrat +5
We introduce Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present GAALOP (Geometric Algebr…
Quantum computing based on complex Clifford algebras
Jaroslav Hrdina, Ales Navrat, Petr Vasik
We propose to represent both --qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension In this f…
Note on geometric algebras and control problems with SO(3)-symmetries
Jaroslav Hrdina, Ales Navrat, Petr Vasik +1
We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step invariant with resp…
On symmetries of a sub--Riemannian structure with growth vector
Jaroslav Hrdina, Aleš Návrat, Lenka Zalabová
We study symmetries of specific left--invariant sub--Riemannian structure with filtration and their impact on sub--Riemannian geodesics of corresponding control problem. We…
Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra
Ales Navrat, Jaroslav Hrdina, Petr Vasik +1
We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat…
Geometric control theory of vertical rolling disc using symmetries
Jaroslav Hrdina, Ales Navrat, Lenka Zalabova
We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. W…
Local geometric control of a certain mechanism with the growth vector (4,7)
Jaroslav Hrdina, Lenka Zalabova
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control…
Nilpotent approximation of a trident snake robot controlling distribution
Jaroslav Hrdina, Ales Navrat, Petr Vasik
We construct a privileged system of coordinates with respect to the controlling distribution of a trident snake robot and, furthermore, we construct a nilpotent approximation with…
The generic rank for --plannar structures
Jaroslav Hrdina
The paper mostly collects material on generic rank of --modules with respect to differential geometric applications. Our research was motivated by geometry of --structures. I…
Geometry of almost Cliffordian manifolds: classes of subordinated connections
Jaroslav Hrdina, Petr Vasik
An almost Clifford and an almost Cliffordian manifold is a --structure based on the definition of Clifford algebras. An almost Clifford manifold based on $\mathcal O:= \cc l (s,…
Generalized planar curves and quaternionic geometry
Jaroslav Hrdina, Jan Slovak
Motivated by the analogies between the projective and the almost quaternionic geometries, we study the generalized planar curves and mappings. We follow, recover, and extend the cl…