2 citations · 5 across the 9 of their papers we have counts for
9 papers
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…
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…
Nonstandard operators in Grassmannian geometry
Aleš Návrat
We present a construction of curved analogues of the nonstandard operators on Grassmannians parallel to the construction of the Paneitz operator via the curved Casimir operator, bu…