Current survey of Clifford geometric algebra applications

E Hitzer, C Lavor, D Hildenbrand - Mathematical Methods in …, 2024 - Wiley Online Library
We extensively survey applications of Clifford Geometric algebra in recent years (mainly
2019–2022). This includes engineering; electric engineering; optical fibers; geographic …

From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited

C Cafaro, N Bahreyni, L Rossetti - Symmetry, 2024 - mdpi.com
Alternative mathematical explorations in quantum computing can be of great scientific
interest, especially if they come with penetrating physical insights. In this paper, we present …

Quantum computing based on complex Clifford algebras

J Hrdina, A Návrat, P Vašík - Quantum Information Processing, 2022 - Springer
We propose to represent both n-qubits and quantum gates acting on them as elements in
the complex Clifford algebra defined on a complex vector space of dimension 2 n. In this …

Quantum Register Algebra: the mathematical language for quantum computing

J Hrdina, D Hildenbrand, A Návrat, C Steinmetz… - Quantum Information …, 2023 - Springer
Abstract We present Quantum Register Algebra (QRA) as an efficient tool for quantum
computing. We show the direct link between QRA and Dirac formalism. We present …

Complex Clifford algebra in repeated quantum prisoner's dilemma

I Eryganov, J Hrdina - Mathematical Methods in the Applied …, 2024 - Wiley Online Library
This paper introduces an application of complex Clifford algebra in a representation of the
quantum prisoner's dilemma. The authors propose a novel modification of the Eisert …

[PDF][PDF] Current status on Shor's algorithm via quantum computing

NA Abu, Z Mahad - … of the 9th International Cryptology and …, 2024 - einspem.upm.edu.my
Since its inception in 1994, Shor's Algorithm has given an avenue to render RSA modulo
factoring theoretically in real time. After 3 decades, this paper will investigation its practicality …

Quantum register algebra: The basic concepts

J Hrdina, D Hildenbrand, A Návrat, C Steinmetz… - … of Geometric Algebra, 2022 - Springer
Abstract 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 …

Quantization of two-and three-player cooperative games based on QRA

I Eryganov, J Hrdina, A Návrat - Journal of Physics A …, 2024 - iopscience.iop.org
In this paper, a novel quantization scheme for cooperative games is proposed. The circuit is
inspired by the Eisert–Wilkens–Lewenstein protocol, which was modified to represent …

[PDF][PDF] From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited. Symmetry 2024, 16, 734

C Cafaro, N Bahreyni, L Rossetti - 2024 - inspirehep.net
Alternative mathematical explorations in quantum computing can be of great scientific
interest, especially if they come with penetrating physical insights. In this paper, we present …

[PDF][PDF] PROJECTIVE GEOMETRIC ALGEBRA-BARYCENTRIC AND PL UCKER COORDINATES COMPUTATION

V Skala - Mathematics, Information Technologies and Applied …, 2022 - mitav.unob.cz
This paper presents the computation of the barycentric coordinates and Plücker coordinates
using the projective extension of the Euclidean space and geometric algebra. Using the …