The Quantum Geometric Algebra Algorithm

Diederik Aerts, Marek Czachor

In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but employ additional algebraic structures typical of geometric algebra -- structures absent in standard quantum computation. As a test we reformulate in Geometric Algebra terms the Deutsch-Jozsa problem.

Eduardo Jose Bayro-Corrochano

Liyabona manase Ngconde mdange ka tshiwo

Jincheng Zhang

This paper introduces the Geometric-Algebraic Hybrid Quantum Computing (GAHQ) framework, a novel algorithmic approach designed to efficiently perform high-precision geometric operations and leverage quantum entanglement for accelerated computation and storage. Traditional methods struggle with the complexities of accurate geometric calculations, prompting the development of this framework. GAHQ integrates geometric transformations with algebraic operations, employing quantum entanglement to enhance computational efficiency and storage capabilities. This paper details the design of the GAHQ algorithm, its theoretical advantages, and initial experimental results demonstrating its potential for significant advancements in geometric computation and quantum information processing.

Demosthenes Ellinas, Christos Konstandakis

A toy model relaxation of the unitarity of a quantum search algorithm is introduced and the resulting parametric quantum search is investigated mathematically via a one-parameter family of completely positive trace preserving maps by introducing the oracle algebra (an SU(2) isomorphic matrix algebra). The parametric search is shown to be conditionally as fast as the original algorithm. Geometrically, it is related to spherical geodesics which exhibit an azimuthal symmetry, while its search map and density matrix enjoy geometric and structural symmetries.

Song Yuan Yan