An improved formalism for the Grover search algorithm

James M. Chappell , M. A. Lohe, Lorenz von Smekal, Azhar Iqbal and Derek Abbott School of Electrical and Electronic Engineering, University of Adelaide 5005, Australia School of Chemistry and Physics, University of Adelaide, South Australia 5005, Australia c Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany Email: [email protected] Abstract The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford’s formalism of geometric algebra, provides a significantly more efficient representation than the conventional Bra-ket notation, and secondly, that the basis defined by the states of maximum and minimum weight in the Grover search space, allows a simple visualization of the Grover search as the precession of a spin-12 particle. Using this formalism we efficiently solve the exact search problem, as well as easily representing more general search situations.