Grover's Algorithm and the Secant Varieties
Mathematical Physics
2016-07-22 v1 Algebraic Geometry
math.MP
Quantum Physics
Abstract
In this paper we investigate the entanglement nature of quantum states generated by Grover's search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and auxiliary algebraic varieties built from the set of separable states. This new perspective enables us to propose qualitative interpretations of earlier numerical results obtained by M. Rossi et al. We also illustrate our purpose with a couple of examples investigated in details.
Cite
@article{arxiv.1607.06128,
title = {Grover's Algorithm and the Secant Varieties},
author = {Frédéric Holweck and Hamza Jaffali and Ismaël Nounouh},
journal= {arXiv preprint arXiv:1607.06128},
year = {2016}
}
Comments
20 pages, 12 figures