Constructive Quantum Shannon Decomposition from Cartan Involutions
Quantum Physics
2009-11-13 v1
Abstract
The work presented here extends upon the best known universal quantum circuit, the Quantum Shannon Decomposition proposed in [Vivek V. Shende, Stephen S. Bullock and Igor Markov, Synthesis of Quantum Logic Circuits, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 25 (6): 1000-1010 (2006)]. We obtain the basis of the circuit's design in a pair of Cartan decompositions. This insight gives a simple constructive algorithm for obtaining the Quantum Shannon Decomposition of a given unitary matrix in terms of the corresponding Cartan involutions.
Cite
@article{arxiv.0806.4015,
title = {Constructive Quantum Shannon Decomposition from Cartan Involutions},
author = {Byron Drury and Peter J. Love},
journal= {arXiv preprint arXiv:0806.4015},
year = {2009}
}