We have studied the algebraic structure underlying the quantum circuits composed by \cZ and \Swap gates. Our results are applied to optimize the circuits and to understand the emergence of entanglement when a circuit acts on a fully factorized state.
@article{arxiv.1810.01769,
title = {Quantum circuits of c -- Z and SWAP gates optimization and entanglement},
author = {Marc Bataille and Jean-Gabriel Luque},
journal= {arXiv preprint arXiv:1810.01769},
year = {2019}
}