We consider the application of the pentagon equation in the context of quantum circuit compression. We show that if solutions to the pentagon equation are found, one can transpile a circuit involving non-Heisenberg-type interactions to a circuit involving only Heisenberg-type interactions while, in parallel, reducing the depth of a circuit. In this context, we consider a model of non-local two-qubit operations of Zhang \emph{et. al.} (the A gate), and show that for certain parameters it is a solution of the pentagon equation.
@article{arxiv.2209.14356,
title = {Transpiling Quantum Circuits using the Pentagon Equation},
author = {Christos Aravanis and Georgios Korpas and Jakub Marecek},
journal= {arXiv preprint arXiv:2209.14356},
year = {2022}
}