# Percolation Toolkit The software implements Newman-Ziff algorithm for finding critical point of non-weighted lattice. This is especially useful to map Haar-random quantum circuit to a network and calculate critical points of measurement-induced phase transition (c.f. Hashizume et al. (2022)). ## Cite Please cite the following: The software is based on: * M. E. J. Newman, R. M. Ziff. (2001). [Phys. Rev. E 64, 016706](https://doi.org/10.1103/PhysRevE.64.016706). Efficient Find-Union algorithm is based on: * J. E. Hopcroft, J. D. Ullman (1973). [SIAM Journal on Computing 2, 294](https://doi.org/10.1137/0202024). * R. E. Tarjan. (1975) [Journal of the ACM (JACM) 22, 215](https://doi.org/10.1145/321879.321884). Cite this software as: * Tomohiro Hashizume. (2022). Percolation Toolkit 0.1. [https://doi.org/10.5281/zenodo.7245837](https://doi.org/10.5281/zenodo.7245837). Results obtained from this his and older versions of the software are Published in: * Tomohiro Hashizume, Gregory Bentsen, Andrew J. Daley. (2022). [Phys. Rev. Research 4, 013174](https://doi.org/10.1103/PhysRevResearch.4.013174). ## Usage Please see examples in `test/source`. ## Contact * Tomohiro Hashizume (original developer) tomohiro.hashizume.overseas@gmail.com ## Project status Please visit https://gitlab.com/TomohiroHashizume/percolationtoolkit for the latest version.

{"references": ["M. E. J. Newman, R. M. Ziff. (2001). Phys. Rev. E 64, 016706.", "J. E. Hopcroft, J. D. Ullman (1973). SIAM Journal on Computing 2, 294.", "R. E. Tarjan. (1975). Journal of the ACM (JACM) 22, 215."]}