QGLAB: A MATLAB Package for Computations on Quantum Graphs
Roy H. Goodman, Grace Conte, Jeremy Louis Marzuola · SIAM Journal on Scientific Computing · 2025
Abstract. We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use features. The package allows one to construct a quantum graph and accurately compute the spectrum of elliptic operators, solutions to Poisson problems, the linear and nonlinear time evolution of a variety of PDEs, the continuation of branches of steady states (including locating and switching branches at bifurcations), and more. It overcomes the major challenge of discretizing quantum graphs—the enforcement of vertex conditions—using nonsquare differentiation matrices. It uses a unified framework to implement finite-difference and Chebyshev discretizations of differential operators on a quantum graph. For simplicity, the package overloads many built-in MATLAB functions to work on the class. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/manroygood/Quantum-Graphs/ and in the supplementary materials ( Quantum-Graphs-master.zip [13.5MB]). [Formula: see text]