A computing device, including memory storing a quantum computing device model. The quantum computing device model may include a plurality of quantum computing device components having a respective plurality of actual boundaries, including a boundary between a superconductor and a semiconductor. The computing device may further include a processor configured to receive, via an application-program interface (API), a nonuniform grid having a nonuniform spacing along at least a first spatial dimension. The processor may receive, via the API, a Schrödinger equation including a Hamiltonian having one or more operators. The processor may discretize the quantum computing device model using the nonuniform grid. The processor may compute a finite-difference solution estimate to the Schrödinger equation over the quantum computing device model as discretized with the nonuniform grid. The processor may output the finite-difference solution estimate via the API.