Large Scale HEOM Solver Using PETSc

This project aims to scale QuTiP's HEOM solver beyond single-node limitations by integrating PETSc to distribute ODE integration across multiple MPI ranks on HPC clusters. HEOM can exactly simulate open quantum system dynamics, but propagating a full hierarchy of coupled auxiliary density matrices makes it brutally expensive — the current scipy-based single-process implementation hits a hard wall at hierarchy depth > 6 or larger Hilbert spaces. The core design challenge is partitioning the coupled density matrices across ranks without making inter-process communication the new bottleneck. The work covers profiling the existing solver, building the distributed path on PETSc's TS interface, correctness validation against the original solver, and scaling benchmarks across node counts and hierarchy depths — all without touching the existing solver or changing anything the user sees.