mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics.

The article presents **mpsqd**, a Python package designed to simulate multidimensional quantum dynamics by employing matrix product states (MPS) and matrix product operators (MPO). It efficiently solves both the time-dependent Schrödinger equation (TDSE) for closed quantum systems and the hierarchical equations of motion (HEOM) for open quantum systems, representing wave functions and density operators in MPS form and Hamiltonians or generalized Liouvillians as MPOs. The package supports propagation via the fourth-order Runge–Kutta method and the time-dependent variational principle, and includes prebuilt models such as vibronic dynamics in pyrazine, excitation energy transfer (EET) in molecular aggregates and photosynthetic complexes, the spin-boson model, the Holstein model, and charge transport in the Anderson impurity model. Demonstrations show that mpsqd achieves accurate results consistent with established methods like ML-MCTDH and TD-DMRG, offering a versatile and open-source tool for research in quantum dynamics of complex molecular and condensed matter systems.