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We present MISTIQS, a Multiplatform Software for Time-dependent Quantum Simulations. MISTIQS delivers end-to-end functionality for simulating the quantum many-body dynamics of systems governed by time-dependent Heisenberg Hamiltonians across multiple quantum computing platforms. It provides high-level programming functionality for generating intermediate representations of quantum circuits which can be translated into a variety of industry-standard representations. Furthermore, it offers a selection of circuit compilation and optimization methods and facilitates execution of the quantum circuits on currently available cloud-based quantum computing backends. MISTIQS serves as an accessible and highly flexible research and education platform, allowing a broader community of scientists and students to perform quantum many-body dynamics simulations on current quantum computers.