In this thesis, applications of sparsity, specifically sparse-tensors are motivated in physics.An algorithm is introduced to natively compute sparse-tensor's partial-traces, along with direct implementations in popular python libraries for immediate use. These applications include the infamous exponentially-scaling (with system size) Quantum-Many-Body problems (both Heisenberg/spin-chain-like and Chemical Hamiltonian models). This sparsity aspect is stressed as an important and essential feature in solving many real-world physical problems approximately-and-numerically. These include the original motivation of solving radiation-damage questions for ultrafast light and electron sources.