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We discuss from a pedagogical perspective the use of tensors in many-body electronic structure methods, especially the relevant storage and computational aspects used by modern quantum chemistry software packages. We consider the implementational consequences of the various symmetries—spin, spatial, and permutational—that appear in tensors representing the Hamiltonian, wave functions, and other important quantities in many-body methods. In addition, we review a number of state-of-the-art approaches to tensor frameworks on modern high-performance computing architectures.more » « less
