Quantum Information Science Meets Quantum Chemistry Hamiltonians: Streamlining Entanglement Complexity of Molecular Interactions for Highly Resource-Efficient Quantum Chemistry Computation

In quantum information science (QSI), a key aspect of quantum algorithms is their ability to rapidly access information stored in nonlocal degrees of freedom. This capability is particularly relevant to the transformation between independent local states and those with definite total angular momentum. It also suggests that the entanglement complexity associated with nonlocal states can be streamlined through quantum hidden symmetries. This is evident when applying quantum Schur and Clebsch-Gordan transformations to analyze the entanglement complexity of quantum chemistry Hamiltonians, revealing the entanglement structure of molecular Coulomb interactions within angular momentum tensor networks. Depending on whether local or nonlocal angular momentum states are considered, the entanglement complexity of these interactions can be simplified by leveraging quantum hidden symmetries. Moreover, integrating QSI with electronic density partitioning into angular momentum tensor networks localized at atomic centers can lead to even simpler entanglement structures in quantum chemistry Hamiltonians, resulting in more efficient computations using quantum computers. Notably, all entanglement interactions are confined to the atomic centers of angular momentum tensor networks due to quantum hidden symmetries.