Title: Computationally Efficient Molecular Integrals of Solid Harmonic Gaussian Orbitals Using Quantum Entanglement of Angular Momentum

Abstract: Vector-coupling and vector-uncoupling schemes in the quantum theory of angular momentum correspond to unitary Clebsch-Gordan transformations that operate on quantum angular momentum states and thereby control their degree of entanglement. The addition of quantum angular momentum from this transformation is suitable for reducing the degree of entanglement of quantum angular momentum, leading to simple and effective calculations of the molecular integrals of solid harmonic Gaussian orbitals (SHGO). Even with classical computers, the speed-up ratio in the evaluation of molecular nuclear Coulomb integrals with SHGOs can be up to four orders of magnitude for atomic orbitals with high angular momentum quantum number. Thus, the less entanglement there is for a quantum system the easier it is to simulate, and molecular integrals with SHGOs are shown to be particularly well-suited for quantum computing. High-efficiency quantum circuits previously developed for unitary and cascading Clebsch-Gordan transformations of angular momentum states can be applied to the differential and product rules of solid harmonics to efficiently compute two-electron Coulomb integrals ubiquitous in quantum chemistry. Combined with such quantum circuits and variational quantum eigensolver algorithms, the high computational efficiency of molecular integrals in solid harmonic bases unveiled in this paper may open an avenue for accelerating full quantum computing chemistry.