Grant: Collaborative Science, Technology and Innovation Program - Collaborative R&D Initiatives

In quantum mechanical momentum theory, Clebsch-Gordan (CG) transforms coefficients can measure the degree of momentum entanglement in molecules. The complexity of the degree of entanglement generated by molecular orbital interaction needs to be elucidated in order to develop efficient quantum algorithms based on quantum mechanics, particularly under Coulomb and external fields. The potential of solid harmonic Gaussian orbitals (SHGOs), which are eigenfunctions of the angular momentum operator, has been largely underestimated for this purpose. Using SHGOs, Concordia University (CU) aims to develop an atom-centred angular momentum basis, a projection operator of c fermions acting on spherical harmonics. Compared with the existing tensor hypercontraction (THC) method, this new approach could overcome the need for computationally intensive density adjustment. In the orthogonal, unitary angular momentum basis, we can diagonalize the Coulomb operator. CU can derive a highly efficient quantum algorithm for simulating the electronic Hamiltonian using spherical harmonics as the projection function. The total number of atom-centred angular momentum basis functions is smaller than that of the atomic basis of an original molecular Hamiltonian. This new angular momentum algorithm can achieve O(N) scaling and reduce T complexity by several orders of magnitude compared with state-of-the-art THC methods. Integrating quantum simulation and machine learning into the project enables the team to use available NISQ devices and more mature classical computing techniques using GPUs and CPUs. The strategy involves increasing the complexity of the molecular systems generated as larger quantum computing systems are targeted.