Why bother with Matrix Elements?

Pioneering digital Hartree Fock with tens of electrons, I found that writing down every matrix element takes much longer. Whereas writing down the core 'lookup tables' takes almost no time. Why solve the system with matrix elements (slow deployment) instead of focusing on tying together 'lookup tables' directly? 

In 2018, I realized it was possible. I designed the Andromeda code around the electronic structure lookup tables, facilitating dimensional separation works written by Beylkin and Mohlenkamp, 2005. This paper shows how to treat dense systems as separated dimensional systems. Now, Quantum Dynamics technology can be used to directly access the quantum electron.

A Texas Tech patent, two Army Research Office STIR grants, and several good papers later, including PCCP on quantum computing, demonstrated that faster quantum dynamics algorithms also work with quantum computers.

The ground state is beside the point!

We are concerned with unbiased approach to excited states, allowing for genuine dimensional reductions.

Our techniques reduce complex systems to crisp matrix elements on a many-state basis; these are matrix elements of physical merit. We have the foundations of future technology now. 

Published 12 electronic degrees of freedom in PCCP for quantum as well as classical hardware