Making Small Quantum Computers do Big Things with the Quantum Many Body Expansion*

We investigate the use of a quantum many body expansion method (qMBE) for use on quantum computers. qMBE is based on the classical many-body FCI method with generalizations that allow for efficient usage on quantum computers. In particular, we generalize the objects with respect to which the many-body expansion is performed. Whereas previous methods switched from electrons to (occupied and/or virtual) orbitals and (in more recent implementations) clusters of many-body states, here our generalization consists of using groups rather than individual orbitals as the fundamental expansion object, needing fewer calculations and in some cases leading to faster convergence. qMBE allows complicated molecular systems to be decomposed into smaller, manageable pieces, distributing the effort over near-term resources. We demonstrate our algorithm on a selection of molecular examples.