Improvement using semidefinite-programming hierarchies

Determine whether the approximation results for homogeneous quartic fermionic Hamiltonians can be improved by using semidefinite-programming hierarchies and sums-of-squares bounds.

Background

The analysis uses moment and coefficient matrices but explicitly does not rely on semidefinite-programming hierarchies. The discussion raises the unresolved possibility that SDP hierarchies and sums-of-squares techniques could yield stronger eigenvalue bounds or approximation guarantees.