  Useful relations describing arbitrary parameters of given quantum systems can
be derived from simple physical constraints imposed on the vectors in the
corresponding Hilbert space. This is well known and it usually proceeds by
partitioning the large dimensional Hilbert space into relevant sub spaces and
relating points in the Hilbert space to the expectation values of physical
observables. The aim of this note is quite modest. We describe the procedure
and point out that this parallels the necessary considerations that make
Quantum Simulation of quantum fields and interacting many body quantum systems
on Noisy Intermediate Scale Quantum (NISQ) devices possible. We conclude by
pointing out relevant parts of Quantum Computing where these ideas could be
useful. This work proceeds in density matrix formalism and is a review of
materials found in references. We enrich the literature by suggesting how to
use these ideas to guide and improve parameterized quantum circuits.
