Quantum chemistry is a promising application for noisy intermediate-scale
quantum (NISQ) devices. However, quantum computers have thus far not succeeded
in providing solutions to problems of real scientific significance, with
algorithmic advances being necessary to fully utilise even the modest NISQ
machines available today. We discuss a method of ground state energy estimation
predicated on a partitioning the molecular Hamiltonian into two parts: one that
is noncontextual and can be solved classically, supplemented by a contextual
component that yields quantum corrections obtained via a Variational Quantum
Eigensolver (VQE) routine. This approach has been termed Contextual Subspace
VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on
NISQ devices. The problem we address here is that of the ansatz - a
parametrized quantum state over which we optimize during VQE. It is not
initially clear how a splitting of the Hamiltonian should be reflected in our
CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is
illuminated by a reformulation of CS-VQE in the stabilizer formalism. This
defines an ansatz restriction from the full electronic structure problem to the
contextual subspace and facilitates an implementation of CS-VQE that may be
deployed on NISQ devices. We validate the noncontextual projection ansatz using
a quantum simulator, with results obtained herein for a suite of trial
molecules.Comment: 42 pages, 4 figure