  Contextuality, a generalization of non-locality, has been proposed as the
resource that provides the computational speed-up for quantum computation. For
universal quantum computation using qudits, of odd-prime dimension,
contextuality has been shown to be a necessary and possibly sufficient
resource. However, the role of contextuality in quantum computation with qubits
remains open. The $n$-qubit stabilizer formalism, which by itself cannot
provide a quantum computer super-polynomial computational advantage over a
classical counterpart, is contextual. Therefore contextuality cannot be
identified as a sufficient resource for quantum computation. However it can be
identified as a necessary resource. In this paper we construct a contextual
$\psi$-epistemic ontological model of the $n$-qubit stabilizer formalism, to
investigate the contextuality present in the formalism. We demonstrate it is
possible for such a model to be outcome deterministic, and therefore have a
value assignment to all Pauli observables. In our model the value assignment
must be updated after a measurement of any stabilizer observable. Remarkably,
this includes the value assignments for observables that commute with the
measurement. A stronger manifestation of contextuality than is required by
known no-go theorems.
