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

A Contextual $\psi$-Epistemic Model of the $n$-Qubit Stabilizer Formalism