  We show that qubit stabilizer states can be represented by non-negative
quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism
where Clifford gates are positive state-independent maps. This is accomplished
by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of
two---producing an exterior, or Grassmann, algebra---which results in Clifford
group gates for qubits that act as a permutation on the finite Weyl phase space
points naturally associated with stabilizer states. As a result, a non-negative
probability distribution can be associated with each stabilizer state's
three-generator Wigner function, and these distributions evolve
deterministically to one another under Clifford gates. This corresponds to a
hidden variable theory that is non-contextual and local for qubit Clifford
gates while Clifford (Pauli) measurements have a context-dependent
representation. Equivalently, we show that qubit Clifford gates can be
expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism
whose semiclassical expansion is truncated at order $\hbar^0$ with a finite
number of terms. The $T$-gate, which extends the Clifford gate set to one
capable of universal quantum computation, require a semiclassical expansion of
the propagator to order $\hbar^1$. We compare this approach to previous
quasi-probability descriptions of qubits that relied on the two-generator
Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of
stabilizer states result in a description of evolution under Clifford gates
that is state-dependent, in contrast to the three-generator formalism. We have
thus extended Wigner non-negative quasi-probability distributions from the odd
$d$-dimensional case to $d=2$ qubits, which describe the non-contextuality of
Clifford gates and contextuality of Pauli measurements on qubit stabilizer
states.
