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The Gottesman--Knill theorem gives a classical polynomial-time simulation of quantum computations built from stabilizer-state preparation, Clifford gates, and adaptive Measurements of Pauli observables.

The Gottesman--Knill theorem states that stabilizer-state preparation, Clifford circuits, and adaptive Measurements of Pauli observables can be simulated in classical polynomial time. For $|{\Psi }_{\mathrm{in}}⟩=|+{⟩}^{\otimes 3}$, choose generators $XII$, $IXI$, and $IIX$. With each row written as $[x_1{x}_2{x}_3\mid z_1{z}_2{z}_3]$, its sign-free stabilizer tableau isConjugating these generators successively by ${\mathrm{CNOT}}_{21}$, $H_2\otimes H_3$, and ${\mathrm{CNOT}}_{13}$ gives $XIX$, $XZX$, and $ZIZ$. Hence the output tableau, again ignoring signs, is