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 extended Gottesman--Knill theorem allows arbitrary product-state inputs to a unitary Clifford circuit. Computational-basis output is weakly simulable for any number of measured qubits and strongly simulable for logarithmically many measured qubits.
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The Gottesman-Knill theorem is an important result in quantum computing, specifically in the context of quantum error correction and quantum circuit simulation. It states that any quantum computation that can be executed using only a specific set of gates—namely the gates from the set \{H, CNOT, T\}—can be efficiently simulated classically.
