The Gottesman-Knill theorem states that the following process is efficiently simulatable on a classical computer:
- start of with a set of qubits in a computational basis
- apply any amount of $H, S$ and $CNOT$ gates in any order
- measure all the qubits in the $Z$ basis
The states created after step 2) are known as "stabilizer states". My question is, are there multi-qubit states which are non-stabilizer states but that are also as efficient to classically simulate as the way stabilizer states are simulatable in the above procedure?
