|q⟩ Bad Qubits

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A candidate stabilizer group on 3 qubits is generated by g1 = Z0 Z1 and g2 = Z1 Z2. A set of Pauli operators forms a valid stabilizer group only if every pair of generators commutes (the group is abelian). Computing the symplectic inner product of g1 and g2 over GF(2), is this generating set abelian?