In quantum mechanics and quantum information theory, the Pauli group is a set of important matrices related to the Pauli operators, which play a crucial role in the formulation of quantum gates and quantum error correction. The Pauli group on \( n \) qubits, denoted as \( \mathcal{P}_n \), consists of all \( n \)-qubit operators that can be expressed as the tensor products of the Pauli operators, up to a phase factor.
