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Quantum repetition code

A one-dimensional CSS stabilizer family whose adjacent-pair checks constrain an open chain to a two-dimensional, cat-like code space. In the bit-flip convention, Z_i Z_{i+1} checks turn X errors into domain-wall endpoints; global Hadamard conjugation exchanges X and Z to give the phase-flip convention. The protected logical string spans the chain, but its conjugate has a one-qubit representative, so the ordinary Pauli distance is one: this is a controlled memory for one biased Pauli sector, not protection against arbitrary Pauli noise.