Relations

gauge_fixes_to → shor_nine

For the square three-by-three member in this constructor's orientation, promote all horizontal ZZ gauge pairs to stabilizers. Together with the two X center generators, they reproduce the repository's nine-qubit Shor stabilizer row space exactly; the discarded gauge freedom becomes fixed. The neighboring Shor entry uses encoded-basis names that call the Z column logical X and the X row logical Z, so its logical labels are swapped relative to this card's Pauli-type names even though the protected Pauli algebra is the same.

References: shor1995scheme, bacon2006operator

special_case_of → bravyi_bacon_shor

Plain rectangular Bacon–Shor occupies every site of the defining binary matrix. Bravyi–Bacon–Shor permits a general occupancy matrix and derives encoded dimension and distances from its row and column codes, so its rate claims do not transfer to the full rectangle.

References: bravyi2011subsystem, yoder2019optimal

gauge_fixes_to → compass_code_2d pending

Promoting selected gauge generators to commuting stabilizers produces two-dimensional compass-code descendants between the Bacon–Shor and surface-like extremes. The pattern of promoted checks is part of the target code and is not encoded by changing only rows and columns here.

References: li2019compass

product_of → repetition

The protected X and Z parities are perpendicular repetition constraints, with local pair checks liberated into a gauge subsystem. This quotient is the subsystem analogue of Shor's nested repetition construction rather than an HGP replay recipe.

References: shor1995scheme, bacon2006operator