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Steane transversal

RewriteSteaneTransversalCliffordAdjoints

Bases: RewriteRule


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              bloqade.gemini.logical.rewrite.steane_transversal.RewriteSteaneTransversalCliffordAdjoints[RewriteSteaneTransversalCliffordAdjoints]

              

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Swap adjoints for Steane transversal sqrt-X and sqrt-Z/S gates.

This is specific to the Steane-code logical-operator convention used by the Gemini logical pipeline. Because the logical operators are odd-weight representatives,

\bar X = X_1 X_2 X_3
\bar Y = i \bar X \bar Z = -Y_1 Y_2 Y_3

single-qubit Clifford conjugation signs accumulate across the transversal support. In particular, sqrt(X) Z sqrt(X)^dag = Y on one physical qubit implies

Z_1 Z_2 Z_3 -> Y_1 Y_2 Y_3 = -\bar Y

so transversal physical sqrt(X) implements logical -sqrt(X). Using transversal sqrt(X)^dag instead gives

Z_1 Z_2 Z_3 -> -Y_1 Y_2 Y_3 = \bar Y

which matches the desired logical Pauli action. The same odd-weight sign issue applies to sqrt(Z), represented in Squin IR as S/S^dag.