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To compute the representation matrix, we have: bTx(1) =x, bTx(x) =x 2 = 1 +x+ (1 +x+x 2)≡1 +x, bTy(1) =y=x+ (x+y)≡x, bTy(x) =xy=x 2 +x(x+y) = 1 +x+ (1 +x+x 2) +x(x+y)≡1 +x

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Decoupling 2D translation-invariant topological CSS codes

quant-ph · 2026-08-10 · accept · novelty 7.0

Every 2D translation-invariant topological CSS code is local-unitarily equivalent, at the maximal anyon-preserving translation symmetry, to stacks of toric codes and product states, with an explicit polynomial-time construction.

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  • Decoupling 2D translation-invariant topological CSS codes quant-ph · 2026-08-10 · accept · none · ref 8

    Every 2D translation-invariant topological CSS code is local-unitarily equivalent, at the maximal anyon-preserving translation symmetry, to stacks of toric codes and product states, with an explicit polynomial-time construction.