U(1)-covariant adjacent-charge encoders have an exact n^{-1/2} optimal flagged-erasure error, and the studied local-Haar brickwork circuits cannot reach it before Omega(n^2) cycles.
The logical product code- words are |ψ0⟩=|B 0⟩,|ψ 1⟩=|B 0 ∪ {s0}⟩.(E1) Under the common random interchange permutation, Bt = Πt(B0), S t = Πt(s0), C t =B t ∪ {St}
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Diffusive Speed Limits for U(1)-Covariant Quantum Error Correction
U(1)-covariant adjacent-charge encoders have an exact n^{-1/2} optimal flagged-erasure error, and the studied local-Haar brickwork circuits cannot reach it before Omega(n^2) cycles.