Syndrome detection rates are locally convex in drifted control parameters after Pauli twirling, giving O(1/ε²) self-calibration that is code-distance-independent for local LDPC codes.
C(δ ⃗θ+νu)−C(δ ⃗θ) ν uj # . Stacking the coordinates proves the claim. Lemma 20(Hessian identity of Gaussian smoothing).For everyδ ⃗θ∈P, we have ∇2Cν(δ⃗θ) =E u
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Provably Efficient Self-Calibrating Quantum Fault Tolerance
Syndrome detection rates are locally convex in drifted control parameters after Pauli twirling, giving O(1/ε²) self-calibration that is code-distance-independent for local LDPC codes.