Threshold theorem: p < p_th ⇒ concatenated encoding drives logical error to 0 exponentially

Layer 1 — Physicsin the quantum-error-correction subtree

Aharonov-Ben-Or / Kitaev / Knill / Zurek / Preskill 1997 threshold theorem. For a code correcting t errors, the logical error rate at concatenation level ℓ scales as p_L(ℓ) ≤ (p/p_th)^(2^ℓ) — double-exponentially suppressed in ℓ. Exists…

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