Surface Code Error Threshold — Fault-Tolerant Quantum Computing

Logical error rate p_L vs physical error rate p. Threshold p_th ≈ 1%: larger codes better below, worse above.

Physical Error p 0.8%

Max distance d 15

Threshold: p_th ≈ 1.0%

Below threshold:

p_L ≈ A·(p/p_th)^⌈(d+1)/2⌉

Above threshold:

p_L grows with d — quantum advantage lost

Physical qubits:

~2d² per logical qubit

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