Willow Threshold Reconstruction — Surface Code Error Rates

p_L ≈ A · (p/p_th)^{⌈(d+1)/2⌉} | A = 0.1, p_th = 0.01 | Google Willow: Λ = 2.14

Logical Error Rate p_L vs Physical Error Rate p (log–log)

d = 3

d = 5

d = 7

Willow data

Controls

2.14

Suppression factor Λ = p_L(d) / p_L(d+2)
Google Willow: Λ = 2.14
p_eff = p_th/Λ = 0.00467

4.67×10⁻³

At p = —:

Willow gap annotation
d=7 formula → —%
Willow measured → 0.143%
Factor below formula: —×

Overhead Calculator — Physical Qubits per Logical Qubit (≈ 2d²)

p_L target

10⁻⁶

p (phys.)

4.67×10⁻³

p_L target	d req.	Phys. qubits	Willow?

Google Willow chip: 105 physical qubits (d=5 surface code, ~50 per logical)

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