Does logical error suppression continue exponentially to large code distance? · revision history

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Revision 1: Does logical error suppression continue exponentially to large code distance
Revision 2: Does logical error suppression continue exponentially to large code distance?
Plain
Recent chips showed that enlarging an error-correcting code cuts the error rate by a constant factor at each step. It is unknown whether this continues to the much larger codes that useful computations need, or whether rare correlated events set a floor.
Precise
For surface-code memories on superconducting hardware, the logical error per cycle is modeled as $\epsilon_L(d) \sim A \Lambda^{-(d+1)/2}$ with code distance $d$; Google Quantum AI (Nature 638, 920, 2025, arXiv:2408.13687) reported $\Lambda$ of about 2.1 up to $d = 7$. Determine whether this law holds to $d \ge 15 \text{ and } \epsilon_L \le 10^{-10}$ per cycle, or whether correlated, leakage or drift events produce a floor; the answer is the measured $\epsilon_L(d)$ curve or a validated model of its floor.
Settled by
Surface-code memory experiments at $d \ge 15$ with logical error rates measured down to $10^{-10}$ per cycle, or an identified error mechanism that provably caps suppression.
Kind
well-posed
Answer type
yes-no
References
(empty)
Literature status
open
Status note
In the same 2025 work, repetition codes up to $d = 29$ reached a logical-error floor near $10^{-10}\ \text{per cycle}$ (approximate), set by rare correlated events occurring about once per hour.
Posed since
(empty)

Decisions