Coherence gain

Coherence gain, written G, is the single-number score of an error-corrected quantum memory: how many times longer the corrected logical qubit preserves quantum information than the best uncorrected element in the same device. Sivak et al. (Yale, Devoret group) named it in their 2022 demonstration of real-time GKP-code error correction (“beating the best of them with a coherence gain of G = 2.27”), while the break-even comparison against a system’s best component goes back to Ofek et al.’s 2016 cat-code experiment. It is a named figure of merit extracted from device-specific lifetime measurements, not a portable benchmark protocol.

How it works

Encode a logical qubit and keep it alive with repeated error correction (measurement-based feedback or autonomous dissipation) while measuring how the stored information decays with wait time (channel or process-fidelity decay, or effective lifetime). Measure the same decay for the best passive alternative in the same hardware and take the ratio: Sivak et al. define G = Γ_01 / Γ_GKP, the decay rate of the oscillator’s Fock {0,1} encoding divided by that of the corrected GKP qubit.

Strengths and limitations

G is holistic (encoding, ancillas, readout, and real-time feedback must all work for G > 1), and it is the cleanest statement that QEC helps rather than hurts. But it is not standardized: papers differ in the decay quantity (fidelity vs T1/T2) and in the baseline (best passive encoding per Sivak et al., best physical qubit per Google, or both per Li et al.), so values are not strictly comparable across papers. It covers idle memory only; beyond-break-even storage implies nothing about error-corrected gates. Distinct from the error-suppression factor Λ, which tracks how the logical error per round falls with code distance.

Notable results

GKP qubit G = 2.27 ± 0.07 (Sivak et al., Nature 2023); binomial code ~16% beyond break-even (Ni et al., Nature 2023); GKP qutrit and ququart gains of 1.82 and 1.87 (Brock et al., Nature 2025); Google’s distance-7 surface code exceeding its best physical qubit’s lifetime by 2.4 ± 0.3 (Nature 2025); trapped-ion autonomous QEC at roughly 13x the physical qubit (11.6 ms vs 0.9 ms; Li et al., 2025).