# Thread: QEC error floor — Google's "once an hour" bursts

**Scout:** Argus subagent (QEC error floor)
**Date:** 2026-09-14
**Question:** What is known about the unexplained ~once-an-hour correlated error events that set a 10^-10 repetition-code error floor in Google Quantum AI, Nature 638, 920–926 (2025)?
**Status:** complete.

**Headline (do not bury):** Cosmic rays / ionizing radiation were **not** ruled out. The 2024/2025 Nature paper distinguished these bursts from the *old* (T1-catastrophic, ~25 ms, once-per-10 s) QP-tunneling events that gap engineering had already killed. In June 2025, Google itself identified the residual floor as **the same ionizing-radiation impacts, acting through a different channel**: quasiparticle-induced *frequency shifts* that cause correlated *phase* errors. Mundane. Not a mystery. Not fundamental physics.

Evidence class for that identification: **Established** (same group, same 72-qubit Willow processor, interleaved QEC + Ramsey experiment). Remaining caveats below.

---

## 1. What the paper itself says

**Paper:** Google Quantum AI and Collaborators, "Quantum error correction below the surface code threshold", *Nature* **638**, 920–926 (2025). doi: [10.1038/s41586-024-08449-y](https://doi.org/10.1038/s41586-024-08449-y). arXiv: [2408.13687](https://arxiv.org/abs/2408.13687) (v1, 24 Aug 2024; journal ref Nature 638, 920–926). Open access. SI is bundled in the arXiv PDF. Author correction (axis-label only): *Nature* doi:[10.1038/s41586-026-10559-8](https://www.nature.com/articles/s41586-026-10559-8) — Fig. 3a x-axis was mislabeled "Surface code distance"; should be "Repetition code distance". No physics change.

### Main-text quotes (Established)

Intro / Main (Nature wording of the requested sentence; arXiv HTML has "whose origins"):

> "To identify possible logical error floors, we also implement high-distance repetition codes on the 72-qubit processor, with error rates that are dominated by correlated error events occurring once an hour. These errors, the origins of which are not yet understood, set a current error floor of 10−10 in the repetition code."

Abstract:

> "To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 × 10^9 cycles."

Conclusions:

> "Our repetition code experiments also identify a noise floor at an error rate of 10−10 caused by correlated bursts of errors. Identifying and mitigating this error mechanism will be integral to running larger quantum algorithms."

### Section IV — "Probing the ultra-low error regime with repetition codes" (Established; all numbers measured unless noted)

Experiment:
- Device: **72-qubit Willow** processor (not the 105-qubit d=7 chip).
- Code: **distance-29 repetition code**, 1000 cycles/shot.
- **2 × 10^7 shots**, split evenly bit-flip (ZZ) and phase-flip (XX).
- Total: **2 × 10^10 cycles**, **5.5 hours** of processor time. (Provenance: measured. Cross-check: 2e10 cycles × 1.1 µs cycle ≈ 6.1 h wall-clock of QEC; they quote 5.5 h.)
- Logical error per cycle inferred as ε_d = ½ (1 − (1−2p_L)^{1/1000}).
- Lower distances **subsampled** from the same d=29 dataset (method of Chen et al. 2021 / Ref. 38).
- Fit d=5 to 11: **Λ = 8.4 ± 0.1**. Breaks the previous **10^{-6}** floor.

Previous floor they compare to (Google 2023, not this paper):
> "In previous work running repetition codes, we found that high-energy impact events occurred approximately once every 10 seconds, causing large correlated error bursts which manifested a logical error floor around 10^{-6}."

That previous work is Acharya et al., *Nature* **614**, 676 (2023), doi:[10.1038/s41586-022-05434-1](https://doi.org/10.1038/s41586-022-05434-1) / arXiv:2207.06431: d=25 repetition code, floor **1.7 × 10^{-6} per cycle** set by a single high-energy event (1.6 × 10^{-7} excluding it).

Mitigation of *that* floor:
> "We attribute the mitigation of high-energy impact failures to gap-engineered Josephson junctions" [McEwen et al., PRL **133**, 240601 (2024); arXiv:2402.15644].

New floor:
> "However, at code distances d ≥ 15, we observe a deviation from exponential error suppression at high distances culminating in an apparent logical error floor of 10^{-10}. Although we do not observe any errors at distance-29, this is likely due to randomly decoding correctly on the few most damaging error bursts."

Two high-distance failure modes:

1. **Mild:** one or two detectors jump by >3×, recover in tens–hundreds of cycles. Speculative causes given by authors: transient TLS near a qubit frequency, or coupler excitations. Mitigable in principle (they cite TLS/coupler papers). **Serious speculation** (authors' hypothesis; not tested here).

2. **Catastrophic (the floor):** many detectors spike together.
   - **Spatial extent:** "anisotropic error bursts are spatially localized to neighborhoods of roughly **30 qubits**" (Fig. 3d inset). Not chip-wide.
   - **Count:** **six** large bursts in 2 × 10^{10} cycles. These cause the highest-distance failures.
   - **Rate:** "approximately **once an hour**, rather than once every few seconds"
   - **Decay:** exponential time constant "**around 400 µs**, rather than tens of milliseconds." Fig. 3d example: **369 ± 6 µs**.
   - Explicit contrast to prior high-energy impacts: "These bursts … are different from previously observed high-energy impact events."
   - **Cause (as of this paper):** "We do not yet understand the cause of these events."

### SI §V.1 "Low Probability Events in the Repetition Code" (Established)

> "These events account for **all the distance-27 logical errors** we observe, and **half of the distance-21 to distance-25 errors**. The measure qubits corresponding to the firing detectors are grouped **spatially, not necessarily in sequence with the snaking repetition code order**. The bursts occur roughly once per hour, or once every **3 × 10^6 shots**, in both bit- and phase-flip codes. The decay timescale from fitting the detection fractions to a decaying exponential is around **400–700 µs**. This is in stark contrast to the detection fraction bursts caused by quasiparticles observed in previous work, which happened once every **10 seconds** with a recovery time of **25–30 ms**."

Second independent limiter (not the 30-qubit burst):
> "The other type of limiting event presents as a **single noisy detector**, whose likelihood of firing rapidly increases and stays high for **1–2 ms**. This event causes a high-distance (d > 19) error also about **once per hour** of data acquisition. The detector which is noisy varies from event to event."

Fig. S7: burst vs single-noisy-detector, spatial maps on the qubit grid. Burst detections clustered in a spatial neighborhood; single-noisy-detector is one site.

**What they ruled out in 2024/25 (this paper only):** they ruled out *identity with the old T1-QP-tunneling cosmic-ray signature* (rate, recovery time, spatial extent). They did **not** run a muon-veto, underground, or lead-shield test on these new bursts. They did **not** claim radiation was excluded.

**Numbers, provenance:**
| quantity | value | provenance |
|---|---|---|
| floor ε | ~10^{-10} / cycle | measured (apparent; d≥15 deviation) |
| large bursts | 6 in 5.5 h | measured |
| large-burst rate | ~1 / hour ≈ 1 / 3×10^9 cycles ≈ 1 / 3×10^6 shots | measured |
| spatial size | ~30 qubits, anisotropic, localized | measured (Fig. 3d inset) |
| decay τ | 369±6 µs (ex.); 400–700 µs (SI fits) | measured |
| d=29 errors | zero observed | measured; attributed to lucky decoding |
| old floor | 10^{-6} / cycle, ~1 / 10 s, τ~25–30 ms | inherited from 2023 paper |
| cycle time | 1.1 µs | measured (surface-code section) |

---

## 2. Have cosmic rays / ionizing radiation been ruled out?

**No. The opposite happened.** (Established)

### Old signature (ruled out *as the remaining floor*, not as a physical process)

Google already knew the cosmic-ray / ionizing-radiation T1-burst signature:

- **McEwen et al.**, "Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits", *Nat. Phys.* **18**, 107–111 (2022), arXiv:[2104.05219](https://arxiv.org/abs/2104.05219). Sycamore: 10 mm × 10 mm qubit chip on 20×24 mm carrier. **λ = 1/(10 s)** Poisson events. Initially localized hotspot, then chip-wide. Largest events: chip-wide T1 **< 1 µs**. Exponential tail **~25 ms**. Mechanism: particle → phonons → Cooper-pair breaking → QP tunneling across JJs → T1 collapse. **415 events** in 100 × 60 s datasets.
  - Expected rates they quote for a 20×26 mm carrier: **gamma ~1/(7.6 s)**, **cosmic (muons) ~1/(38 s)**. Combined order-of-magnitude match to 1/10 s. (Measured vs estimated.)
- **Vepsäläinen et al.**, "Impact of ionizing radiation on superconducting qubit coherence", *Nature* **584**, 551 (2020), arXiv:[2001.09190](https://arxiv.org/abs/2001.09190). Environmental radioactivity + cosmic rays elevate steady-state QP density; lead shielding correlates with longer T1; would ultimately limit transmons to **millisecond** T1 if unmitigated. Continuous QP generation, not a QEC burst-floor paper.
- **McEwen, Miao et al.**, "Resisting high-energy impact events through gap engineering in superconducting qubit arrays", *Phys. Rev. Lett.* **133**, 240601 (2024), arXiv:[2402.15644](https://arxiv.org/abs/2402.15644). Strong gap engineering (δΔ/h ≈ 12 GHz ≫ f_q) **eliminates correlated T1 bursts**. Weakly gap-engineered qubits on the same chip still show them. Event flux **2.6 s^{-1} cm^{-2}**, matching prior large-device flux **2.1 s^{-1} cm^{-2}**. 154 events / 6000 s ≈ **1 / 40 s** on that 12-qubit test chip.

Sea-level vertical muon flux is canonically **~1 cm^{-2} min^{-1} ≈ 0.017 s^{-1} cm^{-2}**. McEwen's **~2 s^{-1} cm^{-2}** event flux is **~100× the muon flux**, so the **once-per-10 s (old) events are mostly environmental gammas**, with muons a minority — which is what McEwen's 1/7.6 s (γ) vs 1/38 s (μ) split says. (Established / estimated.)

**Willow 2024/25 comparison table (why they said "not yet understood"):**

| | Old HE impacts (2021–23) | New floor bursts (Willow 2024) |
|---|---|---|
| Rate | ~1 / 10 s | ~1 / hour |
| Recovery | 25–30 ms | 400–700 µs |
| Spatial | chip-wide (after ~ms) | ~30-qubit neighborhood, anisotropic |
| Error type (then known) | T1 / QP tunneling | unknown in 2024 |
| Gap engineering | kills this channel | residual remains |

Rate mismatch with raw muon/gamma flux is **expected** once gap engineering removes the T1 channel: most impacts no longer produce a high-distance *logical* error. The 1/hour rate is a **size cut** (only the largest remaining bursts fail d≳21), not a new particle species.

### What Google published 10 months later (the explanation)

**Kurilovich, Roberts, Martin, McEwen, … Opremcak**, "Correlated Error Bursts in a Gap-Engineered Superconducting Qubit Array", arXiv:[2506.18228](https://arxiv.org/abs/2506.18228) (v1, 23 Jun 2025). Google Quantum AI, **same 72-qubit Willow processor**. Search also lists a PRX version (title variant "Correlated Phase Error Bursts…", DOI-like 10.1103/1bl4-b2f7); treat journal status as **unchecked** — arXiv v1 is the citable object.

They name the Willow paper as Ref. [20] and answer it in the first pages:

> "Indeed, recent work [20] has shown that the LER floor of a repetition code in a gap-engineered qubit array remains set by error bursts. These 'residual' bursts are less frequent than before, now occurring on **hour rather than second** timescales, and have a shorter recovery time (**~1 ms vs. ~25 ms**). What mechanism causes them, and why does it persist with gap engineering? The QEC data of Ref. [20] offers little insight into these questions."

**Mechanism (Established):** ionizing-radiation impacts still dump energy into the substrate → phonons → elevated QP density. Gap engineering **blocks QP tunneling**, so T1 no longer collapses for milliseconds. QPs remaining in the JJ region **shift qubit frequencies negative** (up to **3 MHz**, lasting **~1 ms**), producing **correlated phase errors**. A 1 MHz shift over a 1 µs QEC cycle is ~2π of spurious phase. Brief residual T1 burst still exists at the start, **~10 µs** (two orders of magnitude shorter than ungapped devices).

Direct QEC correlation (Established):
- Interleaved **repetition code on one patch + Ramsey/T1 monitors on an adjacent patch**.
- **8 hours**, **105 bursts**.
- Repetition-code detection bursts **align in time and duration with Ramsey (phase) bursts, not with T1 bursts**.
- Spatiotemporal correlation exceeds 3σ both ways.

Rates (measured):
- Coherence sampling: **101 bursts in 2 hours → 1/(71 s)**. Footnote: "**only the largest of these bursts will give rise to errors in a high distance repetition code. This is why logical errors in Ref. [20] have a smaller rate.**"
- Tomography: **265 bursts in 5.2 h**, same 1/71 s; "**smaller than the burst rate on comparable-size devices without gap engineering by a factor of ≈10**."

They thank Joe Fowler (NIST) for cosmic-ray modeling of **event rate vs minimum energy-deposition threshold** — i.e. they treat the rate as an energy-thresholded radiation spectrum, not a new mystery.

**Mitigation they demonstrated (not a new published floor):** extra echo / retimed dynamical decoupling in the repetition-code circuit **reduces sensitivity to frequency shifts**. After that, remaining QEC detections track the short **T1** transient, not the 1 ms Ramsey tail. They recommend **QP traps** (to cut frequency shifts) and **phonon traps** (to localize bursts). They note DD that works for repetition codes **may not transfer** to surface codes.

**Bottom line on radiation:** the "origins not yet understood" sentence was true in Aug 2024. It is **not** true after Jun 2025. The once-an-hour *logical* floor is the **high-energy tail of the same ionizing-radiation process**, visible only because gap engineering removed the much more frequent T1 disasters. Expected muon flux at the site is **consistent** with a minority of all impacts and with a still-smaller subset of *logical-killing* impacts. A 1/hour logical-error rate is **not** in conflict with ~1 muon cm^{-2} min^{-1}.

**Not tested / still open (honest):**
- No underground vs surface comparison published specifically for the Willow 10^{-10} floor.
- No tagged muon-veto coincidence on the Willow d=29 dataset.
- The **single-noisy-detector, 1–2 ms, 1/hour** events are a **separate** floor contributor; authors' 2024 guess is TLS/coupler, **not** radiation. Kurilovich 2025 does not claim to explain those.

---

## 3. Follow-ups 2025–2026

**Google, same problem, explained:** Kurilovich et al. arXiv:2506.18228, above. This is the paper. (Established)

**Google, prior mitigation of the old floor:** McEwen/Miao PRL 133, 240601 (2024) / arXiv:2402.15644. (Established)

**Has the 10^{-10} floor moved?** **No published high-distance repetition-code result beating 10^{-10} found.** Kurilovich shows a *circuit* that should suppress the phase-error contribution; they do not quote a new ε_d floor from a 5-hour d=29 run. Surface-code papers after Willow were not found to re-measure this ultra-low floor (surface codes at d=5–7 sit at ~10^{-3}/cycle, far above it). (Null result, this scout.)

**Other groups, radiation in superconducting arrays (not Google's floor, but same physics):**
- Harrington et al., "Synchronous detection of cosmic rays and correlated errors in superconducting qubit arrays", *Nat. Commun.* (2025), doi:[10.1038/s41467-025-61385-x](https://www.nature.com/articles/s41467-025-61385-x). Coincidence with cosmic-ray detectors; rates match GEANT4 × lab muon flux. Suggests gap engineering may remove need for deep underground. (Established, MIT Lincoln Lab / AWS-adjacent authorship in related work.)
- Li et al., "Cosmic-ray-induced correlated errors in superconducting qubit array", *Nat. Commun.* **16**, 4677 (2025). Ta-film devices: QP bursts relax faster than Google Sycamore; they cite that as why IBM Falcon R6 showed little radiation impact (Thorbeck et al.). (Established / serious speculation on the IBM comparison.)

**IBM, Quantinuum, PsiQuantum, AWS — comparable unexplained 10^{-10} hour-scale QEC floor?** **Not found.** IBM superconducting devices have reported weaker radiation impact (different films / QP recombination). Trapped-ion (Quantinuum) and photonic (PsiQuantum) architectures do not have this phonon/QP substrate channel. No 2025–2026 paper from those groups was found quoting an analogous "once an hour, origins unknown, 10^{-10} repetition-code floor." (Null result of this search, not a proof of absence.)

**Candidate list, status:**
| candidate | tested? | verdict |
|---|---|---|
| Cosmic rays / muons / γ (T1, QP tunneling) | yes, 2021–24 | **old floor; killed by gap engineering** |
| Same radiation, QP frequency shifts / phase errors | yes, Jun 2025 | **explains the residual ~1/h large bursts** |
| Gamma background vs muons | modeled, not vetoed on Willow d=29 | gammas dominate count rate; muons rarer, more energetic |
| QP poisoning bursts (generic) | yes | that's the mechanism; two channels |
| TLS fluctuators | hypothesized for *single-noisy-detector* events | untested |
| Leakage | DQLR used; not the 30-qubit burst | not the floor |
| Crosstalk / stray CZ | in error budget (17%); not rare 1/h | no |
| Control-electronics glitches | not specifically excluded | **unlikely** given spatial phonon-like maps and QP recombination kinetics in 2025 paper |
| Phonon bursts in substrate | yes, that's the energy-transport step | engineering target (phonon traps) |

---

## 4. Irreducible error floors / correlated-noise threshold theorems

**No serious claim that this 10^{-10} floor is irreducible or fundamental.** Google treats it as an engineering problem (gap engineering, then QP/phonon traps, then DD). (Established as Google's stance; **your own inference** that it is not a law-of-nature floor, but a strong one: they already moved the floor 4 orders of magnitude once.)

**What "error floor" means in this literature:** a distance-independent leftover set by rare events that hit too many qubits at once for the code distance to help. Standard independent-noise threshold scaling ε ∝ (p/p_th)^{(d+1)/2} **assumes** errors are not space-time-correlated across O(d) qubits. A burst that lights up ~30 qubits in a patch can produce a logical error at arbitrarily large d if it covers a logical operator. That is a **practical** floor, not a theorem forbidding FTQC. (Serious speculation → established as the operational meaning in Google 2023/2025 and Kurilovich 2025.)

**Aharonov, Kitaev, Preskill**, "Fault-tolerant quantum computation with long-range correlated noise", *Phys. Rev. Lett.* **96**, 050504 (2006), arXiv:[quant-ph/0510231](https://arxiv.org/abs/quant-ph/0510231).

What it actually proves (Established): threshold theorem **survives** non-Markovian noise with **always-on pairwise** system-bath couplings, provided for each qubit i, Σ_j ||H_ij|| t_0 is below a constant, equivalently spatial decay **faster than 1/r^D** in D dimensions (||H_ij|| < δ/|i−j|^z with z > D). It is **not** a theorem about rare, high-weight, spatially clumped bursts (cosmic-ray phonon events). Those are a different correlation structure: almost-zero most of the time, then a patch-wide correlated error. AKP does **not** say "radiation bursts break FTQC"; it also does **not** save you from them. What breaks the usual threshold argument is **high-weight, simultaneous, spatially extended errors** whose probability does not factor into local ε^{t+1}. (Your own inference, but standard.)

Related: Novais/Baranger/others on long-range 1/f; "Rare Events and Griffiths Phases in Topological Quantum Error Correction", arXiv:[2409.03325](https://arxiv.org/abs/2409.03325) — rare events that temporarily elevate error rates over a whole patch (they explicitly mention cosmic rays) produce Griffiths-like slowdowns, not necessarily a hard floor if the elevated-p interval is short compared to code distance in time. Willow bursts last ~400 µs ≈ 400 cycles, vs d=29, so they *can* still kill a repetition code. (Serious speculation / theory.)

**General "irreducible QEC floor" claim:** not found as a community consensus. The closest hardware claim is Martinis-style: without mitigation, radiation **single-handedly prevents** algorithmically relevant LER in superconducting devices (McEwen 2024 PRL intro). That is a statement about **unmitigated superconducting hardware**, not about QEC as a theory.

---

## 5. Non-mundane physics (collapse models, gravitational decoherence)

**Nobody in the collapse-model community has commented on these specific Google QEC bursts.** (Null result; checked Bassi + superconducting + burst/floor/cosmic-ray queries.)

Closest: **Vischi, Ferialdi, Trombettoni, Bassi**, "Fundamental limits of superconducting quantum computers" / "Possible limits on superconducting quantum computers from spontaneous wave-function collapse models", arXiv:[2201.05114](https://arxiv.org/abs/2201.05114), *Phys. Rev. B* **106**, 174506 (2022). CSL:
- **Direct** collapse of computational-basis superpositions: **negligibly small**.
- **Indirect:** CSL dissipation generates extra quasiparticles, raising steady-state x_qp and limiting T1. They argue this could matter for large algorithms if other noise is removed, and propose tests.
- This is a **continuous, chip-wide QP generation** effect, not a 1/hour spatially localized 400 µs burst. It does **not** explain Willow's error floor, and they do not cite it. (Established as what the paper says; connecting it to the bursts would be **your own inference, and a bad one**.)

No gravitational-decoherence paper was found tying Penrose/Diósi rates to Google's 1/hour bursts. Do not invent one.

---

## Verdict

The mundane explanation is **almost certainly right**, and as of June 2025 it is **Google's own explanation**:

1. 2021–23: ionizing radiation (mostly γ, some μ) → chip-wide QP tunneling → T1 bursts every ~10 s → repetition-code floor ~10^{-6}.
2. 2024 gap engineering: that T1 channel is gone. Floor drops **four orders of magnitude**.
3. Residual 10^{-10} floor at d≥15 = **the largest remaining radiation impacts**, now as **QP-induced frequency shifts / correlated phase errors**, ~6 events in 5.5 h, ~30 qubits, τ ~ 0.4–1 ms. Plus a separate ~1/hour single-detector (likely TLS) channel.
4. Not a simulation glitch, not collapse models, not an irreducible QEC theorem. Engineering next steps already named: QP traps, phonon traps, better DD; possibly shielding / underground for the high-energy tail.

**Most valuable sentence, as requested:** This was explained in 2025 by Kurilovich, Roberts, McEwen, Opremcak et al. (arXiv:2506.18228), as ionizing-radiation-induced quasiparticle frequency shifts that survive gap engineering.

---

## Sources (primary)

- https://arxiv.org/abs/2408.13687 — Willow QEC paper + SI
- https://www.nature.com/articles/s41586-024-08449-y
- https://arxiv.org/html/2408.13687v1 — HTML of main+SI (used for SI §V.1)
- https://arxiv.org/abs/2506.18228 — 2025 explanation
- https://arxiv.org/html/2506.18228
- https://arxiv.org/abs/2402.15644 — gap engineering PRL
- https://arxiv.org/abs/2104.05219 — McEwen 2021/22 cosmic-ray bursts
- https://arxiv.org/abs/2001.09190 — Vepsäläinen 2020
- https://arxiv.org/abs/quant-ph/0510231 — Aharonov–Kitaev–Preskill 2006
- https://arxiv.org/abs/2201.05114 — Bassi group CSL / transmons
- https://www.nature.com/articles/s41586-022-05434-1 — 2023 10^{-6} floor
- https://www.nature.com/articles/s41467-025-61385-x — Harrington 2025 coincidence
- https://www.nature.com/articles/s41586-026-10559-8 — 2026 author correction (labels only)