Correlated / loss-aware decoding (transversal, atom loss) dec_corr

Not hardware, a decoding discipline. Loss-aware decoding consumes the herald: a missing atom is an erasure at a known site, so stabilisers touching the vacancy multiply into higher-weight supercheck operators that still commute with the surviving code [4]. Correlated decoding solves the joint syndrome history across transversal (block-to-block) layers rather than block-by-block; Cain et al. (Harvard, 2024-03-05) showed the rounds between Clifford gates drop O(d)→O(1) [738], generalised as algorithmic fault tolerance (Nature 2025) [152].
f = loss + erasure; a/c/d/e/g = none — classical compute, no fab or placement [graph].

The herald is the asset: >80% of Rydberg-array leakage is atom loss, and imaging finds it [4]. A located erasure costs the decoder only the Pauli frame, not the position — why erasure conversion lifts circuit-level thresholds 3–4× at fixed gate physics [8]. The price is distance: each supercheck is a product of two stabilisers, so every vacancy locally thins the code. Correlated decoding pays differently: transversal CNOTs propagate errors between blocks, so the graph grows with circuit depth, not d. Nothing moves the floor — the unheralded residual is untouched, m_F leakage 0.008(1)% per atom per gate against atom loss 0.087(5)% fact.

Same circuit: 2.14(13)×, d=3→5, four rounds. Dominant term: atom loss, not Pauli error.

Not published: the closing date and price of BTQ's full acquisition of QPerfect, whose option was exercised between 2025-04 and 2026-07, and a dated patent family for loss-aware or correlated decoding.

No fab: classical compute already bought for matching. Latency sets scope: 144 µs/round fits a 1–4.5 ms atom cycle with 7–30× margin [739] but is ~130× over a 1.1 µs superconducting cycle — why this stays atom-specific. Loss-flag bandwidth is one bit per site per round, so the wall at 10³–10⁴ atoms is the ~0.5–1 ms imaging and a decode window scaling with logical depth, not the link. Inherited single points of failure: Hamamatsu qCMOS imaging fact and two AOD vendors fact.

The primary decoder on both Rydberg tweezer arrays, alkali (Rb/Cs) and alkaline-earth(-like) (Yb/Sr). Requires high-rate concatenated codes with transversal gates; provides the decoding half of algorithmic fault tolerance, whose constant-round claim is otherwise unbacked on hardware. Derived clock = sum of the syndrome round (gates 1 µs, transport 800 µs, 1Q 10 µs, readout 501 µs) ≈ 1.3 ms, ~0.76 kHz; the decoder must return inside it, not set it. Verification: 1.73× is a decoder-vs-decoder ratio on one lab's data, unreplicated; 4% is simulation [739]. Four rounds test neither drift nor reloading; Atom Computing's toric code is the control, suppression vanishing with reloading (0.63% vs 0.64% per cycle) [148]. Princeton's 1.9(4)×/3.6(1)× discrepancy is resolved: one paper, two quantities fact.

Money.
2025-04-09 · BTQ Technologies · €2 M into QPerfect at €10 M pre-money (16.67%) · term sheet P[741]
2026-07-22 · QPerfect · aQCess twin, Equipex+ ANR-21-ESRE-0032 · announced C[740]
2026-06-16 · Atom Computing · $100 M Series C (Third Point) + $100 M CHIPS LOI · closed + LOI C[154]fact
2025-11-06 · DARPA QBI Stage B · Atom Computing, QuEra among eleven · ≤$15 M each fact

Market & supply chain. No component market: GPU/FPGA cycles already bought for matching; concentration risk sits upstream, in imaging and AODs. Pays G3/G4 only.

IP & standards. No dated patent family names loss-aware or correlated decoding as of 4 Sep 2026; methods open, code academic.

Roadmaps & track record. O(d)→O(1) rounds (2024-03): in Nature 2025, shown only in a four-round circuit. QuEra 100 logical (2024-01, for 2026): now Libra 2028 fact. Physics on time, products late.

Strategic reading. If it holds, atoms turn their worst liability into a cheap accounted channel and transversal architectures beat lattice surgery on spacetime cost: QuEra, Atom Computing, Pasqal and Infleqtion gain, superconducting vendors lose decoder latency as a differentiator. Substitution threat: a Rydberg CZ past 99.95% shrinks the loss term. Non-rival: no supplier can rent it.

Confirm if the QPerfect decoder runs on real syndromes or a second vendor publishes its own loss-aware gain; demote if the gain dies under reloading or past four rounds. Best case 2029: default across neutral-atom FT stacks; worst case, one group's architecture, never past 10³ atoms. Open: does 1.73× hold at 10⁴ atoms, at depths where the correlated graph outgrows memory, and on ions [667]?