Metastable ('omg') erasure encoding enc_omg

An omg encoding places the computational basis inside a long-lived metastable manifold, chosen so the dominant decay takes the atom or ion out of the qubit subspace into a state a cycling transition lights up. The error is then not a Pauli flip on an unknown qubit but a heralded, located loss — an erasure.

The name is the ion-side blueprint: optical–metastable–ground, three manifolds in one species so one ion serves as qubit, ancilla and coolant (Allcock, Campbell, Chiaverini, Chuang, Hudson, Wineland and colleagues, 2021) D[333]. Wu, Kolkowitz, Puri and Thompson made it quantitative for neutral atoms: 98% of ¹⁷¹Yb errors convertible, threshold rising from 0.937% under Pauli noise to 4.15% under erasure noise S[8]. Kang, Campbell and Brown carried it to ions S[392]. First hardware: Princeton, 2023 D[141].

Attributes (technology graph): a carrier affinity 0.0, natural carriers. b no characteristic time, no entangling mechanism of its own. c no readout of its own; it delegates to the mid-circuit erasure check it enables. d no mobility. e no control modality or placement. f error structure as the code sees it: erasure. g no manufacturing. Shared by both host families: neutral atoms and trapped ions.

The mechanism is a hierarchy of lifetimes. In ¹⁷¹Yb the qubit is the nuclear spin of the 6s6p ³P₀ clock state; in ⁴⁰Ca⁺ two Zeeman sublevels of D₅/₂. Both live long against circuit duration and decay to the ground manifold, which scatters photons on a strong transition while the metastable one does not. A short fluorescence check therefore reports which site left the code space without touching those that stayed — Princeton measured the induced error on survivors below 10⁻⁵ D[141].

The floor is set by errors that stay inside the manifold — Raman scattering back into the qubit subspace, magnetic dephasing across small Zeeman splittings, off-resonant coupling between the computational sublevels — all un-heralded Pauli noise. Oregon measured the split: ~94% of spontaneous Raman scattering and nearly all decay events detected, but only half the total error budget converted D[393]; Princeton's [[4,2,2]] run converted 38(6)% D[142]. Erasure buys more per unit rate — at 1% erasure the surface code tolerates 0.51% Pauli error, 5.2× the standard protocol S[334]fact — but the gain scales with conversion fraction, so the residual is a floor only better gate physics removes.

Best demonstrated as of 3 Sep 2026: a two-qubit gate at 99.16% after erasure subtraction on ⁴⁰Ca⁺ D[393], and a [[4,2,2]] block whose decay slows 1.9(4)× with erasure information D[142]. Typical at scale: nothing — every shipped machine uses ground-manifold qubits.

The dominant term is the unconverted residual: half the ≈1.4% raw ⁴⁰Ca⁺ gate error survives the check D[393], as does 62(6)% of a 1.6(1)% CZ error on ¹⁷¹Yb D[142] — far worse than 99.854% raw on Harvard's Rb array D[4] or 7.9×10⁻⁴ on Helios D[97].

No fabrication step: the manufacturing attribute is "none" and the encoding rides whatever trap the host uses. What it changes is optics — a shelving/clock laser (578 nm for ¹⁷¹Yb, 674 nm for Ca⁺, 1762 nm for Ba⁺), repumps out of the manifold, and in Oregon's case a Raman pair at 976 nm detuned −43 THz, bought with power D[393]. Suppliers are the field's usual set: Toptica, M Squared, Menlo Systems and NKT Photonics for sources; Stable Laser Systems for ultra-low-expansion cavities; Hamamatsu and Andor for check cameras. Single points of failure: the ULE cavity and the clock laser, both sub-ten-vendor markets. Export-control exposure runs through the lasers, not the encoding — Wassenaar Category 6 controls and the US BIS quantum rule of 2024-09-06 apply whichever manifold carries the qubit.

Per-qubit line count is unchanged — the encoding's main commercial attraction. What grows is wavelength count and calibration: extra state preparation, a shelving fidelity, and a check whose false-positive rate feeds the decoder. The check's cost against the clock is the decisive number, and it is favourable on both hosts. Atom arrays already pay 0.5–1 ms imaging inside a 1–4.5 ms round D[4]S[31], so a check that is the imaging is nearly free; ion machines run ~55 ms per layer D[97], making a few-hundred-µs fluorescence check ~1% of it. Yale and AWS showed erasure qubits win only when check time is short against the cycle S[395]fact — here it is. The wall at 10³–10⁶ qubits is decoder bandwidth, not I/O: erasure flags roughly double the syndrome payload.

Three architectures carry it: Rydberg tweezer array — alkaline-earth(-like) (Yb/Sr), erasure-native as the primary encoding (Atom Computing with Microsoft, Princeton, Caltech), and two trapped-ion architectures as an alternate — linear Paul trap with individual laser addressing (IonQ, AQT, Quantum Art) and electronic qubit control (laser-free, microwave-driven gates) (IonQ with Oxford Ionics, eleQtron). It requires an alkaline-earth(-like) atom or a trapped ion with an accessible metastable manifold; it provides the detectable-decay structure a mid-circuit erasure check consumes; it replaces ground-manifold hyperfine encoding. Switching costs a re-calibrated preparation and readout chain plus one or two lasers. Derived clock = sum of the syndrome round: gate layers + transport + readout + reset: 1.5×10⁻³ s on the electronic-gate ion architecture (gate-set), where the encoding adds ≈1%, and 1.3×10⁻³ s on the alkaline-earth tweezer array (transport-set), where it adds nothing. A rare Layer-2 node with no clock penalty, so conversion fraction, not speed, is what to watch. Empty neighbouring slots: no erasure-native encoding for fabricated carriers, and no sub-100-µs erasure check for ions D[394].

Headline numbers come from Bell-state and randomised-benchmarking estimators with post-selection: shots where the check fired are discarded, so the "erasure-subtracted" fidelity is conditional — legitimate for a channel, illegitimate as a system figure of merit. Princeton's [[4,2,2]] result is the honest form: 1.9(4)× is logical, with erasure information actually used D[142]. Not captured: the check's false-positive and false-negative rates, which can halve effective distance S[395], and correlated leakage.

Conflicts. (i) The graph record records the [[4,2,2]] improvement as 3.6×; arXiv:2506.13724 v1 and v2 both state 1.9(4)×, which we use, treating 3.6× as superseded fact. (ii) Oregon's Bell fidelities read 98.56%/99.14% in the arXiv HTML and 98.61%/99.16% in Physical Review A, detuning −43 vs −44 THz; journal values used D[393]. (iii) The 98% conversion figure S[8] is an upper bound on an idealised error inventory, not a missed target.

Not published: the duration and fidelity of Oregon's quantum-logic non-destructive metastable readout [394].

Money. No financing event is earmarked for metastable encoding; this money buys the host platforms.

• 2025-09-17 · IonQ · M&A, Oxford Ionics · $1.075 B · announced 2025-06-09 · closed fact
• 2025-11-04 · US DOE · five National QIS Research Centers renewed · $625 M / five years · closed fact
• 2025-11-06 · DARPA · QBI Stage B, 11 teams incl. Atom Computing, QuEra, IonQ · ≤$15 M each · selected fact
• 2026-02-17 · Infleqtion · IPO, NYSE (INFQ) · >$550 M gross · closed fact
• 2026-04-27 · Quantum Art · Series A extension · $140 M · closed P[125]
• 2026-05-21 · US Dept of Commerce · CHIPS LOIs, Atom Computing $100 M, Infleqtion $100 M · $2.013 B total · non-binding fact
• 2026-06-16 · Atom Computing · Series C plus DoC LOI · >$300 M cumulative · Third Point · closed + LOI C[154]fact
• 2026-06 · Quantinuum · IPO, Nasdaq (QNT) · $1.68 B · after $600 M at $10 B pre-money · closed G[123]
• 2026-07 · IonQ · M&A, SkyWater Technology · $1.8 B · closed G[19]
• 2026-08-28 · Pasqal · SPAC completion · ~$360 M cash · €16.5 M 2025 revenue · closed P[156]

Market & supply chain. No one sells an omg product; the enabling lasers, cavities and cameras are already a dependency of every host platform, so adoption adds one or two laser channels against systems like Magne (€80 M, 50 logical) fact. Only G3 and G4 (early and large-scale fault tolerance) pay for it; G1 benefits marginally via erasure excision in simulators D[143]. G2 and G5–G7 do not.

IP & standards. No patent family specific to metastable erasure encoding was found in a named database as of 3 Sep 2026; nearest granted art is Amazon Technologies US 11,748,652 B1 on heralded amplitude-damping decay (2023-09-05) fact. No litigation, no standards body; Stim models the encoding in software C[397].

Roadmaps & track record. (2021 · omg blueprint · partly delivered — Oregon entanglement 2024 D[393], mid-circuit cooling 2026 D[394]; no product.) (2022-01 · 98% conversion · missed by 2.6×, 38(6)% measured D[142].) (2028 · QuEra Libra >256 logical · on roadmap, no metastable commitment fact.) (2026/27 · Magne 50 logical · installing, ground-manifold Yb fact.) The vendors made no omg promises to break.

Strategic reading. Winners would be alkaline-earth(-like) atom vendors and ion vendors still using laser gates; losers, decoder stacks tuned for Pauli noise. Substitution bites from both sides: atom loss is >80% of array leakage and Harvard detected it on ground-manifold Rb for 2.14(13)× below threshold D[4], while laser-free ion gates at 8.4×10⁻⁵ delete the error omg catches D[102].

Confirm if a gate reports >70% of total error converted with residual below 3×10⁻³, or a vendor announces a metastable product line. Demote if no conversion fraction above 50% is published by end-2027, or a laser-free ion gate below 10⁻⁴ ships at scale. Best case by 2029: an alkaline-earth array runs a distance-5 code with erasure-aware decoding and reports Λ above the loss-only baseline. Worst case: atom loss remains the only erasure anyone needs and this stays a two-laboratory programme.

Open questions. (1) Why is measured conversion 38–50% when the model says 98% — gate, check, or error inventory? (2) Does erasure information still help once false negatives are folded in at distance ≥5? (3) Is the residual Pauli error set by sublevel choice or by the gate laser? (4) Can a metastable ancilla be read non-destructively inside a 1 ms atom cycle? Watch the next Princeton follow-up, whether Atom Computing exposes the metastable manifold, and whether Quantinuum's unpublished "novel code family" is erasure-structured.