Hyperfine / clock-state qubit enc_hf

Two hyperfine (or nuclear-spin) ground-state sublevels at a bias field where the first-order Zeeman shift vanishes, leaving only the quadratic term: coherence in seconds to hours, with single-ion memories reaching hour scale [104]. The lineage is the field's own: NIST's first ion-trap logic gate stored a qubit in the internal states of one laser-cooled ion (Monroe, Meekhof, King, Itano, Wineland, PRL 75, 4714, 1995) [374], the default for ions and later atoms ever since.
f = Pauli + leakage — leakage into neighbouring sublevels, invisible to a Pauli decoder; reach: four architectures, QCCD and electronic-gate ions, alkali atoms, and alkaline-earth and alkaline-earth-like atoms (Sr, Yb) [graph].

The clock point kills first-order field sensitivity; what remains is the quadratic Zeeman term plus field gradients across the register, so memory degrades with register size, not only time. The memory is not the limit — the drive is. Raman gates carry a spontaneous-scattering error falling only as ~1/Δ, and the scattered photon usually lands outside the qubit manifold: leakage, not Pauli error. Deleting the laser deletes that term — 2Q 99.97(1)%, 1Q 99.99916(7)% on a ten-qubit seven-zone trap Dfact, 8.4×10⁻⁵ without ground-state cooling D[102]. The control modality moves the floor, not the encoding.

On atoms, Cs hyperfine T2 = 12.6 s in a 6,100-atom array D[138]. Fleet-scale term: two-qubit-gate leakage, ~10⁻⁵ per Clifford on ions against ~10⁻⁴ per atom per gate on arrays.

The PatSnap counts mix patents and papers. Not published: the isotope and transition of the hour-scale Yb⁺ memory, which its abstract calls "a single Yb ion-qubit memory"; a multi-qubit fleet-average equivalent of Oxford's 1.5(4)×10⁻⁷; and a dated supplier of isotopically enriched ¹³⁷Ba or ¹⁷¹Yb, so the enrichment chokepoint is unconfirmed.

No dedicated process; the encoding rides whatever surrounds the species (Ba⁺, Yb⁺, Ca⁺, Cs, Rb, Sr). Two control families, two supply chains: Raman gates need the optical stack — Helios runs seven-plus wavelengths across 1,228 electrodes — while chip microwave traces delete it and move the burden to trap fabrication, internalised by IonQ's SkyWater purchase C[19]; eleQtron sells the same idea as MAGIC C[129]. Enriched ¹³⁷Ba and ¹⁷¹Yb are the plausible chokepoint, but no dated supplier fact was found; no specific ECCN.

Architectures: the primary encoding of all three trapped-ion architectures (QCCD; linear Paul trap with individual laser addressing; electronic qubit control) and of the alkali Rydberg tweezer array, and the alternate on the alkaline-earth tweezer array. Requires nothing — the base encoding, the most reused node in the tree. Its "replaces" edge to omg is an extension: omg keeps these ground states and adds a metastable manifold so one species supplies qubit, ancilla and coolant fact. It adds nothing to the derived clock, set on the QCCD architecture by transport — a 9.66 ms round against the measured ~55 ms full-width layer (≈18 layers/s) and a 70 µs gate. Verification: Oxford's 1.5(4)×10⁻⁷ is one qubit in a dedicated apparatus, Quantinuum's 2.5×10⁻⁵ a 98-ion fleet average — three orders apart; only the fleet number is an architectural input.

Money.
2026-06-03 · Quantinuum · IPO, Nasdaq QNT, after a Sep-2025 round at $10 B pre-money · $1.68 B gross · closed Cfactfact
2026-07-31 · IonQ · SkyWater acquisition closed · ~$1.8 B Cfact

Market & supply chain. Nothing is sold as "hyperfine encoding": the money is in the drive, laser chains against microwave traps. Concentration is low in optics, rising in traps now IonQ owns a fab. Pays G3/G4/G7, the substrate under nearly every logical qubit yet demonstrated.

IP & standards. PatSnap Eureka (2026) ranks IonQ first among named assignees, 9+ records (5 JP, 2 EP, 2 IL pending) on gate pulses and motional modes; the count mixes patents with papers P[375].

Roadmaps & track record. Quantinuum: Sol 2027, Apollo 2029 (promised 2024-09-10); Helios on schedule 2025-11-05, 10×/year quantum volume held. IonQ: 256 qubits at 99.99% slipped to H1 2027, and 4,000 qubits by 2026 (promised 2020) missed ~40×. Quantinuum delivers dates, IonQ physics.

Strategic reading. Universality is the point: everyone uses it, so it is neither moat nor lock-out. The contest is the drive. If all-electronic control scales past ten qubits the laser chain becomes a liability for Quantinuum and every atom vendor; if not, IonQ bought a foundry for a lab result.

Confirm if all-electronic control reaches a fleet average below 10⁻⁵ with published leakage, or a second group replicates 8.4×10⁻⁵; demote if it stays a ten-qubit result. Best case 2029: microwave-driven hyperfine qubits the default. Worst case: gradient-limited leakage caps ions near 10⁻⁵ and omg takes the base.