Ground–Rydberg analogue qubit enc_gr

The qubit is a level pair inside one atom: |g⟩ in the 5S₁/₂ ground manifold and |r⟩ = |70S₁/₂⟩ in QuEra's ⁸⁷Rb machine Aquila, reached by a two-photon 420 nm + 1013 nm drive via 6P₃/₂ C[262]. "Encoding" names the computational basis of an analogue machine, not a code: the program is a Hamiltonian, the output a g/r pattern. The line starts with the 51-atom Harvard–MIT Ising-type simulator of 2017 D[384], co-authored by QuEra's CEO Alexander Keesling C[262]; Pasqal's architecture paper calls it the analogue level, "programming Hamiltonian sequences" C[385]. Attributes: natural carrier, nothing fabricated; no step time, control modality or placement of its own; loss and coherent errors.

Aquila runs H(t) = (Ω/2)Σᵢ(e^{iφ}|gᵢ⟩⟨rᵢ| + h.c.) − ΔΣᵢnᵢ + Σ_{i<j} C6/|xᵢ−xⱼ|⁶ nᵢnⱼ, nᵢ = |rᵢ⟩⟨rᵢ|, with C6 = 5.42×10⁶ rad µm⁶ µs⁻¹ for 70S, |Ω| ≤ 15.8 rad/µs, |Δ| ≤ 125 rad/µs C[262]; Pulser uses the same convention for Pasqal's "ground-rydberg" basis C[386]. Blockade forbids two excitations within R_b = (C6/Ω)^{1/6} ≈ 8.4 µm at full drive S[262].

Three limits act on |r⟩. Decay: Rb 70S lives 410 µs at 0 K but 152 µs at 300 K (60S: 104 µs) S[387], black-body radiation carrying ~63% of the rate — the ceiling, and a loss channel. Doppler: for counter-propagating beams (k_eff ≈ 8.8 µm⁻¹) at 10 µK, a detuning spread σ ≈ 0.27 rad/µs gives a Ramsey 1/e time ≈ 5 µs S[262], matching the measured T2* = 4.5(1) µs D[388]. Phase noise and scattering: echo leaves T2 = 32(6) µs; T1 = 51(6) µs combines the 146 µs Rydberg lifetime with ~80 µs of 6P3/2 scattering D[388]. The 12.6(1) s hyperfine T2 of a Cs tweezer array D[138] does not apply: |r⟩ cannot be shelved, so there is no memory.

The window has barely moved: T2* rose from 4.5 to 5.8 µs, and Aquila stops programs at 4 µs, the "approximate timescale of coherent evolution" C[262].

Nothing is fabricated at this layer; fabrication sits in fab_optics. The demand is spectral: a Rydberg laser pair beside 780 nm tweezers C[262] whose phase noise, not power, sets coherence; the 2018 gain came from reference-cavity filtering (FWHM ≈ 2π × 500 kHz) and injection locking D[388]. A cold enclosure would move 70S from 152 µs toward 410 µs S[387]; the register profiles the commercial machines as room-temperature.

Aquila drives one global Ω(t), Δ(t), φ(t) set C[262], so drive I/O is flat in atom number; local detuning, the first site-resolved knob, drove the string-breaking quench D[226] and is promised for Pasqal's Vela R[390]. Readout is destructive imaging with an asymmetric budget — Rydberg read as ground 0.08, ground as Rydberg 0.01, filling error 0.007 C[262] — so r-populations are undercounted S[262]. At under 10 shots per second C[262], 10⁴ shots take over a quarter-hour.

On the architecture "Neutral-atom analogue simulator (Rydberg arrays, lattice gases)" (atom_analog) the technology fills slot 2; slots 7–9 (code to interconnect) are empty. It requires an atom with a Rydberg level (alkali), provides the ground–Rydberg states g_rydanalog requires, and is replaced by enc_hf. Register machines: Aquila (primary, ✅), Fresnel / Fresnel 2 (primary, 🔎), Orion Alpha/Beta/Gamma (alternate, analogue mode on atom_rb, 🔎 inferred). Gate-model lines use enc_hf: QuEra's Gemini is a 260-qubit digital machine C[137]; the Harvard–MIT gate work encodes in |F=1,mF=0⟩, |F=2,mF=0⟩ and visits 53S1/2 only during gates D[391]; Pasqal drives a separate "digital" basis |g⟩,|h⟩ by Raman channel C[386]. The gap ledger stands: enc_hf does not describe analogue machines. Its atom_rb/atom_ae placement became atom_analog; the alkaline-earth variant D[143] has no register machine.

Gate benchmarks do not apply; the figures are T2*, echo T2, Rabi damping, blockaded-pair coherence and readout asymmetry. Aquila publishes all of them (Rabi 7.5 µs, blockaded Rabi 8.9 µs) C[262], none independently re-measured; beyond classical simulation, programs are checked against phase diagrams D[226]. Grades: Aquila ✅; Fresnel 🔎, the paper's abstract confirming only the analogue/digital split C[385]; Orion 🔎, its cited blog naming neither analogue mode nor encoding C[390] — Pulser's basis definition is better evidence.

Gemini's product page names ⁸⁷Rb and a digital mode, not the hyperfine pair; its placement under hyperfine encoding rests on the Harvard–MIT gate papers. The string-breaking abstract does not name Aquila; only QuEra's authorship points to it. Not published: the Rydberg level, T2* and echo time of Pasqal's Fresnel and Orion, on Pasqal's pages; and, in the Aquila text, the beam geometry assumed in the Doppler estimate and the F, mF sublevel of |g⟩ in analogue mode.

Money. No dated financial item is specific to the ground–Rydberg encoding as of 2026-09-26.

Market & supply chain. Two commercial actors, both also selling gate-model machines; Pasqal lists five hosting clouds and five sites, mode unstated C[390]. Concentration sits in Rydberg lasers and cavities. Pays into G1.

IP & standards. No standard for analogue-qubit figures was found as of 2026-09-26; the shared Hamiltonian convention is the de facto interface C[262]C[386].

Roadmaps & track record. Pasqal (2026-01-29): Vela in 2026, over 256 qubits with local detuning; measurable quantum advantage before mid-2026 R[390] — not scored here. QuEra's next product is gate-model C[137].

Strategic reading. Scale without per-qubit control, code or storage, bounded by a few-microsecond window. If analogue results survive classical challenge, it keeps a G1 niche as a mode of digital machines; if not, both vendors already sell the hyperfine alternative.

Confirm if by 2027-12-31 a commercial analogue machine publishes T2 above 20 µs; demote if Vela ships without coherence figures or no peer-reviewed analogue-advantage result appears by 2027-06-30. Open questions. (1) Why is Aquila's echo time a third of the 2018 value? (2) How does T2 scale with register size? (3) Will erasure-detecting alkaline-earth g–r qubits reach a product? (4) Which Rydberg level and coherence do Fresnel and Orion run? (5) Does the readout asymmetry bias published phase diagrams?