Analogue Rydberg Hamiltonian evolution g_rydanalog

The array evolves under one Hamiltonian, H/ℏ = Σᵢ (Ω(t)/2) σˣᵢ − Σᵢ [Δ(t) + hᵢ Δ_loc(t)] nᵢ + Σ_{i<j} C₆ r_ij⁻⁶ nᵢ nⱼ: global waveforms, one static site pattern h_i, couplings fixed by atom positions C[262]C[429]. Technology g_ryd uses the same blockade for a two-atom CZ inside a circuit; here it acts on all pairs for the whole run, and the output is a bit-string sample. Technology g_anneal, the rf-SQUID flux annealer, sets couplings with programmable on-chip couplers D[430]; here geometry is the coupling matrix, and blockade confines the dynamics to independent sets of a unit-disk graph, the basis of MIS encoding D[431]. Lineage: 51 atoms in 1D, Harvard/MIT, 2017 D[384]; Pasqal's 2020 architecture naming analogue "Hamiltonian sequences" beside circuits D[385]; Aquila on Amazon Braket C[262].
Attributes: natural carrier; no step time (one evolution, ≤4 µs on Aquila); readout inherited; no mobility during the program; optical control at room temperature; coherent and loss errors; optics manufacturing.

Aquila: Ω ≤ 15.8 rad/µs, |Δ| ≤ 125 rad/µs, C₆ = 5,420,503 µm⁶ rad/µs (70S), spacing ≥4 µm, program ≤4 µs, T2* 5.8 µs, driven T2 7.5 µs C[262]: a blockade radius (C₆/Ω)^1/6 ≈ 8.4 µm at full drive, and a program of ~half the driven T2, ~10 Rabi periods S. Named error terms: laser amplitude and phase noise; thermal motion (Doppler, 0.200 µm position spread); scattering via the intermediate state, which continues with the drive off; detuning inhomogeneity, 0.37 rad/µs RMS across the field and 0.18 rad/µs shot-to-shot C[262]. Via r⁻⁶ the position spread gives ~30% shot-to-shot spread of a 5.5 µm bond (δV/V = 6δr/r) S — harmless deep in blockade, decisive where V ≈ Ω, which selects the ordered phase. Local detuning is a fixed pattern with a waveform ≤0, and programs using it decohere faster than the listed T2 C[429]. Errors integrate coherently over a run with no point to measure a syndrome, so no code acts S; erasure detection on Sr raised a Bell-pair fidelity bound from ≥0.9971 to ≥0.9985 by discarding flagged shots D[143] — post-selection, not correction.

Interaction time, not atom number, caps analog Rydberg programs at a few microseconds. Two laser-trapped circular Rydberg atoms (long-lived states of maximal angular momentum) at Laboratoire Kastler Brossel, Paris, sustained spin exchange for more than 60 µs and 40 oscillation periods, with a decay time of 59 µs, about ten times the previous record; the oscillation contrast is post-selected (79% against 33% raw) P[899].

Above ~100 atoms nothing is checked exactly: the 196-atom work matched numerics only to ~100 D[433]. The 2022 speed-up did not survive: classical solvers reach optimality on the same Union-Jack-like instances to thousands of nodes within minutes D[431]. Pasqal offers a 100-qubit analogue QPU on Google Cloud (2025-05-13) C[437]; no Fresnel datasheet like Aquila's was found as of 2026-09-26.

No wafer; optical assembly shared with the digital atom architectures. Orion Gamma: 140 qubits, room temperature, 3 kW average, 5 µm minimum spacing C[438]. The analogue-specific addition is a site-resolved detuning field whose hardware QuEra has not described C[439]; nothing else in the sources separates the analogue bill of materials from the digital one S.

Control is independent of N: a few waveforms, one pattern and a geometry C[262]. The cost moves to readout and repetition. Aquila misreads 8% of Rydberg and 1% of ground atoms and leaves 0.7% of sites empty C[262], so a 256-site snapshot, half excited, reads error-free with probability 0.92¹²⁸×0.99¹²⁸ ≈ 6×10⁻⁶, and ~17% of shots have a defect-free register S. Shots run below 10 Hz on Aquila C[262] and at ≥0.25 Hz effective on Orion Gamma C[438]: 10⁴ shots take ≥17 min to ~11 h S.

Slot 3 of the "Neutral-atom analogue simulator (Rydberg arrays, lattice gases)" architecture (alkali atom → ground–Rydberg analogue qubit → this technology → AOD transport → laser + AOD/SLM control → fluorescence imaging; layers 7–9 empty; optical assembly), serving G1. It requires the alkali atom, the ground–Rydberg encoding and global Rydberg lasers; it provides nothing upward; it replaces nothing and is replaced by g_ryd when a machine turns digital. Register: Aquila (QuEra, 256 sites) and Fresnel/Fresnel 2 (Pasqal, 100 qubits) carry it as primary, both ✅; Pasqal's Orion line carries it as alternate on the "Rydberg tweezer array — alkali (Rb/Cs)" architecture, 🔎. The gap ledger proposed the alkali and alkaline-earth(-like) array architectures; the technology got its own architecture, and no alkaline-earth(-like) register machine runs it, though the fidelity benchmark above used Sr D[436] — the requires-alkali edge is narrower than the physics.

With no gate error, fidelity comes from observables: order parameters against numerics, valid to ~100 atoms D[433]; F_d, which weights measured bit-strings by simulated probabilities — 0.095(11) at 60 atoms, where a lightcone MPS at χ* = 3400 (~110 GB, ~180 core-days) keeps pace D[436]; and problem output such as MIS size, cheap to validate but not to prove optimal D[431]. F_d needs classical probabilities, so what it certifies can be simulated. Λ is undefined. The Orion cell stays 🔎: its cited page (2026-01-29) mentions local detuning for materials simulation and a 2026 Vela with over 256 qubits, but not analogue mode, MIS, Orion or ≤100 qubits C[390].

Aquila's continued Braket service is inferred from QuEra's 2026-06-15 release, which does not state it. Not published: the hardware mechanism of Aquila's local detuning (light-shift beam or otherwise), whose magnitude, resolution and per-site calibration error appear only as Braket SDK device properties; a Rydberg lifetime or atom-loss rate during evolution for Aquila; and a Fresnel datasheet (Ω, Δ, T2, detection errors).

Money.

• 2025-09-09 · QuEra · Series B extended, NVentures joins · USD 230 M · announced; aimed at fault tolerance C[153]
• 2026-08-28 · Pasqal · SPAC merger, Nasdaq PSQL · ~USD 360 M cash · closed P[156]

Market & supply chain. Two vendors, two cloud channels. Pasqal reports seven QPUs deployed and markets its platform as analogue today P[156]; QuEra's analogue offer is one machine. It pays into G1 only.

IP & standards. No analogue-specific patent count as of 2026-09-26; the program format is cloud-defined (Braket AHS) C[429]; no standards body.

Roadmaps & track record. Pasqal promised 10,000 physical qubits for 2026 (2024-03-13) R[167]; its 2026 launch is Vela, over 256 qubits R[390] — ~39× short S — and its brochure says delivery 2027, 200+ C[438]. QuEra's Libra (2028) is digital, with no analogue specification R[162].

Strategic reading. Analogue is both vendors' revenue bridge while g_ryd matures. With certified advantage above ~100 atoms it stays a G1 instrument; without, it becomes a mode of digital machines, as on Orion.

Confirm if, by 2027-12-31, a commercial analogue machine publishes a many-body fidelity at ≥60 atoms, or an analogue result survives a year of classical challenge; demote if Vela and QuEra's next systems ship without analogue specifications. Open questions. (1) Can F_d certify beyond the size where MPS keeps pace? (2) What are per-site local-detuning calibration errors? (3) How does driven-T2 loss split between phase noise, Doppler and scattering? (4) Can erasure excision post-select many-body runs at tolerable shot cost? (5) Will the requires-alkali edge survive alkaline-earth(-like) analogue machines?

A benchmark that needs no per-atom addressing has been proposed for it: prepare U†AU with a global y-rotation A and probe with a collective z-rotation; the quantum Fisher information (how sharply the output responds to the probe angle) grows with the number of atoms for Haar-random-like dynamics and is exactly zero for Clifford circuits, so circuit randomness can be graded without computing ideal output probabilities, provided the evolution can also be run backwards (U†) P[892]. It is a theory proposal, not yet run on an analog array.