Rydberg-blockade CZ g_ryd

Two atoms ~2 µm apart in tweezers are driven on the qubit-to-Rydberg transition by one beam covering both. Because a doubly-excited pair repels through a van der Waals shift V=C₆/R⁶ far larger than the drive, double excitation is pushed out of resonance and the pair acquires a phase set by how many atoms started in the coupled state — a controlled-phase gate. Jaksch, Cirac, Zoller, Rolston, Côté and Lukin proposed it in 2000 D[427]; blockade between two atoms was seen in 2009 (~58% fidelity) P[140], with the first gates and a CNOT in 2010. Levine et al. replaced the three-pulse addressed sequence with a two-pulse global time-optimal CZ in 2019 (97.4%) D[428] — the form every leading group still runs, and why the gate needs no per-qubit control line.

Attributes (technology graph). a — carrier affinity: fully natural; the gate adds no fabricated structure to the qubit. b — characteristic time: 10^-6.6 s ≈ 250 ns, deterministic rather than heralded. c — readout: not set here; inherited from the atom and imaging nodes. d — mobility: connectivity by physically transporting atoms between gate zones, not fixed couplers. e — control @ placement: optical, generated entirely at room temperature. f — error structure as the code sees it: atom loss, leakage out of the qubit space, coherent over/under-rotation. g — manufacturing: optics, not lithography.

Three scales set everything. The drive Ω (Harvard: peak 2π×17 MHz, two-photon 420 + 1015 nm at 7.8 GHz intermediate detuning, Rb 53S_1/2) fixes the gate at 270 ns D[134]D[4]; the blockade shift must satisfy V≫ℏΩ, residual double excitation costing roughly (Ω/V)². The Rydberg lifetime (tens of µs at n≈53, blackbody-limited) costs the Rydberg dwell time divided by it. Raising Ω cuts decay and raises leakage, so the optimum is shallow: a 2026 review adds spontaneous Rydberg emission (0.05–0.1%), laser phase noise (0.1–0.2%) and thermal motion (~0.1%) and concludes the standard blockade CZ has a "physical limit of 99.9%" absent new mechanisms such as Förster-resonance gates P[140].

The measured budget agrees in shape but not in villain. In the April 2026 Harvard result the largest single term is atom loss, 0.087(5)% per gate, about 60% of the total error, with leakage to other hyperfine levels 0.008(1)% per atom per gate; the authors assign the remainder to ground-Rydberg coherence (T₂^), intermediate-state scattering and unwanted coupling to a nearby Rydberg level, and project 99.9–99.95% from better T₂^, suppression of that coupling and more laser power D[134]. That makes the gate structurally interesting: its dominant failure is detectable — the atom is gone from the image — so it converts to an erasure, not an unlocated Pauli. Loss-post-selection lifts the same data from 99.854(4)% to 99.941(3)% D[134], and in the 448-atom architecture >80% of leakage events are atom loss, used as "supercheck" information in decoding D[4]fact.

What moves the floor: single-photon UV excitation, with no intermediate state to scatter from — the Yb and Sr route D[135]D[136]; spectrally clean lasers against servo-bump phase noise at Ω; ground-state cooling against Doppler and position spread; and new gate physics (Förster resonance, modulated off-resonant driving, circular Rydberg states) P[140]. None is demonstrated above 99.9% raw as of 3 Sep 2026.

Best-versus-typical is the story: the record comes from ~8 sparsely spaced gate sites at 20–30 Hz D[134], the shipped figure is 99.2% global on 260 qubits C[137], the largest array under fault-tolerant control is 448 atoms D[4], and arrays of 6,100 and 11,000 atoms exist without gates at these fidelities D[138]D[145].

There is no wafer; the manufacturing surface is the laser and beam-steering chain. Alkali two-photon excitation needs a fibre-amplified 1013–1015 nm source of tens of watts plus a frequency-doubled 420 nm beam; Yb/Sr need a single ~300–320 nm UV source; all need phase noise suppressed near the Rabi frequency, plus acousto-optic deflectors and spatial light modulators for placement. Yield and uniformity become intensity and phase homogeneity across the array; Harvard's 10-hour run drifted mainly through Rydberg laser power and pointing D[134]. The vendor pool for narrow-linewidth high-power lasers, UV sources, AODs and SLMs is small — TOPTICA, M Squared, Coherent, AA Opto-Electronic, Gooch & Housego, Hamamatsu, Meadowlark are the usual names — but no dated procurement disclosure ties a machine to a supplier (see Open verification items). Export control runs through the US BIS quantum controls of September 2024 (ECCN 3A901 and related) and Category 6 laser entries; which applies to a 10 W 1013 nm amplifier is unsettled in any public ruling found.

The gate is global: one beam pair entangles every blockaded pair at once, so per-qubit control lines scale as O(1), not O(N). The cost is optical power — holding 2π×17 MHz over N atoms scales power linearly in N — and beam steering: an acousto-optic deflector resolves as many spots as its rf bandwidth times the acoustic transit across the beam, a transit that also bounds how fast it re-points, while liquid-crystal modulators reframe at tens of hertz. At 10³ nothing breaks; at 10⁴ power and steering bind; at 10⁶ multi-core optical interconnects are required and undemonstrated. The gate's own control latency is sub-µs, but it sits inside a round dominated by ~0.8 ms of transport between gate layers and ~0.5 ms imaging, giving measured QEC rounds of ~1–4.5 ms D[4]S[31]; the compensating theory is transversal gates with correlated decoding, keeping syndrome rounds constant per logical gate S[152].

The gate serves both Rydberg tweezer-array architectures — alkali (Rb/Cs: Harvard/MIT, QuEra, Pasqal, Infleqtion, Google) and alkaline-earth(-like) (Yb/Sr: Atom Computing/Microsoft, Princeton, Caltech). It requires an atom in a tweezer plus the laser and deflector chain, and provides the entangling channel every atom-based code consumes; it has no in-platform replacement at comparable fidelity, so the switching price is the platform itself. A natural, unfabricated carrier gets a sub-microsecond deterministic entangler where trapped ions pay 10–100 µs — hence the platform's clock problem lives in imaging and transport, not the gate. Derived clock = sum of the syndrome round (gates 1×10⁻⁶ s, transport 8×10⁻⁴ s, 1Q 1×10⁻⁵ s, readout 5×10⁻⁴ s) ≈ 1.3 ms on both tweezer-array architectures, of which the gate is 0.08%. Neighbouring empty slots: sub-100 µs non-destructive array readout, and a blockade gate whose dominant error is not atom loss.

The 2026 record uses echo randomised benchmarking and symmetric stabiliser benchmarking on ~8 sparse gate sites D[134]; Atom Computing used Clifford and symmetric-subspace RB with >200 CZ gates per circuit D[135]; Caltech built a fidelity-response theory and quotes 0.9971(5) downward-corrected for leakage D[136]. What these miss: loss-post-selection removes 60% of the error, so 99.941% is not a circuit-level number and must not be set against a raw superconducting figure; sparse-site benchmarking misses dense-array crosstalk and next-nearest-neighbour blockade error; and none measures the gate inside a transport-and-image cycle, where re-trapping and heating act. Conflict: the August 2026 review tabulates a 2025 USTC CZ of 99.84% P[140] that no primary source corroborates, so this brief uses Harvard's 99.854(4)% D[134]. Note also three conventions behind three headline numbers — Atom Computing's 99.72/99.40 is post-selected/raw D[135], Caltech's is leakage-corrected D[136], Harvard's is raw plus post-selected D[134].

The 270 ns gate duration is the value in [4]; the April 2026 record paper gives a peak Rabi frequency of 2π×17 MHz but no extractable gate duration, so the two are treated as one scheme. Not published: the laser, AOD or SLM supplier of any specific neutral-atom machine in a dated procurement disclosure — the vendor names under Manufacturing are the field's usual pool; an export-control ruling on high-power 1013 nm Rydberg-laser subsystems (US BIS quantum ECCNs against Category 6 laser entries); and QuEra Gemini's availability date, deployment site and price.

Money.

• 2025-07-17 · QuNorth · order (Magne, from Atom Computing/Microsoft) · €80 M · EIFO + Novo Nordisk Foundation · ordered Cfact
• 2025-09-09 · QuEra · financing round · $230 M+ · Google, SoftBank Vision Fund 2, NVentures · closed Cfact
• 2025-11-06 · Atom Computing, QuEra · DARPA QBI Stage B · up to $15 M each · DARPA · selected fact
• 2026-02-17 · Infleqtion · IPO (NYSE: INFQ) · >$550 M gross · SPAC · closed Cfact
• 2026-03-24 · Google · neutral-atom hardware programme · amount undisclosed · internal · announced Cfact
• 2026-05-21 · Atom Computing, Infleqtion · CHIPS letters of intent · $100 M each, of $2.013 B to nine companies · US Dept of Commerce · LOI, non-binding fact
• 2026-06-16 · Atom Computing · Series C plus LOI · $100 M equity, >$300 M cumulative · Third Point · closed + LOI Cfact
• 2026-08-28 · Pasqal · SPAC completion (Nasdaq: PSQL) · ~$360 M cash; 2025 revenue €16.5 M · closed Pfact

Market & supply chain. What is sold is systems, not gates: Magne prices 1,225 physical / 50 logical qubits at €80 M, roughly €65 k per physical qubit Cfact; Gemini packages 260 physical qubits at 1 shot/second C[137]. The enabling-equipment pool — high-power 1013 nm amplifiers, UV sources, AODs, SLMs — is narrow enough that one vendor's lead time can gate a machine build, though it is shared with atomic clocks and cold-atom sensing. G1 (analogue simulation) and G5 (optimisation) pay for atom arrays today; the gate fidelity discussed here is bought almost entirely for G3 (early fault tolerance) and, through Magne and Libra, G4. G6 (networking) has no demonstrated atom-to-atom photonic link at this scale.

IP & standards. No dated patent-family count from a named database was found for Rydberg-gate IP, so none is asserted. Open stacks: QuEra's Bloqade, Pasqal's Pulser, Infleqtion's Superstaq, with AWS Braket the named delivery channel for QuEra's 2028 system Cfact; no gate-level standard or consortium specific to Rydberg CZ exists as of 3 Sep 2026.

Roadmaps & track record. QuEra (promised 2024-01 · 100 logical qubits in 2026 · not delivered; superseded 2026-06 by Libra, >256 logical in 2028 — a two-year slip) Cfact. Atom Computing/Microsoft (promised 2025-07 · Magne, 50 logical, turn of 2026/27 · being installed as of 3 Sep 2026) Cfact. Pasqal (promised 2024-03 · 10,000 physical in 2026 · slipped to 2028; 100 logical 2029) Cfact. Infleqtion (promised 2025 · 30 logical in 2026 · unverified as of 3 Sep 2026) C[150]. Judgment: Harvard/MIT's device claims have survived replication and are the most credible; Atom Computing has a customer, a price and a delivery date, the strongest commercial commitment here; QuEra and Pasqal have each slipped a headline number by two years, so their 2028–29 dates read as intentions.

Strategic reading. If raw fidelity crosses 99.9% while loss stays erasure-convertible, neutral atoms reach fault tolerance without a wiring problem: platform vendors and laser suppliers win, and the superconducting camp's argument that only cryogenic integration scales loses. If it stalls at 99.85%, the millisecond cycle leaves atoms as the analogue-simulation and optimisation platform while ions and superconductors take fault tolerance. There is no substitution threat within the platform — every neutral-atom company runs this gate — making the ceiling a sector risk, not a company risk, and giving these laser suppliers more bargaining power than their revenue suggests.

Confirm/demote milestones for 12–24 months: (1) a raw CZ ≥99.9% in a dense array by 2027-09 confirms the review's ceiling was engineering, not physics; failure demotes the gate to saturated; (2) Magne accepted at QuNorth with 50 logical qubits by mid-2027; (3) a >50-round below-threshold memory run with continuous reloading showing Λ>2 — the Atom/Microsoft 90-round toric-code run lost its suppression once reloading was included D[148]; (4) a CZ fidelity measured inside a transport-and-image QEC cycle. Best case by 2029: 99.95% raw, loss converted to erasures, Libra-class 256-logical machines on a cloud channel. Worst case: 99.85% raw persists, the millisecond cycle stays, atoms hold G1/G5 and cede G3/G4.

Open questions. Does the loss channel scale with array density and transport, or is 0.087% per gate a floor set by trap depth? Can single-photon UV excitation recover the phase-noise and scattering terms without new UV-induced loss? Is Förster-resonance or modulated-driving physics real above 99.9%? Does erasure conversion survive at circuit level, where a decoder must locate losses inside a 1 ms budget? Watch for a raw record without post-selection, and whether Google's atom track publishes a gate before 2027.