Mølmer–Sørensen / light-shift laser gate g_ms

Two laser tones detuned symmetrically about a motional sideband drive a spin-dependent force; the pair traces a closed loop in the phase space of a shared vibrational mode and acquires a geometric phase set by the enclosed area, so the spins entangle and the motion returns to its start. The phase depends on loop area, not mode occupation, so a hot bus is tolerated — why this, not Cirac–Zoller, became the production mechanism. Mølmer and Sørensen proposed it in 1999–2000; the light-shift (σzσz geometric-phase) variant, a state-dependent optical dipole force, shares the error budget and dates the deployed line to about 2003.
Attributes: natural trapped-ion carrier; deterministic entangling at ≈63 µs (10^−4.2 s) over a shared motional bus.
Optical control from room temperature; error coherent, leakage, Pauli; manufacturing is optical assembly.

Gate duration follows the detuning δ from the addressed sideband — one closed loop takes 2π/δ — and δ cannot be opened freely, because the beat note must stay clear of every spectator mode. In an N-ion chain the axial spectrum crowds, δ shrinks and the pulse lengthens: 1.6 µs on a pair D[441] against a 672 µs median on one 30-ion chain D[100], roughly 400× for 15× the ions. Two floors remain. Off-resonant Raman scattering is incoherent, no pulse shape cancels it, and it falls only as the Raman detuning is pushed past the fine-structure splitting. Laser noise and motional heating supply the rest: a 2026 perturbative model weights noise spectral density by a position-dependent sensitivity function and finds distant pairs ~10× more sensitive at ~25 kHz than neighbours, while ~1 kHz noise costs percent-level infidelity independently of position S[442]. The residue is coherent and leakage-like, not depolarising, so averaged benchmarks understate what a code sees.

Best demonstrated: 99.8% at 1.6 µs on a ⁴³Ca⁺ pair, entanglement still generated at 480 ns — under one motional oscillation period (Oxford, 2018) D[441], still the fastest published laser gate. At scale, Helios logs 7.9×10⁻⁴ error in ≈70 µs across 98 Ba⁺ in eight zones D[97]; IonQ's single 30-ion chain, benchmarked over all 435 pairs, gives 550–883 µs, median 672 µs D[100].

Nothing here is fabricated into the trap: the gate is delivered by stabilised lasers, acousto- and electro-optic modulators and beam optics, covered as its own node. Helios needs at least seven wavelengths against 1,228 trap electrodes D[97] — the optical half is the larger bill of materials. Traps by contrast are merchant goods (Infineon, Villach); Honeywell makes Quantinuum's in-house C[320]. Export exposure is at system level — the 2024-09-06 BIS rule created ECCN 4A906 for quantum computers above qubit-count and error-rate thresholds, but no ECCN names ion traps or beam optics G[301].

The two global tones do not scale with ion count; individual addressing does, at ~one modulator channel and beam path per ion. The pulse is the cheap part of the cycle: a full-width Helios layer runs ≈55 ms once sorting, transport and re-cooling are counted — three orders above the 70 µs gate — transport alone was ~60% of runtime on H2 D[97]. At 10³ ions, power and crosstalk trade addressing quality against zone count; at 10⁴–10⁶, gate time growing with chain length makes any single-bus design trade throughput for connectivity, which is why every roadmap subdivides the trap.

Entangling mechanism of two trapped-ion architectures — QCCD (Quantinuum) and the linear Paul trap with individual laser addressing (IonQ's Aria, Forte and Tempo, Alpine Quantum Technologies, Qudoor, Quantum Art) — and the historical one for lines migrating to laser-free, microwave-driven electronic control (IonQ with Oxford Ionics, eleQtron). It requires a trapped-ion carrier and a laser subsystem delivering phase-stable bichromatic beams to a chosen pair, and provides the entangling layer zoned architectures assume. Its substitute is the near-field electronic gate at 8.4×10⁻⁵ D[102]; switching writes off the optics stack but deletes photon scattering and laser noise. It conflicts with any single-bus design. Derived clock on the QCCD architecture = sum of the syndrome round: gate layers + transport + readout + reset ≈ 9.7 ms, transport 9.0 ms of it, against a measured ~55 ms full-width layer D[97]. No neighbouring empty slot is flagged.

Headline numbers are benchmarking averages over a zone or chain; no vendor publishes pair-resolved error against chain position, and the ~10× neighbour-versus-distant gap remains theory S[442]. Quantum-volume claims need the same care: AQT's 32,768 is 2¹⁵ against 2²⁵ published for Quantinuum's 56-qubit H2 C[98] — a record inside the rack-mounted class, not at the frontier. Neither 7.9×10⁻⁴ nor 8.4×10⁻⁵ has an independent replication as of 2026-09-04.

Randomised benchmarking over a native gate set built from two Mølmer–Sørensen gates, MS(π/2, 0) and MS(π/2, π/4) (a 192-element group), is not multiplicity-free: three irreducible representations occur two or three times and give matrix-valued rather than single-exponential decays, so a fidelity robust to state-preparation and measurement (SPAM) errors needs benchmarking against a larger 'lifting' group, here SU(4) P[895]. The demonstration is numerical; a native-gate benchmarking figure for MS gates should be read with its protocol named.

The 480 ns entangling result in [441] carries no fidelity in its abstract; only the 1.6 µs / 99.8% pair is a complete figure of merit. Not published: the gate time and fidelity of AQT's LYNX behind quantum volume 32,768, so its noise-desensitisation claim has no physical number to be checked against.

Money.

• 2023-12-05 · Alpine Quantum Technologies · sale to Leibniz Supercomputing Centre · ≈EUR 9.8 M, 20 qubits · closed C[323]
• 2025-09-04 · Quantinuum · equity · USD 600 M at USD 10 B pre-money · NVentures, Quanta, QED · closed C[122]
• 2025-09-17 · IonQ · M&A, Oxford Ionics · USD 1.075 B · closed C[18]
• 2026-06-03 · Quantinuum · IPO · USD 1.68 B gross, Nasdaq QNT · closed C[123]

Market & supply chain. Optics are integrated in-house at Quantinuum and IonQ, so no outside vendor holds pricing power; the ion stack's one merchant chokepoint is trap fabrication, which this gate does not use. Q-CTRL sells pulse-optimisation tooling C[443]. Unit economics: EUR 9.8 M for a turnkey 20-qubit rack ≈ EUR 0.5 M per qubit C[323], the only publicly quotable trapped-ion price as of 2026-09-04. Q2-2026 revenue: USD 8.0 M at Quantinuum, USD 80.1 M at IonQ C[123], [326]. G2 and G3 pay for it; the ≈55 ms layer routes G4 elsewhere.

IP & standards. PatSnap's 2026 landscape lists 9+ IonQ families filed across JP/EP/IL in 2025–2026, including "universal gate pulse for two-qubit gates" (JP, 2025), and two pending Quantum Art filings (IL, KR) on ion-array reconfiguration P[375] — not cross-checked elsewhere. No standards body covers this gate.

Roadmaps & track record. Quantinuum (promised 2024-09-10 · Helios 2025, Sol 2027, Apollo 2029 · Helios on schedule 2025-11-05) R[118] — the only met dated promise here. IonQ (promised 2025-06-13 · 256 qubits at 99.99% in 2026 · slipped to H1 2027); its 2020 roadmap missed 4,000 qubits by 2026 by ~40× R[132] — dates are directional. AQT (promised 2026-05-05 · LYNX units Q4 2026 · unscored) C[128].

Strategic reading. If laser gates hold, the vertically integrated optics teams win and no one buys an ion computer as components. If electronic gates win, IonQ with Oxford Ionics takes the cost curve and AQT and Quantum Art lose their optical differentiation. Exposure is asymmetric: Quantinuum, listed since June 2026, is the largest laser-gate incumbent, with Sol and Apollo still laser-driven — a laser-free gate at product scale is its biggest technical risk.

Falsifiable in 12–24 months: confirm/demote that Sol ships in 2027 with laser gates; that a vendor publishes pair-resolved error against chain position; that AQT discloses LYNX gate time and fidelity at the Q4-2026 rollout. Best case by 2029: pulse engineering and zone subdivision hold laser gates at ≈10⁻⁴ with transport still the clock. Worst case: electronic gates reach product scale first and this becomes legacy. Open: does the AQT variant generalise beyond quantum-volume circuits; can scattering-limited error go below 10⁻⁴ at usable power; which binds first at 10⁴ ions, power or transport.