Tunable-coupler CZ / iSWAP g_tc

A flux-tunable coupler is a third element — usually a tunable transmon — bridging two data qubits. Its frequency sets an indirect coupling path that interferes with the direct capacitive one, so a bias sweep tunes net exchange through zero: at the off point static ZZ cancels; a pulse away from it drives a deterministic CZ or iSWAP via the |11⟩–|20⟩ crossing. Google/UCSB introduced it as the gmon in 2014, coupling settable to zero at nanosecond resolution without spoiling coherence D[422].
Attributes: carrier affinity a = 1.0, fully fabricated, no natural analogue. Gate time ≈40 ns (10^−7.4 s), deterministic.

The coupler buys speed and isolation at the cost of a third noisy degree of freedom. Tens of MHz on-coupling sets 25–70 ns gates. Three mechanisms set the floor. Coherence: at 40 ns against Willow's mean T1 of 68 µs, relaxation and dephasing during the pulse already cost a few 10⁻⁴, most of the gap between the 99.88% device mean and unity D[1] — pulse shaping cannot recover it, only longer T1 or shorter gates. Leakage: the pulse passes near |20⟩ and the coupler's second level, so population leaves the computational space — an unheralded, sticky error to the code. And 1/f flux noise on the bias moves the off point between calibrations, leaving a drifting residual ZZ that appears as coherent, correlated error. What moves the floor: higher T1, larger anharmonicity (fluxonium couplers), shaped flux pulses, and couplers biased at a flux-insensitive point.

Three regimes, not one number: a characterised pair reaches 99.93% D[38]; a 105-qubit device averages 99.88% D[1]; IBM's full-width fleet benchmark reads 0.37% typical, 0.19% best C[34]. Zuchongzhi 3.0 sits at 99.62% over 105 qubits D[35]. The two-qubit gate is still ~40% of Google's colour-code error budget, leakage next D[41].

There is no separate coupler process: the coupler is another junction and SQUID loop in the same superconducting lithography, so its defects are the platform's own — junction-frequency spread and two-level-system defects pulling the off point. The manufacturing cost is I/O, not lithography: Nighthawk carries 218 couplers across 120 qubits, each demanding a bias line C[49]. QuantWare is the only merchant seller of tunable-coupler chips, funded by a $178 M Series B and building a Delft fab P[298]. Export control names whole computers (4A906) and cryogenic electronics (3A901), not gate mechanisms G[301]. No coupler yield or cost is published.

On a square lattice couplers outnumber qubits about two to one, each needing a fast flux line with its own DAC and filtering. At 10³ qubits that is thousands of flux lines; at 10⁴ it binds before fidelity does, and the only demonstrated escape is an on-chip bias source, as in D-Wave's flip-chip flux DAC on a fluxonium at 10 mK C[316]. The recurring cost is calibration, not latency: off points drift with 1/f flux noise, so calibration scales with coupler count — hence Google steering it by reinforcement learning during error correction, at 7.72×10⁻⁴ logical error per cycle at d=7 D[2].

It belongs to the transmon lattice with tunable couplers (Google, IBM, Rigetti, IQM, OQC, USTC, Fujitsu) and requires the transmon carrier. It replaces fixed-frequency cross-resonance; the switching price is redesigning every qubit-coupler-qubit cell, roughly double the bias lines and a new calibration stack — the trade IBM accepted at Heron (2023-12) after a decade on cross-resonance and kept in Nighthawk C[49]. Its clock contribution is small: derived clock = sum of the syndrome round: gate layers + transport + readout + reset is 0.65 µs, its gate-layer term ~0.16 µs at 0.048 µs per layer D[1], so this node moves the error budget more than the clock. No neighbouring empty slot in the technology graph.

The 99.90% and 99.93% headlines are interleaved randomised benchmarking on one characterised pair, and RB is blind to leakage unless a leakage protocol runs alongside — leakage being this gate's second error term. EPLG is a different observable, full-width layered gates including crosstalk, so the 0.37% versus 0.07% gap is definitional as much as fleet variability. Neither record has been replicated by an independent laboratory. One attribution conflict: the cited "25 ns at 99.8%" Oxford result is a fixed-coupling coaxmon pair with no coupler at all C[423].

Not published: the gate duration of IQM's 99.93% CZ, of which only the fidelity and the 40-hour averaging window are stated; a coupler-specific yield or defect rate from any vendor; and the share of IBM's fleet EPLG due to residual coupler-off ZZ rather than coherence or crosstalk.

Who.
| Organisation | Role | Country | What exactly they do with this technology | Evidence |
|---|---|---|---|---|
| Google | developer | US | Originated the gmon; Willow uses tunable couplers | D[422] |
| IBM | developer | US | Nighthawk: 218 couplers on 120 qubits; coupler patent | C[49] |
| IQM | developer | Finland | Record CZ 99.93% with a floating tunable coupler | D[38] |
| QuantWare | supplier | Netherlands | Sells tunable-coupler transmon chips; Delft fab | P[298] |
| Rigetti | developer | US | Tunable-coupler chiplets, median 2Q 99.1% | Cfact |

Money.

• 2026-06-02 · IBM · programme (5-year quantum commitment) · >$10 B · — · announced fact
• 2026-05-05 · QuantWare · Series B · $178 M (€152 M) · Intel Capital, In-Q-Tel, ETF Partners · closed P[298]fact
• 2026-07-02 · IQM · listing (Nasdaq/Helsinki) · cash €337 M, H1-2026 revenue €8.9 M · closed fact
• 2025-11-06 · DARPA · QBI Stage B, IBM the only transmon vendor of eleven · ≤$15 M each · announced fact

Market & supply chain. What this gate consumes is flux control — multi-channel AWGs (arbitrary waveform generators) and DACs from Zurich Instruments, Quantum Machines and Keysight, none coupler-specific — so concentration risk sits in chips, not instruments. QuantWare is the only merchant route; everyone else fabricates in-house, making coupler design proprietary and control electronics commodity. G2 and G3 pay for this node: both need 10⁻³ two-qubit error at fleet width.

IP & standards. IBM holds US 11,727,297 B2, "Tunable quantum coupler facilitating a quantum gate between qubits" (granted 2023-08-15), claiming an opposite-sign second coupling path that cancels unwanted coherent rotation G[424]; Google's 2014 gmon work is published prior art D[422]. No litigation identified, no standards body for coupler design or reporting.

Roadmaps & track record. IBM: Nighthawk 5,000 two-qubit gates per circuit (promised 2025-06-10 · for 2025 · delivered 2025-12) → 7,500 in 2026 → 10,000 in 2027 Rfact, on schedule, though the coupler switch is one generation old. IQM: 2Q above 99.94% (promised for 2025–26) is within error of the 99.93% delivered D[38]. Rigetti: 108 qubits at 99.5% slipped to "later 2026", the gap sitting in the coupler-mediated gate Cfact.

Strategic reading. IBM's move off cross-resonance settles the architecture argument for tunable coupling, strengthening control-electronics vendors — every coupler is another channel sold — and merchant chip suppliers. The substitution threat is not cross-resonance but passive ZZ cancellation by design: a fixed-coupling coaxmon pair reached 25 ns at 99.8% with no coupler and no flux line C[423]; if that scales, the line tax becomes a liability. Bargaining power stays with whoever owns the fab.

Confirm or demote within 12–24 months: does Nighthawk reach 7,500 two-qubit gates by end-2026; does any fleet report typical EPLG below 0.2%; does a second laboratory reproduce 99.93%. Best case by 2029: fleet-width error near 10⁻³ at 10³ qubits, on-chip biasing removing the line tax. Worst case: coupler count caps chips near 10³ qubits and the 40 ns coherence limit holds error at a few 10⁻⁴, too high for Λ to grow. Open questions: does IBM's patent constrain merchant coupler chips; can fluxonium couplers cut leakage; will fixed coupling remove the line tax at scale.