Cross-resonance (fixed-frequency, all-microwave) g_cr

Driving a control transmon at its neighbour's frequency through a fixed bus produces a ZX interaction (Z on the control, X on the target); Chow, Córcoles, Gambetta et al. (IBM), 2011 D[425]. Kandala et al. reached CNOT 99.77(2)% in a single 180 ns pulse in 2021 by suppressing the static ZZ intrinsically, two fixed-frequency coupling elements retuning the dressed levels rather than extra cancellation drives D[287].
Attributes: fabricated carrier, static connectivity, microwave control at room temperature; deterministic entangling at 10^-6.5 s (~320 ns typical, 180 ns best).
Coherent plus Pauli error; standard superconducting lithography, no added process.

The ZX rate is second order, ∝ JΩ/(Δ(Δ+α)), fastest in the straddling regime −α < Δ < 0, so the detuning must sit inside a band of order the anharmonicity, ~300 MHz. The static ZZ, ∝ 2J²α/(Δ(Δ+α)), never switches off, so coherent error dominates the budget. The floor is not one pair but frequency targeting: every neighbour adds a collision constraint inside that band, and junction spread as fabricated is of order a per cent, so collision-free yield collapses with lattice size. What moves the floor is post-fabrication trimming — annealing junctions to target, 97.4% success D[294] — not better pulses.

No fleet-average cross-resonance (CR) number was ever published; IBM's EPLG today (3.7×10⁻³ D[34]) is Heron hardware, which replaced CR in 2023-12 C[72]. The painful reference is Oxford/OQC's fixed-coupling CZ, 99.8% in 25 ns C[423] — no coupler control either, seven times faster.

The PRL by Kandala et al. reports intrinsic ZZ suppression through two fixed-frequency coupling elements, not active cancellation. Not published: a fleet-average CR fidelity for IBM's pre-Heron generations (Falcon to Condor), beside the isolated-pair 99.77(2)%, and a dated CR-specific patent count.

No process of its own. The cost lands in binning and trimming: a collision cannot be detuned away after fabrication, only masked in software or annealed out, so frequency targeting — laser annealing at IBM, alternating-bias annealing at Rigetti D[294] — is the supply-chain item CR drives. Its advantage is the I/O ledger: one drive line per qubit and nothing per coupler, where tunable couplers add a flux line and a DAC channel each, roughly 1.5–2× the lines. At 10³ that is a crowded fridge against an impossible one; at 10⁴–10⁶ it is the whole wiring budget. Export exposure is the carrier's (ECCN 3A901).

The fixed-frequency branch of the transmon-lattice architecture — IBM Falcon through Condor, 2019–2023 C[72], and Lawrence Berkeley National Laboratory's Advanced Quantum Testbed (AQT) to date — providing entanglement with no coupler control; its alternative is the tunable coupler, and switching is a chip redesign, not firmware. On the derived clock it loses: 180–500 ns against ~50 ns for a tunable-coupler CZ, so every QEC cycle pays 3–7× on the gate layer. Verification: 99.77% is interleaved RB on an isolated pair, blind to spectators; CR error is coherent, so RB understates it and gate-set tomography is the honest measurement.

Money.
2026-06-02 · IBM · investment commitment · > $10 B over five years · announced G[57]fact
2026-06-03 · OQC · Series C · £260 M · Bullhound lead · closed C[60]fact

No funding event or QBI stage names cross-resonance.

Market & supply chain. No incremental supplier: the same lithography, cryostat and coax chain, minus per-coupler flux electronics. It paid for G1 and early G2 only.

IP & standards. IBM holds the foundational family (Chow 2011, Kandala 2021); no dated CR-specific patent count was found as of 2026-09-04. Qiskit still ships CR as a native two-qubit template.

Roadmaps & track record. IBM (2022-05-10 · no long-term CR commitment · retired on schedule at Heron, 2023-12 fact). Hanyang (2026-06-25 · simulation only · nothing fabricated). IBM's record is good precisely because it dropped CR when yield turned.

Strategic reading. Nobody wins from CR's supersession except tunable-coupler and cryogenic-control vendors. Its residual value is cheap wiring: if annealing reaches near-unity frequency-targeting yield, a fixed-frequency chiplet undercuts a tunable-coupler chip on cost. Power now sits with the control-electronics vendors — what CR was designed to avoid.

Confirm by 2028: a fabricated fixed-frequency processor above eight qubits with CR fidelity published under simultaneous operation, or the Hanyang patch measured above 98%; else demote to legacy. Best case 2029: a cheap fixed-frequency chiplet; worst case, CR survives only as a Qiskit compilation target. Does anyone outside IBM run CR in production? Does frequency targeting reach collision-free yield past ~100 qubits? Would a foundry pick CR on cost rather than physics?