All-Fluxonium Cross-Resonance Architecture

• All-fluxonium cross-resonance architecture is a superconducting quantum design that employs fluxonium qubits, operated at the half-flux sweet spot, to enable drive-activated conditional ZX interactions with minimal static ZZ.
• The design leverages diverse coupling methods—including inductive, capacitive, and multipath layouts—to finely tune inter-qubit interactions and optimize gate performance and coherence.
• Gate implementations using techniques like selective darkening and flat-top pulse shaping achieve sub-200 ns CNOT operations while ensuring high fidelity and scalability in processor-level designs.

All-fluxonium cross-resonance architecture denotes a class of superconducting quantum-computing designs in which both the control and target qubits are fluxoniums, while the entangling interaction is generated by a microwave drive applied near the target-qubit transition frequency. Across the reported implementations and proposals, the central objective is to obtain a drive-activated conditional $ZX$ interaction together with strongly suppressed static $ZZ$, while retaining fluxonium’s long coherence, large anharmonicity, and operation at the half-flux-quantum sweet spot (Lin et al., 2024, Nesterov et al., 2022, Nguyen et al., 2022, Huang et al., 18 Mar 2026). The architecture has been studied in inductively coupled devices that emulate transversely coupled spin-$1/2$ systems, in capacitively coupled devices using selective darkening, and in scalable multipath-coupled processor layouts that explicitly target large detuning bandwidth and fabrication robustness (Lin et al., 2024, Nesterov et al., 2022, Nguyen et al., 2022).

1. Conceptual definition and operating regime

In this architecture, each computational node is a fluxonium qubit: a loop containing a Josephson junction and a large shunt inductance, with computational states defined by the two lowest eigenstates at half-flux bias. Reported computational transition frequencies lie well below those of conventional transmon-based processors. One experimentally characterized inductively coupled pair operated at $f_{01}^A=150\,\text{MHz}$ and $f_{01}^B=230\,\text{MHz}$ (Lin et al., 2024), while processor-level proposals place $\omega_{01}/2\pi$ in the range of approximately $0.5$ to $1.2\,\text{GHz}$ (Nguyen et al., 2022) and a selective-darkening study used $\omega_{01}^A/2\pi=0.53\,\text{GHz}$ and $\omega_{01}^B/2\pi=1.02\,\text{GHz}$ (Nesterov et al., 2022).

The cross-resonance mechanism is activated by driving the control qubit at a frequency close to the target qubit’s $ZZ$0 transition. After projection into the computational subspace and transformation to an appropriate rotating frame, the dominant driven interaction takes the form

$ZZ$1

in the scalable multipath treatment (Nguyen et al., 2022), or equivalently

$ZZ$2

in the selective-darkening analysis (Nesterov et al., 2022). The architectural target is therefore not merely a nonzero entangling rate, but a hierarchy in which the conditional $ZZ$3 term is appreciable, the always-on $ZZ$4 term is minimized, and unwanted single-qubit terms are either suppressed by design or corrected in calibration (Nguyen et al., 2022, Nesterov et al., 2022).

A recurring feature is operation at the half-flux-quantum sweet spot. The capacitive-only analysis explicitly states that drive-activated cross-resonance gates preserve qubits at their half-flux sweet spot, with minimal dephasing (Huang et al., 18 Mar 2026). This suggests that the architecture is intended to combine the microwave-only tunability of cross-resonance with the low dephasing typically associated with sweet-spot biasing.

2. Circuit models and coupling topologies

Three coupling topologies appear in the cited work.

First, the experimentally characterized inductive device consists of two fluxonium qubits, each with shunt inductance $ZZ$5, Josephson energy $ZZ$6, and shunt capacitance $ZZ$7, sharing a common junction of inductance $ZZ$8 that produces a mutual inductive coupling $ZZ$9. The antenna pads simultaneously create weak stray capacitances, producing a capacitive interaction $1/2$0 and a spurious lumped $1/2$1 mode (Lin et al., 2024). In node-flux variables, the qubit Hamiltonians are

$1/2$2

with permanent couplings

$1/2$3

For that device, the reported parameters were $1/2$4, $1/2$5, $1/2$6, $1/2$7, $1/2$8, $1/2$9, $f_{01}^A=150\,\text{MHz}$0, and $f_{01}^A=150\,\text{MHz}$1 (Lin et al., 2024).

Second, the selective-darkening proposal studies a purely capacitively coupled pair with

$f_{01}^A=150\,\text{MHz}$2

and a microwave drive

$f_{01}^A=150\,\text{MHz}$3

In its representative parameter set, $f_{01}^A=150\,\text{MHz}$4 and the static $f_{01}^A=150\,\text{MHz}$5 rate is $f_{01}^A=150\,\text{MHz}$6 (Nesterov et al., 2022).

Third, the scalable processor proposal introduces a two-path coupling network designed to combine a sizable exchange interaction with static-$f_{01}^A=150\,\text{MHz}$7 cancellation. In that setting,

$f_{01}^A=150\,\text{MHz}$8

with $f_{01}^A=150\,\text{MHz}$9 and $f_{01}^B=230\,\text{MHz}$0. The capacitive and inductive contributions are tuned so that $f_{01}^B=230\,\text{MHz}$1, while maintaining an effective exchange interaction $f_{01}^B=230\,\text{MHz}$2 between $f_{01}^B=230\,\text{MHz}$3 and $f_{01}^B=230\,\text{MHz}$4 (Nguyen et al., 2022).

The capacitive-only 2026 analysis further isolates a fixed-coupling architecture in which the two-qubit Hamiltonian is

$f_{01}^B=230\,\text{MHz}$5

with the control driven as

$f_{01}^B=230\,\text{MHz}$6

There the emphasis is on deriving a simple upper-bound estimate for the conditional interaction strength under strong driving (Huang et al., 18 Mar 2026).

3. Effective spin mapping and the origin of the cross-resonance interaction

A defining observation of the inductively coupled experiment is that two inductively coupled fluxoniums can behave very closely to two transversely coupled spin-$f_{01}^B=230\,\text{MHz}$7 systems (Lin et al., 2024). When the full Hamiltonian is projected onto the computational basis $f_{01}^B=230\,\text{MHz}$8, the effective two-qubit Hamiltonian contains the qubit frequencies, a residual static $f_{01}^B=230\,\text{MHz}$9 term, and a transverse exchange term generated by the inductive coupling through the flux operators:

$\omega_{01}/2\pi$0

with

$\omega_{01}/2\pi$1

Using flux matrix elements $\omega_{01}/2\pi$2--$\omega_{01}/2\pi$3, the reported value was $\omega_{01}/2\pi$4 (Lin et al., 2024).

Under microwave driving, the control-target detuning converts this underlying hybridization into a conditional target rotation. In the inductive device, driving qubit $\omega_{01}/2\pi$5 near $\omega_{01}/2\pi$6 and applying a Schrieffer-Wolff expansion for $\omega_{01}/2\pi$7 yields

$\omega_{01}/2\pi$8

where, to leading order,

$\omega_{01}/2\pi$9

The same source states that choosing $0.5$0 only can suppress $0.5$1 and $0.5$2 and maximize the true $0.5$3 term (Lin et al., 2024).

The selective-darkening formulation reaches the same general structure from a different route. There, the driven interaction is engineered so that the matrix element for the target transition conditioned on control state $0.5$4 vanishes:

$0.5$5

For the tabulated device, $0.5$6, so $0.5$7 (Nesterov et al., 2022). Under this condition, the darkened transition suppresses the unwanted $0.5$8 component and leaves a native CNOT generator up to local $0.5$9 rotations (Nesterov et al., 2022).

The strong-drive capacitive analysis gives an additional nonperturbative perspective. It states that the conditional $1.2\,\text{GHz}$0 rate saturates near

$1.2\,\text{GHz}$1

which implies a minimum CNOT time

$1.2\,\text{GHz}$2

The physical interpretation given there is that the strong off-resonant control drive induces a conditional polarization $1.2\,\text{GHz}$3, and the target is driven through the weak $1.2\,\text{GHz}$4 coupling by that oscillating polarization (Huang et al., 18 Mar 2026). This suggests a unifying picture: the architecture relies on weak fixed hybridization to encode control-state dependence, then converts that dependence into a target rotation by resonant or near-resonant microwave driving.

4. Static $1.2\,\text{GHz}$5 suppression as a central design objective

Suppression of always-on $1.2\,\text{GHz}$6 coupling is a primary architectural criterion, but the cited works achieve it by different mechanisms.

In the inductively coupled experiment, the residual shift is written as

$1.2\,\text{GHz}$7

The paper attributes its smallness to cancellation among virtual transitions involving noncomputational states. Although static $1.2\,\text{GHz}$8 generally scales through second-order processes involving $1.2\,\text{GHz}$9 levels, the relevant flux matrix elements satisfy $\omega_{01}^A/2\pi=0.53\,\text{GHz}$0, so the contributions nearly cancel; numerically, $\omega_{01}^A/2\pi=0.53\,\text{GHz}$1, confirmed by conditional Ramsey (Lin et al., 2024).

In the scalable processor proposal, static $\omega_{01}^A/2\pi=0.53\,\text{GHz}$2 suppression is engineered explicitly through the multipath coupler. A shared-superinductor path contributes one dispersive $\omega_{01}^A/2\pi=0.53\,\text{GHz}$3 channel, while a small capacitive path contributes another with opposite sign. When $\omega_{01}^A/2\pi=0.53\,\text{GHz}$4 is tuned appropriately, $\omega_{01}^A/2\pi=0.53\,\text{GHz}$5 (Nguyen et al., 2022). The same study reports that over $\omega_{01}^A/2\pi=0.53\,\text{GHz}$6 parameter drift, $\omega_{01}^A/2\pi=0.53\,\text{GHz}$7 remains below $\omega_{01}^A/2\pi=0.53\,\text{GHz}$8 (Nguyen et al., 2022).

By contrast, the selective-darkening work does not eliminate static $\omega_{01}^A/2\pi=0.53\,\text{GHz}$9 at the hardware level in its main numerical example. For $\omega_{01}^B/2\pi=1.02\,\text{GHz}$0, it reports $\omega_{01}^B/2\pi=1.02\,\text{GHz}$1 (Nesterov et al., 2022). There, high-fidelity operation is instead obtained by pulse design, selective darkening, and software $\omega_{01}^B/2\pi=1.02\,\text{GHz}$2 rotations before and after the gate (Nesterov et al., 2022). A common misconception is therefore that all all-fluxonium cross-resonance schemes inherently exhibit negligible static $\omega_{01}^B/2\pi=1.02\,\text{GHz}$3. The cited literature does not support that blanket claim: negligible $\omega_{01}^B/2\pi=1.02\,\text{GHz}$4 is achieved in some designs by matrix-element structure or multi-path cancellation, whereas capacitively coupled designs may tolerate a larger residual $\omega_{01}^B/2\pi=1.02\,\text{GHz}$5 and compensate at the control level (Lin et al., 2024, Nesterov et al., 2022, Nguyen et al., 2022).

The 2026 capacitive-only treatment occupies an intermediate position. It states that residual $\omega_{01}^B/2\pi=1.02\,\text{GHz}$6 is $\omega_{01}^B/2\pi=1.02\,\text{GHz}$7 in the Floquet-Schrieffer-Wolff treatment, and reports a design point with residual always-on $\omega_{01}^B/2\pi=1.02\,\text{GHz}$8 for $\omega_{01}^B/2\pi=1.02\,\text{GHz}$9 (Huang et al., 18 Mar 2026). This suggests that capacitive-only all-fluxonium cross-resonance need not imply MHz-scale $ZZ$00, but the achievable value depends strongly on parameter choice and optimization criterion.

5. Gate implementations, pulse prescriptions, and reported performance

The architecture admits several concrete gate constructions.

The selective-darkening protocol realizes a CNOT by simultaneously driving control and target at the target frequency with amplitudes satisfying the darkening condition. A Gaussian-derivative-subtracted envelope is used,

$ZZ$01

with $ZZ$02 and total amplitude chosen so that $ZZ$03 (Nesterov et al., 2022). For $ZZ$04, $ZZ$05, $ZZ$06, and $ZZ$07, the reported total fidelity is $ZZ$08; improving to $ZZ$09 and $ZZ$10 pushes the error below $ZZ$11 (Nesterov et al., 2022). The same work reports coherent infidelity decreasing from approximately $ZZ$12 at $ZZ$13 to approximately $ZZ$14 at $ZZ$15 (Nesterov et al., 2022).

The scalable processor proposal uses a flat-top control drive with cosine ramps and quotes an analytical small-drive estimate

$ZZ$16

For $ZZ$17 and detuning $ZZ$18 up to $ZZ$19, it reports $ZZ$20 at small $ZZ$21 and $ZZ$22 even at $ZZ$23 for $ZZ$24 (Nguyen et al., 2022). Corresponding CNOT gate times are reported as approximately $ZZ$25 to $ZZ$26, with simulated coherent errors $ZZ$27 across $ZZ$28 and $ZZ$29 at small detuning; leakage is reported below $ZZ$30 for $ZZ$31 (Nguyen et al., 2022).

The inductively coupled experimental study gives a lower-rate but very low-$ZZ$32 operating point. Its summary reports conditional $ZZ$33 for equal drive amplitude $ZZ$34, static $ZZ$35, and a cross-resonance gate time $ZZ$36--$ZZ$37, with simulated two-qubit fidelities exceeding $ZZ$38 and limited by $ZZ$39--$ZZ$40 of fluxonium (Lin et al., 2024).

The strong-drive capacitive-only analysis reports a somewhat different optimization frontier. For half-flux-bias parameter choices with $ZZ$41--$ZZ$42, $ZZ$43--$ZZ$44, $ZZ$45, $ZZ$46, and a residual-$ZZ$47 budget $ZZ$48, it sets $ZZ$49 and predicts $ZZ$50--$ZZ$51, typically under $ZZ$52 (Huang et al., 18 Mar 2026). Time-domain simulations with soft-square $ZZ$53 confirm $ZZ$54 at optimum drive, with coherent infidelity $ZZ$55 (Huang et al., 18 Mar 2026).

Taken together, these results show that all-fluxonium cross-resonance admits both low-rate, ultra-low-$ZZ$56 regimes and faster, more strongly driven regimes with higher hardware coupling. The trade-off is explicit in the published numbers rather than merely qualitative.

6. Readout, control infrastructure, spurious modes, and scalability

Processor-level implementations pair the cross-resonance interaction with a specific readout and control stack. In the scalable proposal, each fluxonium is dispersively coupled to its own $ZZ$57 coplanar-waveguide resonator with $ZZ$58--$ZZ$59, and four resonators are capacitively connected to a common $ZZ$60 readout bus (Nguyen et al., 2022). The bare resonator linewidth is $ZZ$61, and no Purcell filters are needed because $ZZ$62 (Nguyen et al., 2022). For $ZZ$63, the typical dispersive shift is $ZZ$64 across $ZZ$65--$ZZ$66 qubit frequencies, while the quoted thermal-photon dephasing estimate gives $ZZ$67 for $ZZ$68 at $ZZ$69 (Nguyen et al., 2022).

Control is supplied by diplexed on-chip lines carrying both DC bias and RF pulses, with a symmetric “hole-in-ground” geometry used to null stray capacitance to ground and neighboring lines (Nguyen et al., 2022). The same source argues that operating below $ZZ$70 pushes microwave crosstalk from wire-bond and package modes below levels seen at $ZZ$71, especially with tightly shielded $ZZ$72 RF lines (Nguyen et al., 2022).

An experimentally important caveat is the appearance of spurious modes generated by the physical interconnect structure. The inductively coupled device exhibited a bosonic $ZZ$73 mode at $ZZ$74, arising from the coupling inductance together with capacitive links among qubit terminals (Lin et al., 2024). In the more complete Hamiltonian,

$ZZ$75

with $ZZ$76 and $ZZ$77 (Lin et al., 2024). Two-tone spectroscopy showed weak anticrossings with the $ZZ$78 lines of both qubits, shifting noncomputational levels by a few MHz and producing extra lines in high-power scans (Lin et al., 2024). The same work states that the mode does not materially affect the cross-resonance gate when far detuned from the $ZZ$79--$ZZ$80 computational band, but should be considered carefully in future designs (Lin et al., 2024).

Scalability analyses focus strongly on collision statistics and fabrication tolerance. The multipath processor study imposes frequency-allocation constraints including addressability $ZZ$81, two-photon separation $ZZ$82, two-qubit detuning in $ZZ$83, and drive-spectator detuning thresholds of $ZZ$84 (Nguyen et al., 2022). Under those assumptions, it reports a cross-resonance cell yield $ZZ$85 for $ZZ$86, scaling to a device yield of approximately $ZZ$87 for $ZZ$88 qubits at $ZZ$89 (Nguyen et al., 2022). The capacitive-only 2026 study similarly analyzes control-target, control-spectator, and multiphoton collision windows and reports that zero-collision yield remains above $ZZ$90 for device sizes up to distance-$ZZ$91 provided $ZZ$92--$ZZ$93 (Huang et al., 18 Mar 2026). By contrast, the same source states that analogous transmon cross-resonance layouts require $ZZ$94 relative standard deviation for comparable yield (Huang et al., 18 Mar 2026).

A final misconception is that all-fluxonium cross-resonance necessarily requires mixed inductive-capacitive coupling. The literature does not support that as a necessity. Inductively dominated devices can realize the desired spin-$ZZ$95 analogy with nearly absent static $ZZ$96 (Lin et al., 2024); capacitive schemes can realize selective-darkening CNOT gates (Nesterov et al., 2022); multipath coupling can be used to cancel $ZZ$97 while keeping exchange large (Nguyen et al., 2022); and capacitive-only fixed-coupling architectures have been analyzed as viable routes to sub-$ZZ$98 CNOT gates with residual $ZZ$99 (Huang et al., 18 Mar 2026). The common architectural theme is therefore not a unique coupler topology, but the combination of fluxonium qubits, fixed interqubit coupling, and microwave-activated conditional dynamics.