Fluxonium-Tunable-Coupler Unit Cell

• Fluxonium–tunable-coupler unit cell is a superconducting-circuit primitive that combines fluxonium qubits with a tunable coupler to achieve both passive crosstalk suppression and activated strong interactions.
• It encompasses various designs—including capacitive FTF, galvanic inductive, plasmon-selective, and distributed long-range realizations—each optimized for distinct coupling modalities and scalability.
• Gate mechanisms, such as microwave-activated CZ and exchange-based operations, demonstrate high fidelities (≈99.9%) while maintaining residual ZZ well below kilohertz levels.

Fluxonium–tunable-coupler unit cell denotes a repeatable superconducting-circuit interaction primitive in which fluxonium qubits are linked through a tunable element engineered to preserve weakly dressed computational states in idle while enabling a strong activated interaction for entangling operations. In the literature, the most common realization is the capacitive fluxonium–transmon–fluxonium (FTF) cell, but the same term also covers galvanically coupled inductive cells, modified-fluxonium couplers, two-mode plasmon couplers, low-shunt-capacitance generalized-flux-qubit couplers, long-range distributed couplers, and hybrid fluxonium–transmon cells. Across these realizations, the recurring objective is passive suppression of residual $ZZ$ together with a controllable interaction channel in a non-computational manifold or an exchange-like channel in the computational manifold (Ding et al., 2023, Zhang et al., 2023, 2504.09888, Zwanenburg et al., 10 Mar 2026).

1. Architectural motif and principal realizations

The unit cell is not a single fixed circuit. Rather, it is a family of local interaction blocks whose common feature is that fluxonium is the protected qubit modality and the coupler is the tunable resource. In the capacitive FTF realization, two fluxoniums couple capacitively to a central flux-tunable transmon and also weakly to each other through a direct capacitive path. In inductive realizations, two heavy-fluxonium qubits are galvanically linked by a tunable inductive element. In plasmon-selective architectures, the coupler is designed to interact weakly with $|0\rangle\leftrightarrow|1\rangle$ but strongly with higher fluxonium transitions such as $|1\rangle\leftrightarrow|2\rangle$. In modular designs, the coupler can itself be distributed over centimeter scales (Zwanenburg et al., 10 Mar 2026, Zhang et al., 2023, 2504.09888, Zhao et al., 14 Apr 2026).

Realization	Coupler element	Characteristic feature
FTF capacitive cell	Flux-tunable transmon	Microwave-activated CZ with passive $ZZ$ suppression
Galvanic inductive cell	Tunable inductive coupler or dc SQUID	Sign-tunable $XX$ and true off-state
Plasmon-selective capacitive cell	Two-mode double-transmon or generalized-flux coupler	Nearly decoupled computational states, tunable non-computational interaction
Distributed long-range cell	Two $\lambda/4$ CPWs linked by an rf-SQUID-like junction	$>1$ cm interconnect for modular processors

Several papers explicitly distinguish the bare hardware motif from the operational unit cell. In isolated-device studies, the natural cell is often a three-body subsystem. In scalable analyses, however, the operational cell can include the frequency configuration of neighboring spectators, because locality is controlled not only by the immediate qubit–coupler triplet but also by how adjacent couplers are parked (Zwanenburg et al., 10 Mar 2026).

2. Circuit descriptions and Hamiltonian structure

For the capacitive FTF cell, the basic three-node Hamiltonian takes the form

$$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$

with each fluxonium biased at its sweet spot and the coupler realized as a SQUID-based transmon with flux-tunable effective Josephson energy (Zwanenburg et al., 10 Mar 2026). A more generic many-cell capacitive lattice model writes

$$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$

with $s=1$ for the fluxonium architecture analyzed there, and then projects the computational manifold into an $|0\rangle\leftrightarrow|1\rangle$0-bit expansion whose coefficients are extracted by a Walsh–Hadamard transform (2504.10298).

Inductive cells employ a different reduction. For the heavy-fluxonium two-qubit unit, the effective low-energy Hamiltonian near half-integer flux is

$|0\rangle\leftrightarrow|1\rangle$1

where the tunable transverse coupling $|0\rangle\leftrightarrow|1\rangle$2 arises from two coupler contributions of opposite sign and $|0\rangle\leftrightarrow|1\rangle$3 is the residual static $|0\rangle\leftrightarrow|1\rangle$4 term (Zhang et al., 2023). Modified-fluxonium capacitive couplers and galvanic dc-SQUID couplers lead to related exchange-dominated effective models, typically of $|0\rangle\leftrightarrow|1\rangle$5- or $|0\rangle\leftrightarrow|1\rangle$6-type with a small residual longitudinal component (Moskalenko et al., 2022, Chakraborty et al., 23 Aug 2025).

Distributed long-range cells replace the local coupler oscillator with two quarter-wave resonators coupled through a central Josephson element. The resulting LTC Hamiltonian contains two resonator modes, a flux-tunable inductive cross-term, and capacitive attachments from the fluxoniums to the resonator endpoints. After diagonalization of the resonator sector and dispersive elimination, the effective remote transition–transition coupling becomes linear in the flux-tunable inter-resonator coupling $|0\rangle\leftrightarrow|1\rangle$7 and quadratic in the qubit–resonator couplings (Zhao et al., 14 Apr 2026).

3. Interaction engineering and idle-state suppression

A defining question for the unit cell is how it suppresses static crosstalk without sacrificing gate speed. In FTF cells, the transmon does not merely add coupling; it balances direct and indirect interaction pathways. In the isolated three-body cell, transmon hybridization with higher fluxonium levels gives the transmon transition a dependence on the joint fluxonium state, while the residual computational $|0\rangle\leftrightarrow|1\rangle$8,

$|0\rangle\leftrightarrow|1\rangle$9

remains below $|1\rangle\leftrightarrow|2\rangle$0 over a wide range of transmon frequencies when the transmon is in its ground state (Zwanenburg et al., 10 Mar 2026).

The perturbative structure of this suppression was analyzed explicitly for the FTF architecture: $|1\rangle\leftrightarrow|2\rangle$1 At $|1\rangle\leftrightarrow|2\rangle$2, the reported coefficients have alternating sign, so second- and fourth-order repulsive contributions are partially canceled by the third-order attractive contribution. For the fitted device, independent errors up to $|1\rangle\leftrightarrow|2\rangle$3 in $|1\rangle\leftrightarrow|2\rangle$4 and $|1\rangle\leftrightarrow|2\rangle$5 would increase $|1\rangle\leftrightarrow|2\rangle$6 by at most $|1\rangle\leftrightarrow|2\rangle$7 in the worst-case scenario (Ding et al., 2023).

Inductive heavy-fluxonium cells suppress $|1\rangle\leftrightarrow|2\rangle$8 by a different mechanism. There the tunable $|1\rangle\leftrightarrow|2\rangle$9 is the sum of a static contribution from a harmonic coupler mode and a flux-tunable contribution from a nonlinear fluxonium-like coupler mode. Because these have opposite signs, the coupler has a true off point. Along the sweet-spot contour, $ZZ$0 over the full coupler-bias range studied, and the measured $ZZ$1 is $ZZ$2 at the off position (Zhang et al., 2023).

Plasmon-selective architectures pursue passive $ZZ$3 suppression more directly by exploiting fluxonium matrix-element asymmetry. In the two-mode double-transmon proposal, the qubit $ZZ$4 dipole is so small that the computational manifold is only weakly dressed, while non-computational plasmon transitions retain strong dipoles. The reported $ZZ$5 stays below $ZZ$6 across the whole bias range for both type-1 and type-2 setups (2504.09888).

The grounded dc-SQUID galvanic coupler shows the same design logic in another form. With perfect SQUID symmetry, static $ZZ$7 vanishes at $ZZ$8. With realistic asymmetry, a shunting capacitor generates a compensating charge coupling $ZZ$9 that can suppress the residual $XX$0 of the grounded design down to sub-kHz levels. The floating variant lacks such a clean mitigation path because the extra sloshing mode introduces additional pairwise $XX$1 and even three-body $XX$2-type structure (Chakraborty et al., 23 Aug 2025).

4. Gate mechanisms and reported performance

Gate protocols fall into two broad classes: exchange-based gates in which the coupler turns on a transverse interaction, and microwave-activated controlled-phase gates in which a computational state is driven into a non-computational manifold and returned with a conditional phase.

The experimentally validated FTF architecture belongs to the second class. A resonant microwave drive on the fluxonium charge lines drives $XX$3 into a hybridized manifold containing $XX$4, $XX$5, and $XX$6. Because the relevant dressed transition can be moved over about $XX$7 by tuning the transmon-coupler flux, the same unit cell provides substantial frequency-allocation freedom. The reported peak CZ fidelities are in the $XX$8–$XX$9 range, and model-free reinforcement learning raised the mean fidelity to $\lambda/4$0 for a $\lambda/4$1 gate (Ding et al., 2023).

A related fluxonium-based three-body cell, with a central fluxonium coupler rather than a transmon coupler, implemented a microwave-activated CZ by driving the coupler’s own transition. The demonstrated gate duration was $\lambda/4$2 with fidelity $\lambda/4$3 characterized by cross-entropy benchmarking (Simakov et al., 2023).

Modified-fluxonium capacitive couplers natively realize exchange-like fSim operations. One experimental unit cell reported an fSim gate with $\lambda/4$4 fidelity and a synthesized CZ with $\lambda/4$5 fidelity, while suppressing residual $\lambda/4$6 to the few-kHz level (Moskalenko et al., 2022). The earlier theory proposal for the same modified-fluxonium family predicted a $\lambda/4$7 resonant fSim with simulated $\lambda/4$8 and a $\lambda/4$9 parametric version with $>1$0 (Moskalenko et al., 2021).

Inductive heavy-fluxonium cells emphasize exchange rather than microwave-activated phase accumulation. The experimentally demonstrated tunable inductive coupler enabled $>1$1 in $>1$2 with fidelity $>1$3 and $>1$4 in $>1$5 with fidelity $>1$6, while maintaining $>1$7 across the whole coupler-bias range and $>1$8 at the off position (Zhang et al., 2023).

Several scalable proposals shift the gate interaction entirely into higher fluxonium levels. The double-transmon plasmon-coupler architecture reports intrinsic CZ error below $>1$9 for both type-1 and type-2 setups for gate lengths $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$0 (2504.09888). The grounded galvanic dc-SQUID design predicts a $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$1-like gate with $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$2 open-system fidelity in less than $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$3 nanoseconds assuming modest relaxation and dephasing rates (Chakraborty et al., 23 Aug 2025). A hybrid alternating fluxonium–transmon architecture uses parametric coupler modulation to couple $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$4 and $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$5; its abstract reports closed-system infidelity orders of magnitude below the coherence limit for gate durations $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$6, and the detailed study adds a second weak correction tone that suppresses leakage-state contributions by more than four orders of magnitude (Heunisch et al., 12 Aug 2025).

5. Scalable embedding and operational locality

A recurrent result is that the isolated cell is not automatically the scalable cell. One many-body ladder study of eight fluxonium qubits and ten tunable transmon couplers found that the idle computational manifold remains unusually local: nearest-neighbor residual $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$7 couplings are on the order of a few kHz, higher-body and longer-range static terms satisfy $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$8, and the average inverse participation ratio remains larger than $$\hat H=\sum_{i\in\{\mathrm F_1,\mathrm T,\mathrm F_2\}}\hat H_0^i+\hbar g_{\mathrm{FT}}\big(\hat n_{\mathrm F_1}\hat n_{\mathrm T}+\hat n_{\mathrm T}\hat n_{\mathrm F_2}\big)+\hbar g_{\mathrm{FF}}\hat n_{\mathrm F_1}\hat n_{\mathrm F_2},$$9 (2504.10298). This establishes that a fluxonium-plus-tunable-transmon architecture can preserve dressed-basis locality unusually well in idle.

A separate FTF scalability study showed that gate locality is a stricter requirement than idle locality. In directly scaled one-dimensional architectures inspired by two-qubit demonstrations, the target $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$0 transition shifts by $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$1 and $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$2 when four spectator fluxoniums are flipped, and the average error over spectator states remains above $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$3 for all investigated gate durations. The paper therefore argues that the practical unit cell is the local FTF gate region together with the parked configuration of nearby spectator couplers and qubits, not merely the isolated FTF triple (Zwanenburg et al., 10 Mar 2026).

The same work proposes a scalable remedy: reduce the coupling strengths to

$$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$4

and dynamically park inactive transmons about $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$5 above the fluxonium $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$6 transition. In this regime, the spectator-state dependence of the target transition drops from the MHz scale to about $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$7 in 1D, and the average spectator-induced gate error falls below $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$8 in the 1D chain and below $$\hat H=\hat H_{\mathrm{loc}}+\sum_{\langle q_1 q_2 c\rangle}\left[T\hat n_{q_1}\hat n_{q_2}+T_c\big(\hat n_{q_1}\hat n_c+s\,\hat n_{q_2}\hat n_c\big)\right],$$9 in the studied 2D architectures for gate durations between $s=1$0 and $s=1$1 (Zwanenburg et al., 10 Mar 2026).

Experimental evidence for composability was then provided in a 22-qubit FTF processor. There the repeated unit cell yielded residual $s=1$2, residual $s=1$3, spectator-induced shifts below $s=1$4 when neighboring couplers remained off, parallel single-qubit gate fidelities approaching $s=1$5, and two-qubit CZ gate fidelities around $s=1$6, with the best CZ reaching $s=1$7 at $s=1$8. The same configuration supported deterministic generation of Greenberger–Horne–Zeilinger states involving up to $s=1$9 qubits (Zhan et al., 15 Apr 2026).

These results also clarify a common misconception. Low idle $|0\rangle\leftrightarrow|1\rangle$00 is necessary but not sufficient. Several scalable studies identify always-on interactions among non-computational levels, spectator-state-dependent drive matrix elements, and dressed-mode delocalization as separate failure modes that do not appear in an isolated two- or three-body calibration (Zwanenburg et al., 10 Mar 2026, 2504.09888).

6. Design rules, variants, and open issues

The most explicit design-rule sets concern coupler parking, capacitance budgeting, and spectral separation. For the scalable FTF cell, the active transmon’s on position should be $|0\rangle\leftrightarrow|1\rangle$01–$|0\rangle\leftrightarrow|1\rangle$02 above the $|0\rangle\leftrightarrow|1\rangle$03 transition of the right fluxonium and at least $|0\rangle\leftrightarrow|1\rangle$04 above the $|0\rangle\leftrightarrow|1\rangle$05 transition of the driven fluxonium; next-nearest-neighbor simultaneously active transmons should differ by at least $|0\rangle\leftrightarrow|1\rangle$06; inactive transmons should be tuned to approximately $|0\rangle\leftrightarrow|1\rangle$07 above the fluxonium $|0\rangle\leftrightarrow|1\rangle$08 transition (Zwanenburg et al., 10 Mar 2026).

Low-shunt-capacitance couplers address another scaling bottleneck: fluxonium capacitance loading. A 2D extensible design based on generalized flux-qubit couplers argues that for $|0\rangle\leftrightarrow|1\rangle$09, $|0\rangle\leftrightarrow|1\rangle$10, and coupler shunt capacitance $|0\rangle\leftrightarrow|1\rangle$11, the unit cell can reach $|0\rangle\leftrightarrow|1\rangle$12 with $|0\rangle\leftrightarrow|1\rangle$13 while keeping $|0\rangle\leftrightarrow|1\rangle$14. The same analysis gives representative coupling-capacitance requirements of $|0\rangle\leftrightarrow|1\rangle$15 for $|0\rangle\leftrightarrow|1\rangle$16 and $|0\rangle\leftrightarrow|1\rangle$17 for $|0\rangle\leftrightarrow|1\rangle$18, compared with $|0\rangle\leftrightarrow|1\rangle$19 and $|0\rangle\leftrightarrow|1\rangle$20 for a transmon-based coupler. In spectator studies, target-transition shifts that are tens of MHz when neighboring couplers remain on collapse below $|0\rangle\leftrightarrow|1\rangle$21 when those couplers are tuned off (Zhao et al., 1 Jun 2026).

Long-range modular fluxonium coupling introduces a different design regime. The distributed LTC proposal uses two $|0\rangle\leftrightarrow|1\rangle$22 quarter-wave resonators, an rf-SQUID-like central junction, and qubit–resonator capacitive couplings $|0\rangle\leftrightarrow|1\rangle$23. Its intrinsic off point occurs near $|0\rangle\leftrightarrow|1\rangle$24, the residual computational-subspace $|0\rangle\leftrightarrow|1\rangle$25 stays below $|0\rangle\leftrightarrow|1\rangle$26, and the abstract reports sub-$|0\rangle\leftrightarrow|1\rangle$27-ns gates with intrinsic errors below $|0\rangle\leftrightarrow|1\rangle$28 for qubits separated by more than one centimeter (Zhao et al., 14 Apr 2026).

Not all variants are equally scalable. The galvanic dc-SQUID study concludes that the grounded version is the viable reusable cell, whereas the floating version develops a low-energy sloshing mode that strongly hybridizes with the qubit modes and produces significantly larger static $|0\rangle\leftrightarrow|1\rangle$29 crosstalk (Chakraborty et al., 23 Aug 2025). The hybrid alternating fluxonium–transmon architecture addresses capacitive loading and frequency crowding by making the fluxonium–coupler capacitance intentionally small and the transmon–coupler capacitance as large as localization allows; it chooses parameters such that the computational-state delocalization $|0\rangle\leftrightarrow|1\rangle$30 remains below $|0\rangle\leftrightarrow|1\rangle$31 (Heunisch et al., 12 Aug 2025).

A final extension appears in bosonic cQED. The storage-cavity–readout-resonator–fluxonium ancilla system is not a canonical two-qubit coupler cell, but it demonstrates a fluxonium-mediated, in-situ tunable effective interaction whose sign can be inverted through zero: the measured dispersive shift $|0\rangle\leftrightarrow|1\rangle$32 ranges from $|0\rangle\leftrightarrow|1\rangle$33 to $|0\rangle\leftrightarrow|1\rangle$34, with a nearest measured point to zero of $|0\rangle\leftrightarrow|1\rangle$35, and does so without an extra tunable coupler element or parametric drive (Atanasova et al., 2024). This suggests that fluxonium-based tunable-coupling ideas are not confined to nearest-neighbor qubit pairs.

Taken together, the literature supports a precise, but non-unique, definition. A fluxonium–tunable-coupler unit cell is a local or modular interaction primitive in which fluxonium’s low computational dipole, large anharmonicity, and accessible higher manifolds are combined with a tunable mediator so that the computational manifold remains nearly decoupled in idle, while entangling interactions are activated through exchange, parametric resonance, or controlled excursions into non-computational states. The specific coupler element may be a transmon, a fluxonium-like mode, a dc SQUID, a two-mode plasmon coupler, a generalized flux-qubit circuit, or a distributed resonator bridge; what defines the unit cell is the co-design of tunability, passive crosstalk suppression, and composability in a larger processor.