Gatemonium

Figure

Description

Gatemonium is a hybrid superconductor-semiconductor fluxonium qubit in which both the small Josephson junction and the superinductive shunt array are realized as planar Al/InAs junctions on a two-dimensional-electron-gas (2DEG) platform. A top gate tunes the small junction; the array supplies the large linear inductance. The name reflects its parentage: a gatemon (gate-voltage-tunable transmon) crossed with the fluxonium architecture (small junction shunted by a superinductance).

The key innovation is that the Josephson energy $E_J$ of the small junction can be tuned continuously by a gate voltage $V_g$, without using a SQUID flux to tune $E_J$. The fluxonium loop still requires an external flux bias to select its operating point. Independent electrical control of $E_J$ lets one device move between different fluxonium regimes while remaining at a chosen flux sweet spot:

• Light fluxonium ($E_J/E_C<1$ in the convention used by Strickland et al.): the Josephson corrugation is weak, the low spectrum approaches a single harmonic well, and transition frequencies become comparatively flat with external flux, suppressing flux-noise dephasing.
• Heavy fluxonium ($E_J/E_C>1$): deep Josephson wells form near half flux and the charge-number matrix element $|⟨0|\hat{n}|1⟩|$ can become small, suppressing dielectric-loss-induced bit flips. This is not simultaneous protection from every charge- and flux-noise channel.

The superinductance is achieved using approximately 600 planar Al-InAs Josephson junctions in series, each with large critical current so they behave as linear inductors. The 2DEG platform offers advantages over nanowire-based gatemons, including the ability to fabricate large junction arrays with controlled parameters.

Hamiltonian

$H=4E_C{\hat{n}}^2+\frac{1}{2}{E}_L{\left(\hat{\phi }-{\phi }_{\mathrm{ext}}\right)}^2+U_J(\hat{\phi };V_g),$

with the sinusoidal weak-link approximation

$U_J(\hat{\phi };V_g)=-E_J(V_g)\cos \hat{\phi },{\phi }_{\mathrm{ext}}=2\pi \frac{{\Phi }_{\mathrm{ext}}}{{\Phi }_0}.$

where:

• $E_C=e^2/(2C_{\Sigma })$ is the charging energy
• $E_J(V_g)$ is the gate-voltage-tunable Josephson energy of the single junction
• $E_L=({\Phi }_0/2\pi {)}^2/L_{\text{array}}$ is the inductive energy from the superinductive shunt
• $\hat{n}$ is the Cooper pair number operator conjugate to $\hat{\phi }$
• $[\hat{\phi },\hat{n}]=i$
• ${\phi }_{\mathrm{ext}}$ is the reduced external flux through the loop

This is the standard single-mode fluxonium Hamiltonian with a gate-dependent junction potential. A static offset charge does not appear as a physical control parameter in this ideal model: because the superinductor makes the phase coordinate noncompact, a term $4E_C(\hat{n}-n_g{)}^2$ is unitarily gauge-equivalent to the expression above. At half-flux-quantum bias, ${\phi }_{\mathrm{ext}}=\pi$; equivalent phase-origin conventions can move this offset from the inductive term into the Josephson term, but it must appear exactly once.

For a short semiconductor junction with channel transparencies ${\tau }_i$, the spectroscopic model instead uses an Andreev weak-link potential of the form

$U_J(\hat{\phi };V_g)=-\Delta {\sum }_i\sqrt{1-{\tau }_i(V_g){\sin }^2(\hat{\phi }/2)},$

which captures the nonsinusoidal current-phase relation and reduces to the cosine model in the many-channel, low-transparency limit.

Motivation

• Enables electrical tuning of $E_J$ without a SQUID-control flux, reducing one source of magnetic crosstalk while retaining the ordinary fluxonium loop bias.
• Allows in-situ exploration of different fluxonium parameter regimes (light vs. heavy) on the same device by adjusting gate voltage.
• The 2DEG platform supports fabrication of large junction arrays with more uniform parameters than nanowire-based approaches.
• Potential path to enhanced coherence times through hybridization of fluxon and plasmon modes, and through high-plasma-frequency junction arrays.
• Demonstrates the viability of an all-superconductor-semiconductor platform for complex superconducting qubit circuits beyond the simple gatemon.

Experimental Status

First demonstration — Strickland et al. (2024 preprint; 2025 peer-reviewed publication):

• Fabricated Device A with 600 planar Al-InAs Josephson junctions in series for the superinductance; Device B used 400.
• Demonstrated electrostatic control of effective Josephson energy via gate voltage on the single junction.
• Performed one- and two-tone spectroscopy revealing the hybrid plasmon-fluxon spectrum.
• Extracted charging and inductive energies by fitting measured spectra with a model accounting for nonsinusoidal current-phase relation.
• Demonstrated Rabi oscillations of a heavy-regime plasmon mode and measured $T_1=78\pm 4$ ns in Device B; the inferred $Q_L\sim 630$ indicates dominant inductive loss, plausibly associated with the thin aluminum film.

Related gate-tunable-fluxonium milestone — Isakov et al. (2026 preprint):

• Used a gate-tunable semiconductor junction in a nanowire fluxonium to realize a drive-induced flux-charge interaction.
• Demonstrated coherent control of the even-parity $|0⟩\to |2⟩$ transition at half flux through gate modulation, where a purely capacitive drive is parity-forbidden.
• Identified a charge-insensitive-with-variable-$E_J$ (ChIVE) operating point: the transition is first-order insensitive to gate-voltage noise while the flux-charge coupling remains finite. This is a related architecture rather than the same all-planar Al/InAs-array device.

Key Metrics

Metric	Value	Notes	Fidelity reference
Heavy-regime plasmon $T_1$	$78\pm 4$ ns	Device B near 6.35 GHz; inferred $Q_L\sim 630$ and inductive-loss limitation	Strickland et al. 2025
Rabi-envelope decay	$102\pm 24$ ns	Device B plasmon mode; this is not a Ramsey $T_2$ measurement	Strickland et al. 2025
Fitted effective $E_J/h$ range	approximately 6–50 GHz	Device A, from gate-dependent spectroscopy with a nonsinusoidal weak-link model	Strickland et al. 2025
Junction-array size	600 (Device A); 400 (Device B)	Planar Al-InAs junctions in series	Strickland et al. 2025
Inductive energy $E_L/h$	2.80 GHz (A); 4.97 GHz (B)	Spectroscopic fits	Strickland et al. 2025
Base temperature	12 mK	Cryogen-free dilution refrigerator	Strickland et al. 2025

References

Original demonstration

• W. M. Strickland, B. H. Elfeky, L. Baker, A. Maiani, J. Lee, I. Levy, J. Issokson, A. Vrajitoarea, and J. Shabani, “Gatemonium: A Voltage-Tunable Fluxonium,” PRX Quantum 6, 010326 (2025); arXiv:2406.09002

Related gate-tunable fluxonium control

• B. D. Isakov, S. Singh, A. Parra-Rodriguez, D. Feldstein-Bofill, Z. Sun, A. Kringhøj, S. Krøjer, A. Blais, M. Kjaergaard, and A. Gyenis, “Observation of coherent flux-charge interaction in a gate-tunable fluxonium,” arXiv:2607.07798 (2026)

Related fluxonium theory

• V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, “Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets,” Science 326, 113 (2009)
• A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. V. Kuzmin, and V. E. Manucharyan, “Millisecond Coherence in a Superconducting Qubit,” Phys. Rev. Lett. 130, 267001 (2023)

Related gatemon work

• L. Casparis, M. R. Connolly, M. Kjaergaard, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, T. Wang, C. Thomas, S. Gronin, G. C. Gardner, M. J. Manfra, C. M. Marcus, and K. D. Petersson, “Superconducting gatemon qubit based on a proximitized two-dimensional electron gas,” Nat. Nanotechnol. 13, 915 (2018)

Linked Papers

• strickland-2024-gatemonium
• isakov-2026-coherent-flux-charge-interaction
• manucharyan-2009-fluxonium
• somoroff-2023-millisecond-coherence-superconducting
• casparis-2018-ge-gatemon

Evergreen context

• josephson-junction-as-nonlinear-element — gatemonium swaps the fixed tunnel junction for a gate-tunable semiconductor weak link.
• cos2phi — the weak link’s nonsinusoidal current-phase relation makes gatemonium a useful bridge note for when higher-harmonic Josephson physics starts to matter inside an otherwise fluxonium-like circuit.
• charge-noise-in-superconducting-qubits — gate-voltage noise modulates the semiconductor weak link, while fluxonium matrix elements and sweet spots determine how strongly that noise reaches a chosen transition.
• charge-noise-sweet-spot — a gate-tunable fluxonium can reach transition-frequency extrema with respect to $E_J$, including the ChIVE mechanism demonstrated in 2026.
• quantum-hardware — it is a useful bridge note for how a super-semi platform can inherit the superconducting control stack while opening a new materials-design axis.

Related Entries

• gatemon — parent device (gate-tunable transmon, no superinductance)
• fluxonium — inductive shunt ancestor with oxide junctions
• transmon — capacitive shunt cousin
• andreev-spin-qubit — shares the Al/InAs material platform
• all-semiconductor-superconducting-qubit — umbrella entry for circuits built entirely from semiconductor weak links
• mergemon — related multi-junction semiconductor-superconductor qubit architecture
• cos2phi-qubit — another protected superconducting qubit with superinductance
• flux-qubit — related persistent-current qubit