Heavy Fluxonium Qubit

Figure

Description

Heavy fluxonium is a fluxonium regime engineered for maximal coherence by increasing effective mass in phase space (large capacitance, moderate $E_J/E_C$), producing wavefunctions with disjoint support and suppressed relaxation matrix elements.

Compared with conventional fluxonium, heavy fluxonium prioritizes coherence and error bias over speed, and has demonstrated millisecond-scale $T_1$ in sweet-spot operation.

Hamiltonian

Same base fluxonium Hamiltonian:

$H=4E_C{n}^2-E_J\cos \phi +\frac{1}{2}{E}_L(\phi -2\pi {\Phi }_{ext}/{\Phi }_0{)}^2$

Heavy-fluxonium regime typically uses lower $E_C$ and operating points where wavefunctions are localized in different wells, suppressing dipole matrix elements.

Motivation

Heavy fluxonium targets a “hardware-protected” operating regime where coherence is improved by circuit design rather than solely by control optimization. By engineering large effective mass in phase space and operating at sweet spots, matrix elements for dominant noise channels are strongly suppressed. This architecture is a practical bridge between conventional superconducting qubits and more strongly protected designs such as 0-π.

Experimental Status

High-coherence fluxonium — Nguyen et al. (2019):

• Demonstrated $T_1$ in the 0.5–1.5 ms range at the half-flux-quantum sweet spot
• Large anharmonicity (GHz-scale) enables selective control with low leakage
• First-order flux-noise insensitivity at the sweet spot

Millisecond coherence — Somoroff et al. (2023):

• Achieved millisecond-scale $T_1$ and $T_2$ coherence times
• Single-qubit gate fidelity exceeding 99.9%
• Confirmed heavy fluxonium as a strong candidate for low-error bosonic/encoded hybrid stacks

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_1$	0.5–1.5 ms	Sweet-spot operation	Nguyen et al. 2019
1Q gate fidelity	99.9%+	Microwave control	Somoroff et al. 2023
2Q gate fidelity (CZ)	99.2%	Conventional fluxonium regime; heavy-regime 2Q gates are active research frontier	Ficheux et al. 2021
Anharmonicity	GHz-scale	Much larger than transmon	—
Operating temperature	10–20 mK	Dilution refrigerator	—

References

Original proposal / first demonstration

• L. B. Nguyen et al., “High-Coherence Fluxonium Qubit,” Phys. Rev. X 9, 041041 (2019) — arXiv:1907.12333

Experimental demonstrations

• A. Somoroff et al., “Millisecond Coherence in a Superconducting Qubit,” Phys. Rev. Lett. 130, 267001 (2023) — arXiv:2301.09549

Linked Papers

• lin-2018-heavy-fluxonium

Related Entries

• fluxonium — parent qubit type
• 0-pi-qubit — related protected superconducting design
• transmon — conventional superconducting qubit for comparison
• ferbo-qubit — dual-protected design using Andreev weak link instead of tunnel junction; achieves disjoint support in Andreev space
• bifluxon-qubit — related protected qubit using superinductor and CPB