The Fluxonium Qubit
Fluxonium shunts a Josephson junction with a large superinductance, producing a heavily anharmonic spectrum and long-lived flux-insensitive states.
What Fluxonium Is
A fluxonium qubit is a superconducting circuit built from a small Josephson junction shunted by a very large inductance, the so-called superinductance, and a capacitance. The superinductance is usually realized as a long array of larger Josephson junctions, giving inductances in the hundreds of nanohenries to microhenries. This is far larger than the geometric inductance of any simple wire loop, and it is what distinguishes fluxonium from the transmon and the flux qubit.
The circuit Hamiltonian is H = 4 E_C n^2 - E_J cos(phi) + (1/2) E_L (phi - phi_ext)^2, where E_C is the charging energy, E_J the Josephson energy, E_L the inductive energy, and phi_ext the external flux bias in units of the flux quantum. The cosine term and the parabolic inductive term together create a washboard-like potential whose shape is tuned by the applied flux.
Why the Spectrum Matters
At the half-flux sweet spot (phi_ext = pi) the potential becomes a double well. The two lowest states are near-degenerate symmetric and antisymmetric combinations localized in the two wells, giving a very low transition frequency, often well below one gigahertz. This low frequency and the first-order flux insensitivity at the sweet spot suppress dephasing, while the transition matrix elements to higher states remain small, yielding strong anharmonicity.
- Large anharmonicity permits faster single-qubit pulses without leakage.
- Low transition frequency reduces thermal photon and dielectric loss contributions.
- First-order flux insensitivity at the sweet spot suppresses 1/f flux dephasing.
Trade-offs
The superinductance array adds fabrication complexity and its own loss and mode structure. The low qubit frequency demands careful readout design because dispersive shifts and thermal populations behave differently than for gigahertz-scale transmons. Even so, fluxonium has demonstrated coherence times exceeding a millisecond in the laboratory, making it a serious alternative to the transmon for high-fidelity gates.
Fluxonium is one of the qubit families that motivates the control and readout infrastructure discussed across this library.