Readout-induced leakage of the fluxonium qubit

Dispersive readout is widely used to perform high-fidelity measurement of superconducting qubits. Much work has been focused on the qubit readout fidelity, which depends on the achievable signal-to-noise ratio and the qubit relaxation time. As groups have pushed to increase readout fidelity by increasing readout photon number, dispersive readout has been shown to strongly affect the post-measurement qubit state. Such effects hinder the effectiveness of quantum error correction, which requires measurements that both have high readout fidelity and are quantum non-demolition (QND). Here, we experimentally investigate non-QND effects in the fluxonium. We map out the state evolution of fluxonium qubits in the presence of resonator photons and observe that these photons induce transitions in the fluxonium both within and outside the qubit subspace. We numerically model our system and find that transitions to higher-excited states and coupling to an external spurious mode are necessary to explain observed non-QND effects.

💡 Research Summary

This paper presents a comprehensive experimental and theoretical investigation into the non-quantum non-demolition (non-QND) effects observed during dispersive readout of fluxonium qubits. Dispersive readout, while enabling high-fidelity measurement, can disturb the post-measurement qubit state when using increased photon numbers to boost signal-to-noise ratios, posing a significant challenge for quantum error correction protocols that demand both high fidelity and QND character.

The authors designed a pulse sequence to directly probe the fluxonium’s state evolution under the influence of resonator photons. After preparing an initial state (|g〉 or |e〉) and performing a weak projective measurement, a “proxy readout drive” populated the resonator with a variable steady-state photon number (n̄). Following a ringdown period, a final, stronger measurement determined the qubit’s resulting state (|g〉, |e〉, or a higher-energy state |o〉).

Key experimental findings include: 1) A monotonic decrease in the probability of remaining in the initial state as n̄ increases, with the effect being significantly more pronounced for the excited state |e〉 than for the ground state |g〉. 2) The appearance of population leakage into states outside the computational subspace (|o〉). 3) A striking non-monotonic feature where the probability of remaining in |e〉 exhibits a resonant-like increase around n̄ ≈ 7 photons, suggesting a more complex mechanism than simple driven transitions.

To explain these observations, the authors performed numerical simulations. A model based on a driven fluxonium-resonator Hamiltonian could account for some of the behavior, particularly photon-induced transitions to higher fluxonium levels (e.g., |e〉 → |i〉). However, it failed to capture the rapid decay from |e〉 and the resonant feature.

The authors successfully explained the full dataset by extending the model to include coupling to a spurious two-level system (TLS). They proposed that the AC-Stark shift induced by the resonator photons tunes the fluxonium |g〉-|e〉 transition frequency into resonance with a nearby, lossy TLS mode. When hybridized with this lossy mode, the |e〉 state decays rapidly. Simulations incorporating a TLS with frequency Δ_TLS/2π ≈ 411 MHz and coupling g_TLS/2π ≈ 1.3 MHz accurately reproduced the sharp decrease in |e〉 population and the resonant peak at n̄ ≈ 7. Further validation came from varying the external flux, which changed the qubit frequency and consequently the photon number at which the resonance occurred, matching model predictions.

In conclusion, the study demonstrates that non-QND effects in fluxonium arise from a dual mechanism: (1) resonator-photon-driven transitions to higher-energy fluxonium states, and (2) resonator-photon-mediated coupling to external, lossy spurious modes (likely material-defect TLS). This insight is critical for advancing fluxonium-based quantum processors, indicating that improving QND measurement fidelity requires simultaneous engineering to suppress higher-level transitions and meticulous materials and fabrication processes to minimize defect densities.