Qubit Noise Sensing via Induced Photon Loss in a High-Quality Superconducting Cavity

Abstract

Characterizing the noise affecting superconducting qubits is essential for improving their performance. Existing noise-sensing techniques use the qubit itself as a detector, but its short coherence time limits both sensitivity and accessible frequency range. Here, we demonstrate a method for measuring qubit frequency noise by converting it into photon loss in a coupled high-quality superconducting cavity. We prepare a single photon in the cavity and perform repeated mid-circuit qubit measurements with post-selection to isolate noise-induced loss from intrinsic cavity decay, placing an upper bound on the intrinsic dressed-dephasing rate of $(0.29 \, \mathrm{s})^{-1}$ at 508 MHz, corresponding to a qubit frequency-noise power spectral density below $5.4\times10^3\,\mathrm{Hz}^2/\,\mathrm{Hz}$. By exploiting the cavity's millisecond-scale lifetime, this technique provides access to high-frequency noise processes that are beyond the reach of conventional qubit-based spectroscopy and that may impose previously unexplored limits on qubit coherence.

Figures (9)

• Figure 1: Detecting transmon frequency noise with a high-$Q$ cavity. (a) Experimental setup. A half-elliptical cavity is coupled to a transmon chip subject to frequency noise (red arrows), corresponding to fluctuations in the transmon's resonance frequency. (b) The sensing protocol. A single photon is initialized in the cavity and the transmon is repeatedly measured during the cavity evolution. In a dressed dephasing event (red arrows), the cavity excitation is transferred to the transmon and detected by a subsequent measurement. Finally, the cavity population is mapped back onto the transmon and read out. (c) Simulated protocol output. The baseline cavity decay curve (pink) includes all measurement outcomes and decays at the total loss rate $\kappa$. The post-selected curve (purple), conditioned on all $\ket{g}$ outcomes, decays more slowly because detected photon loss events have been discarded. The dressed dephasing rate $\kappa_\mathrm{dd}$ is extracted by comparing both curves.
• Figure 2: Characterizing the impact of dressed dephasing on the cavity-qubit system. (a) The cavity single-photon lifetime without injected noise (green), $T_1^\mathrm{c} = 11.3 \, \textrm{ms}$, and with injected noise (blue), $T_1^\mathrm{c} = 4.5 \, \textrm{ms}$. Error bars are smaller than the markers. (b) Transmon excited-state probability as a function of time in the presence of injected noise. Dressed dephasing transfers the cavity excitation to the qubit, resulting in a temporary increase in the qubit's excited-state population. Here, unlike the full sensing protocol (Fig. \ref{['fig3']}), the transmon population is measured only once at each wait time, without mid-circuit measurements, to directly observe the excitation transfer. The noise also induces a small steady-state increase in the transmon excited-state population. The solid line is a simulation with $\kappa_\textrm{dd}$ as the sole free parameter, yielding $\kappa_\mathrm{dd} = (9.1 \, \mathrm{ms})^{-1}$. All other parameters are fixed from independent measurements (Table \ref{['tab:system_parameters_full']}). Error bars represent $\pm1\sigma$ standard error.
• Figure 3: Unconditional (orange) $P_1(t)$ and post-selected (purple) $P_1^g(t)$ single-photon survival probabilities in the presence of injected frequency noise (at a different noise amplitude than in Fig. \ref{['fig2']}). Solid lines are fits to Eq. (\ref{['eq2']}) (Supplemental Material section \ref{['app:bayesian_statistics']}) with shaded regions denoting the 68% highest density interval. Error bars are $1\sigma$ confidence intervals. From the fit we extract $\kappa_{\mathrm{dd}} = (5.4^{+0.1}_{-0.2} \, \mathrm{ms})^{-1}$, corresponding to an induced noise PSD of $S_{\delta\omega}(\Delta) = 293 \cdot 10^3 \, \mathrm{Hz}^2 \, / \,\mathrm{Hz}$, and an unconditional decay rate of $\kappa =(3.46 \pm 0.02 \, \mathrm{ms})^{-1}$. The gray curve shows the fraction of experimental shots surviving post-selection, which decays exponentially at a rate of $(1.7\,\mathrm{ms})^{-1}$, primarily due to thermal qubit excitations and false positive measurements. Each data point corresponds to 20,000 experimental repetitions.
• Figure 4: Extracted dressed-dephasing rate $\kappa_\mathrm{dd}$ as a function of the injected noise PSD $S_{\delta\omega}(\Delta)$ in arbitrary units. The fit line (pink) shows that at high noise power, $\kappa_\mathrm{dd}$ scales linearly with the noise PSD, consistent with Eq. (\ref{['eq1']}). At low noise power, the extracted values plateau, and the signal is no longer resolvable. Error bars denote 68% Bayesian highest density intervals, while the shaded region (red) marks the limit of resolution. The orange star indicates the noise PSD corresponding to the data in Fig. \ref{['fig3']}. Each data point is averaged over 20,000 runs.
• Figure 5: Sectional view of the experimental device, showing the half-elliptical 3D niobium cavity and the transmon chip protruding into it via a coaxial waveguide.