Impact of Josephson junction array modes on fluxonium readout

TL;DR

The paper analyzes measurement-induced backaction in fluxonium qubits due to internal JJA modes, introducing a PMIST mechanism where a readout drive resonantly excites both the qubit and a parasitic mode. Using an adiabatic Floquet framework with a semiclassical readout drive, the authors map PMIST channels, quantify transition probabilities via perturbative and Landau–Zener analyses, and demonstrate post-readout qubit dephasing from residual parasitic occupancy. They show PMIST can occur at realistic readout powers, but identify circuit-design strategies—such as reducing qubit–parasitic coupling and increasing the readout–parasitic frequency gap—that can largely suppress these transitions. The work highlights the importance of considering JJA parasitic modes in fluxonium readout to achieve high-fidelity operations and informs design choices for scalable superconducting quantum processors.

Abstract

Dispersive readout of superconducting qubits is often limited by readout-drive-induced transitions between qubit levels. While there is a growing understanding of such effects in transmon qubits, the case of highly nonlinear fluxonium qubits is more complex. We theoretically analyze measurement-induced state transitions (MIST) during the dispersive readout of a fluxonium qubit. We focus on a new mechanism: a simultaneous transition/excitation involving the qubit and an internal mode of the Josephson junction array in the fluxonium circuit. Using an adiabatic Floquet approach, we show that these new kinds of MIST processes can be relevant when using realistic circuit parameters and relatively low readout drive powers. They also contribute to excess qubit dephasing even after a measurement is complete. In addition to outlining basic mechanisms, we also investigate the dependence of such transitions on the circuit parameters. We find that with a judicious choice of frequency allocations or coupling strengths, these parasitic processes can most likely be avoided.

Figures (24)

• Figure 1: Schematic of a PMIST process. A parasitic back-action effect where a readout drive applied to a cavity (black) simultaneously and resonantly excites extraneous linear modes (red) as well as the qubit (blue).
• Figure 2: Fluxonium readout circuit, qubit and array modes spectrum. (a) The color scheme shows primary components that correspond to various modes, depicted in Fig. \ref{['fig:demo']} when a JJA fluxonium circuit is connected to a readout cavity (R). The subscripts '$\mathrm{p,j}$' denote components of the phase-slip junction and the JJA, respectively. This circuit shows coupling capacitances ($C_\textrm{c}$), readout frequency parameters ($\omega_\textrm{r}=1/\sqrt{L_\textrm{R}C_\textrm{R}}$), parasitic ground capacitances in JJA ($C_\textrm{g,j}$) and next to the phase-slip junction ($C_\textrm{g,p}$). The differential capacitance $C$ adjusts the charging energy of the qubit mode (see Table \ref{['tab:readout_params']}). (b) Fluxonium mode energy levels in units of $h$, with the highlighted area showing the first three levels essential for certain readout schemes zhang_universal_2021. Defining $\omega_{ij}$ as the splitting frequency between the fluxonium states $i,j$, we have $\omega_{01}/2\pi=30 \ \mathrm{MHz}, \ \omega_{12}/2\pi=6.03 \ \mathrm{GHz}$. (c) Parasitic mode frequencies $\omega_\mu/2\pi$. The lowest even mode $\mu = 2$ has the strongest coupling to the qubit (see Fig. \ref{['fig:coupling-strength']} in App. \ref{['app:coupling']}).
• Figure 3: MIST and PMIST processes as seen in Floquet branch simulations. Each column corresponds to the branch associated with a specific undriven (but dressed) eigenstate $i=\ket{\tilde{k},\tilde{0}}$. The Floquet eigenstates were tracked with increase in $\bar{n}_r$ for this branch analysis where each step records the following quantities. Top row: Average fluxonium excitation number in the given branch $\langle n_\phi\rangle$, as a function of drive power ($\propto\bar{n}_\textrm{r}$) and drive frequency $\omega_\textrm{d}$. Bottom row: Average excitation number of the $\mu=2$ parasitic mode, $\langle n_\mu\rangle$. Arrows and numbers indicate each transition (with numbers corresponding to Table \ref{['tab:PMIST']}). The figures are plotted in logarithmic scale to pronounce the numbered streaks, the transitions of interest. Only sharp streaks indicate MIST or PMIST while any background change in color can be ignored. See Figs. \ref{['fig:Trans0']}-\ref{['fig:Trans2']} of App. \ref{['app:Floquet-trans']} for corresponding behavior of quasienergies.
• Figure 4: PMIST processes and eigenstate swapping. Examples of PMIST corresponding to transitions (a)$8$ and (b)$9$ in Table \ref{['tab:PMIST']}, relevant when starting from the undriven dressed state $\ket{\tilde{1},\tilde{0}}$. Top row: Qubit mode average occupation $\braket{n_\phi}$ in the two relevant Floquet adiabatic eigenstates, as a function of drive power $\bar{n}_r$. Middle row: Parasitic mode average occupation $\braket{n_\mu}$. Bottom row:$\tilde{E}_i=E_i \ \textrm{mod} \ (\omega_\textrm{d}/2\pi)$ where $E_i$ is the Stark-shifted energy (dashed) obtained from first-order perturbation theory, or quasi-energy (solid) obtained from Floquet simulations showing avoided crossings. Plots are extracted from numerical data used in Fig. \ref{['fig:Floquet']}. The data points are connected by lines for visual aid.
• Figure 5: PMIST transition probabilities as a function of readout cavity ring-up rate. We plot the probabilities for adiabatic (green) and diabatic (black) transitions for a time-dependent ring-up of the average cavity photon number from $\bar{n}_\textrm{r} = 0$ to $\bar{n}_\textrm{r} = 50$, for different choices of the cavity damping rate $\kappa_\textrm{r}$, which controls the speed of the sweep (see text). We start the system in the qubit's first excited state $\ket{\tilde{1},\tilde{0}}$. The drive frequency is $\omega_\textrm{d}/2\pi=9.05 \ \mathrm{GHz}$, corresponding to the crossing shown in Fig. \ref{['fig:011']}(b). Here, $\ket{f_{\bar{n}_\textrm{r}=50}}$ and $\ket{i_{\bar{n}_\textrm{r}=50}}$ are the final states at the end of branch analyses for $\ket{\tilde{2},\tilde{1}}$ and $\ket{\tilde{1},\tilde{0}}$, respectively. The time-evolution operator is denoted by $\hat{\mathcal{U}}(t_\textrm{f})=\mathcal{T}\exp(-i\int^{t_\textrm{f}}_{0} \hat{H}_\textrm{s.c.}(t)dt)$, where $\mathcal{T}$ indicates time-ordering and $t_\textrm{f}=10/\kappa_\textrm{r}$. The adiabatic (green) curve corresponds to the probability of the occurrence of PMIST. We also plot the predictions of the Floquet branch analysis combined with a Landau-Zener approximation for the probabilities (gray), which are in excellent agreement over a wide range of $\kappa_\textrm{r}$.