Characterization of drive-induced unwanted state transitions in superconducting circuits

TL;DR

The paper addresses drive-induced unwanted state transitions (DUST) in fixed-frequency superconducting qubits, introducing a three-mechanism taxonomy (A: ac-Stark-induced TLS exchange, B: intrinsic multi-photon transitions, C: inelastic scattering with spurious modes). It combines time-resolved pump-probe spectroscopy, Floquet steady-state simulations, and electromagnetic environment modeling to classify observed transitions and predict their conditions. The authors demonstrate that most transitions are explainable by either TLS coupling, intrinsic transmon dynamics, or coupling to parasitic RF modes, and show how to mitigate them via drive-frequency selection and improved circuit design. The work provides a systematic framework and diagnostic toolkit for anticipating and avoiding DUST in superconducting circuits, with implications for high-fidelity quantum control and readout across architectures.

Abstract

Microwave drives are essential for implementing control and readout operations in superconducting quantum circuits. However, increasing the drive strength eventually leads to unwanted state transitions which limit the speed and fidelity of such operations. In this work, we systematically investigate such transitions in a fixed-frequency qubit subjected to microwave drives spanning a 9 GHz frequency range. We identify the physical origins of these transitions and classify them into three categories. (1) Resonant energy exchange with parasitic two-level systems, activated by drive-induced ac-Stark shifts, (2) multi-photon transitions to non-computational states, intrinsic to the circuit Hamiltonian, and (3) inelastic scattering processes in which the drive causes a state transition in the superconducting circuit, while transferring excess energy to a spurious electromagnetic mode or two-level system (TLS) material defect. We show that the Floquet steady-state simulation, complemented by an electromagnetic simulation of the physical device, accurately predicts the observed transitions that do not involve TLS. Our results provide a comprehensive classification of these transitions and offer mitigation strategies through informed choices of drive frequency as well as improved circuit design.

Figures (18)

• Figure 1: Mechanisms of drive-induced unwanted state transitions in a transmon. (a) A cartoon showing a transmon in a 3D cavity. The fundamental mode of the cavity plays the role of the readout resonator. Any parametric drive, including the readout pulse is delivered through designated ports coupled to the cavity. The qubit is defined by the two lowest levels of the cosine potential of tranmson. (b) Mechanism A: Resonant exchange of energy between the qubit and a spurious mode e.g. a two-level system (TLS). Under the drive, the transmon experiences ac-Stark shift and the qubit tunes into resonance with one or more TLS near the qubit frequency. Such an exchange depends only on the amount of ac-stark shift experienced by the qubit, and not on any frequency-matching condition involving the drive frequency. (c) Mechanism B: Intrinsic multi-photon excitation of the transmon by absorbing multiple drive photons, due to its nonlinearity. When the energy gap between the initial and a higher excited state matches an integer multiple of the drive frequency (within selection rules), the transmon is excited through this multi-photon process. (d) Mechanism C: Inelastic scattering of the drive off the transmon, causing it to either excite or relax while transferring the excess energy to the environment. (e) The transition rate of mechanism C depends on the real part of the impedance seen by the transmon at the emission frequencyconnolly_2025. In a realistic system, the transmon is coupled to a complex impedance network, $Z[\omega]$, whose details are often unknown to the experimentalist. The peaks in ${\rm{Re}}~Z_{\rm{env}}$ corresponds to additional modes arising from device geometry or material defects, that couple to the transmon. (f) Simulated ${\rm{Re}}~Z[\omega]$ of the 3D transmon shown schematically in (a), showing multiple resonances due to spurious electromagnetic modes. Material defects introduce additional modes, not shown here, further crowding the spectrum.
• Figure 2: DUST in a fixed frequency 3D transmon. (a) Pulse sequence for the experiment. The transmon is prepared in the excited state with a $\pi$ pulse followed by a $\tau_{\rm{pop}} = 1~\mu$s stimulation pulse. The frequency $\omega_d$ and the power $\bar{n}_r$ of the pulse are swept. The final state of the transmon is measured by single shot readout after each experiment. (b) Example of unwanted transitions from $\ket{1_t}$ of the transmon when it is driven at a frequency $\omega_d/2\pi = 7.97$ GHz. Final populations of transmon state are plotted as a function of the drive power. The drive power is calibrated through the drive induced ac-Stark shift on the qubit, normalized by the transmon anharmonicity. (c) Transitions from $\ket{1_t}$ of the transmon measured by the two-tone spectroscopy with variable drive power and frequency. The color plots show the transition probability from the $\ket{1_t}$ of the transmon at the end of the stimulation pulse. Data for $\ket{0_t}$ initialization is shown in Appendix \ref{['sec:landscape_g_and_e']}. The plot reveals multiple resonant features, showing distinct transitions at particular combinations of drive frequency and power. We label the prominent transitions above the qubit frequency with Roman letters A through P. For drive frequencies below the qubit transition, the resonances appear as densely packed features. We do not assign individual Roman letters to these transitions and instead label them as R1, R2, ‚Ķ, Rn. The blue labels (O and P) correspond to resonant exchange with spurious modes. The green and magenta labels correspond to intrinsic multi-photon resonances and inelastic scattering processes, respectively. The qubit and the readout frequency are shown by the vertical green and violet lines, respectively.
• Figure 3: Qubit brought into resonance with a TLS by ac-Stark shift. (a) The transmon experiences a drive-induced ac-Stark shift, bringing the shifted $\ket{1_t}$ level into resonance with a dissipative TLS, relaxing the transmon into the system‚Äôs thermal ground state. (b) Magnified section of Fig. \ref{['fig:landscape']}(c) to highlight two prominent features P and O showing a transmon relaxation due resonant exchange with TLS. (c) Temporal change of the TLS environment, probed through the decay probability of the transmon, as a function of normalized ac-Stark shift. The TLS bath exhibits both quasi-continuous drift and telegraphic-noise-like switching when monitored over $\sim 22$ hours. The frequency of the drive inducing the ac-Stark shift is chosen such that the drive does not activate other detrimental transitions.
• Figure 4: Intrinsic multi-photon transition to non-computational levels of the transmon. (a) A schematic showing a resonance condition that annihilates two drive photons to excite the transmon from $\ket{1_t}$ to $\ket{5_t}$ (b) A zoom-in of the measured $P(1_t\rightarrow L$) transition, highlighting the feature E. The white solid line represents the driven resonance condition, $\tilde{\omega}_{15} \approx {\omega}_{15} +4\Delta_q^{\rm{ac}}=2\omega_d$, from the leading order perturbation theory. Although the theory shows decent agreement at low power, it deviates at a higher drive power. (c) Branch analysis Dumas_2024_Ionization of the transition, showing a branch swap between $\ket{\tilde{1}_t}$ and $\ket{\tilde{5}_t}$ for $\omega_{d}/2\pi=8.05$ GHz at a relatively low power, $|\xi|^2 = 0.1$. (d) When driving at $\omega_{d}/2\pi=7.825$ GHz, the same transition as in (c) now occurs at a higher drive power, $|\xi|^2 \approx 1.1$, due to the ac-Stark shift. An additional branch-swapping event occurs at $|\xi|^2 = 1.7$, involving the state $\ket{\tilde{11}_t}$ that has itself experienced multiple prior branch swaps. At high drive powers, several such transitions become activated and hybridize with each other. The corresponding resonance conditions are sensitive to offset charge, resulting in a broad, fuzzy feature in the ensemble-averaged experimental data.
• Figure 5: Identification of intrinsic multi-photon transitions through Floquet simulations. (a) Experimental data showing transitions from $\ket{1_t}$, same as Fig. \ref{['fig:landscape']}(c), with the labels highlighting only the intrinsic multi-photon transitions. (b) Floquet steady-state simulation result showing the hybridization $\Theta(1_{t})$ between the driven computational state $|\tilde{1}_t\rangle$ with driven non-computational states. Plotted results are averaged over a uniform distribution of $n_{g}$ values.