Two-Level System Spectroscopy from Correlated Multilevel Relaxation in Superconducting Qubits

Abstract

Transmon qubits are a cornerstone of modern superconducting quantum computing platforms. Temporal fluctuations of energy relaxation in these qubits are widely attributed to microscopic two-level systems (TLSs) in device dielectrics and interfaces, yet isolating individual defects typically relies on tuning the qubit or the TLS into resonance. We demonstrate a novel spectroscopy method for fixed-frequency transmons based on multilevel relaxation: repeated preparation of the second excited state and simultaneous $T_1$ extraction of the first and second excited states reveals characteristic correlations in the decay rates of adjacent transitions. From these correlations we identify one or more dominant TLSs and reconstruct their frequency drift over time. Remarkably, we find that TLSs detuned by $\gtrsim 100\,\mathrm{MHz}$ from the qubit transition can still significantly influence relaxation. The proposed method provides a powerful tool for TLS spectroscopy without the need to tune the transmon frequency, either via a flux-tunable inductor or AC-Stark shifts.

Figures (3)

• Figure 1: The transmon device (a) The anharmonic energy eigenstates of a transmon circuit. The $|2\rangle \rightarrow |1\rangle$ and $|1\rangle \rightarrow |0\rangle$ decay rates $\Gamma_{21}$ and $\Gamma_{10}$ can significantly deviate from the bosonic relation $\Gamma_{21} = 2\Gamma_{10}$. (b) A schematic of the electrical circuit showing the transmon (right) coupled to a readout resonator (middle) and probed through a transmission line (left). (c) Optical image the device.
• Figure 2: $T_1$ experiment with three-levels. (a) Pulse sequence for the $T_1$ experiment. The two $\pi$ pulses acting on the ground state $|0\rangle$ bring the transmon to the second excited state $|2\rangle$. A three-level readout is performed after a variable period $\Delta t$. A waiting time ensures the transmon's relaxation to the ground state. (b) Measured I-Q blobs for the first three energy eigenstates of the transmon. The discrimination boundaries are calculated to minimize assignment error. (c) Confusion matrix obtained from (b) resulting in an assignment fidelity of $\mathcal{F}_3=89.9\%$. (d) Populations traces from a typical $T_1$ experiment. The decay rates are extracted by simultaneously fitting populations of each levels as a function of $\Delta t$.
• Figure 3: Synchronous measurement of transmon relaxation times between different levels. (a) Measured relaxation times $T_\text{1e}$ (transparent blue) and $T_\text{1f}$ (transparent green) of device A as a function of time. A representative region of strong anti-correlation is highlighted by the gray bar. Solid dots denote fits to a single–TLS model. (b) TLS frequency extracted from the single-TLS fits in (a) as a function of time; the shaded bar indicates the extracted TLS linewidth. Dashed lines show the transmon transition frequencies $\omega_{01}$ (blue) and $\omega_{12}$ (green) for reference. (c-d) Same measurements and analysis for device B, where $T_\text{1e}$ and $T_\text{1f}$ exhibit minimal correlation, requiring a two-TLS model for accurate fitting. (e) Correlation plot of measured $T_\text{1e}$ and $T_\text{1f}$ for device A. Solid and transparent dots represent fitted and measured data, respectively. (f) Schematics illustrating the change in qubit transition rates due to the a TLS frequency shift. (g) Correlation plot for device B.