Superconducting qubits are among the most promising platforms for building a quantum computer. Despite tremendous progress in recent years, the realization of a fault-tolerant quantum computer remains a challenging task due to limited lifetimes of superconducting qubits. One of the major noise mechanisms limiting qubit lifetimes is the interaction between a qubit and unwanted two-level-system (TLS) defects. TLS defects are various atomic-scale defects of different microscopic nature which are mainly formed in amorphous layers such as the aluminum-oxide tunnel barrier of an Al/AlOx/Al Josephson junction. Those defects can be phenomenologically modelled as quantum systems with two energy levels, and, conventionally, it is assumed that the dominant type of TLS defects are charge defects that are coupled to a superconducting qubit via fluctuations of the electric charge induced on superconducting islands.

In this work, we introduce a novel method of TLS defect spectroscopy in superconducting qubits that allows one to distinguish different types of TLS defects [1]. In particular, we report the observation of TLS defects coupled to a superconducting qubit through fluctuations of the critical current through a Josephson junction. This type of defect-qubit interaction was discussed theoretically in the literature, but up to the present it has not been reliably observed in experiments. The distinctive feature of critical-current-induced TLS defects is that the interaction between such defects and a superconducting qubit is described by a nonlinear term ∼*cos(φ)**∼**φ ^{2}* for a small superconducting phase difference across the Josephson junction

Our technique of defect detection is based on the resonant AC Stark effect (Autler-Townes splitting) induced by the application of a strong microwave drive at a qubit resonance frequency [1,2]. According to our theoretical model, the resonance interaction between a strongly driven qubit and a TLS defect is realized in the rotating frame when a particular relation between the qubit drive amplitude *Ω* (the Rabi frequency), qubit frequency *ω*_{q}, and defect frequency *ω*tls is met. For TLS defects coupled to a qubit via charge fluctuations, the resonance condition is given by the equation *Ω*=|*ω*_{tls}* − ω*_{q}|. For TLS defects coupled to a qubit via critical current fluctuations, the resonance condition is given by the expression *Ω*=|*ω*_{tls}* − *2*ω*_{q}|. By measuring defect spectral signatures at different values of the applied magnetic flux, we were able to distinguish critical-current-coupled defects from standard TLS defects with the charge-fluctuation coupling.

Our test qubit is a capacitively-shunted flux qubit coupled to a 3D microwave cavity [3]. The qubit consists of the aluminum superconducting loop interrupted by three Al/AlOx/Al Josephson junctions with one of the junctions being shunted by a large capacitance. The qubit frequency can be tuned by applying an external magnetic flux through the qubit loop. At the optimal point of the magnetic flux bias, the qubit is insensitive to the magnetic flux noise to the first order, and the qubit energy-relaxation and dephasing times are close to 100 μs [3]. We detected TLS defect signatures by measuring the qubit population after a long resonant drive pulse as a function of the qubit frequency and drive amplitude. We found that signatures of charge-fluctuation TLS defects follow the qubit frequency value, while signatures of critical-current TLS defects follow the double value of the qubit frequency, in accordance with the theoretical model.

The reported technique of TLS defect spectroscopy can be extended to other types of superconducting qubits, and, hence, it will be a valuable tool for quantifying TLS defects and finding optimal techniques and materials for the fabrication of defect-free qubits.

This work was supported by JST CREST (JPMJCR1774) and JST Moonshot R&D (JPMJMS2067).

[1] L. V. Abdurakhimov, I. Mahboob, H. Toida, K. Kakuyanagi, Y. Matsuzaki, S. Saito, “Identification of different types of high-frequency defects in superconducting qubits”, arXiv:2112.05391 (2022).

[2] L. V. Abdurakhimov, I. Mahboob, H. Toida, K. Kakuyanagi, Y. Matsuzaki, S. Saito, “Driven-state relaxation of a coupled qubit-defect system in spin-locking measurements”, Phys. Rev. B 102, 100502 (2020).

[3] L. V. Abdurakhimov, I. Mahboob, H. Toida, K. Kakuyanagi, S. Saito, “A long-lived capacitively shunted flux qubit embedded in a 3D cavity”, Appl. Phys. Lett. 115, 262601 (2019).

Keywords: superconducting qubit, defect, critical current, microwave spectroscopy