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Nature Communications

Non-Markovian relaxation spectroscopy of fluxonium qubits

Ze-Tong Zhuang, Dario Rosenstock, Bao-Jie Liu, Aaron Somoroff, Vladimir Manucharyan, Chen Wang

Published Feb 24, 2026• 3 citations
Publisher

Abstract

Abstract Recent studies have shown that parasitic two-level systems (TLS) in superconducting qubits, which are a leading source of decoherence, can have relaxation times longer than the qubits themselves. However, the standard techniques used to characterize qubit relaxation is only valid for measuring T 1 under the Born-Markov approximation and could mask environmental memory effects in practice. Here, we introduce two-timescale relaxometry, a technique to probe the qubit and environment relaxation simultaneously and efficiently. We apply it to high-coherence fluxonium qubits over a frequency range of 0.1-0.4 GHz, and reveal a discrete spectrum of TLS with millisecond lifetimes. Our analysis of the spectrum is consistent with a random distribution of TLS in the aluminum oxide tunnel barrier of the Josephson junction chain of the fluxonium, with a spectral and volumetric density and average electric dipole similar to previous TLS studies at much higher frequencies. Our study suggests that investigating and mitigating TLS in the junction chain is crucial to the development of various types of noise-protected qubits in circuit QED.

DOI
10.1038/s41467-026-69910-2

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Abstract Recent studies have shown that parasitic two-level systems (TLS) in superconducting qubits, which are a leading source of decoherence, can have relaxation times longer than the qubits themselves. However, the standard techniques used to characterize qubit relaxation is only valid for measuring T 1 under the Born-Markov approximation and could mask environmental memory effects in practice. Here, we introduce two-timescale relaxometry, a technique to probe the qubit and environment relaxation simultaneously and efficiently. We apply it to high-coherence fluxonium qubits over a frequency range of 0.1-0.4 GHz, and reveal a discrete spectrum of TLS with millisecond lifetimes. Our analysis of the spectrum is consistent with a random distribution of TLS in the aluminum oxide tunnel barrier of the Josephson junction chain of the fluxonium, with a spectral and volumetric density and average electric dipole similar to previous TLS studies at much higher frequencies. Our study suggests that investigating and mitigating TLS in the junction chain is crucial to the development of various types of noise-protected qubits in circuit QED.
Using a fluxonium qubit with in situ tunability of its Josephson energy, we characterize its energy relaxation at different flux biases as well as different Josephson energy values. The relaxation rate at qubit energy values, ranging more than 1 order of magnitude around the thermal energy kBT{k}_{B}TkB​T, can be quantitatively explained by a combination of dielectric loss and 1/f1/f1/f flux noise with a crossover point. The amplitude of the 1/f1/f1/f flux noise is consistent with that extracted from the qubit dephasing measurements at the flux sensitive points. In the dielectric loss dominant regime, the loss is consistent with that arising from the electric dipole interaction with two-level-system (TLS) defects. In particular, by increasing the Josephson energy, thus decreasing the qubit frequency at the flux insensitive spot, we find that the qubit exhibits increasingly weaker coupling to TLS defects, which is desirable for high-fidelity quantum operations. Our work establishes a generic noise model for the design of high coherence fluxonium and future generations of noise resilient superconducting qubits.
Fluxonium superconducting qubits have demonstrated long coherence times and high single- and two-qubit gate fidelities, making them a favorable building block for superconducting quantum processors. We investigate the dominant limitations to fluxonium qubit energy relaxation time T1T_1T1​ using a set of eight planar, aluminum-on-silicon qubits. We find that a circuit-based model for capacitive dielectric loss best captures the frequency dependence of T1T_1T1​, which we analyze within both a two-level and a six-level energy relaxation model. We convert the measured T1T_1T1​ into an effective capacitive quality factor QCeffQ_\mathrm{C}^{\mathrm{eff}}QCeff​ to compare qubits on equal footing, accounting for independently estimated contributions from 1/f1/f1/f flux noise and radiative loss to the control and readout circuitry. We apply this methodology to compare qubits from two fabrication processes: a baseline process and one that applies a fluorine-based wet treatment prior to Josephson junction deposition. We resolve a small improvement of (13.8 ±\pm± 8.4)%)\%)% in the process mean QCeffQ_\mathrm{C}^{\mathrm{eff}}QCeff​, indicating that the fluorine treatment may have reduced loss from the metal-substrate interface, but did not address the primary source of loss in these fluxonium qubits.
We examine the entanglement dynamics of two capacitively connected fluxonium qubits influenced by correlated non-Markovian two-level-system (TLS) noise. The environment is represented by an Ornstein–Uhlenbeck process with a Lorentzian spectrum, and the filter-function formalism is utilized as the main framework to assess finite-memory effects and analyze dynamical-decoupling (DD) performance. We design a TLS-oriented DD sequence by optimizing pulse placements within experimentally motivated control limitations for the low-frequency-dominated TLS spectrum pertinent to fluxonium devices. Numerical results indicate that the optimized protocol more efficiently mitigates spectral overlap with TLS noise and enhances the preservation of two-qubit entanglement throughout empirically pertinent timeframes, in comparison to traditional sequences. A succinct post-Markovian master-equation analysis is incorporated solely as a phenomenological consistency verification for the finite-memory crossover. The results establish a quantifiable standard for entanglement preservation in linked fluxonium qubits subjected to colored non-Markovian noise and underscore the need for spectrum-aware DD design for superconducting qubit systems.
One significant source of decoherence in superconducting circuits is known as two-level systems (TLSs), found in amorphous oxide layers. These circuits can, however, also be utilized as spectral and temporal TLS probes. Comprehensive investigations on the physics of TLSs are now possible thanks to recent advancements in superconducting qubits. Here, we simultaneously measure the tunable Xmon qubit decoherence time as well as the resonance frequency for more than 3 days to investigate stochastic fluctuations. Time-domain Allan deviation and frequency-domain power spectral density analysis indicate that two TLSs in near resonance with the qubit are responsible for the fluctuations. From the extracted oscillation in T1 decay, we locate the two TLSs near the junctions.
Understanding the qubit environment is central to fault-tolerant superconducting quantum computation. Characterization typically relies on relaxation, leaving excitation largely underexplored. Here, we access this information with time-resolved broadband excitation spectroscopy. The resulting qubit excitation spectrum reveals a highly structured landscape, interspersed with cold regions. Combined with postselection, this technique enables full reconstruction of the noise power spectral density (PSD) and separates quantum from classical noise. With feed-forward, it exposes long-lived two-level-systems (TLSs), whose relaxation times span tens of microseconds to milliseconds - uncovering an intrinsic link between the qubit-TLS coupling and TLS relaxation. The data suggest that the long-lived TLSs are intrinsic to the qubit environment, and can cause excitation that lasts for many qubit operation cycles. Consequently, the environment retains a memory of prior dynamics, and properties like gate fidelity become non-Markovian and protocol-dependent. The presented approach enables identifying and bypassing the hidden roadblocks formed by long-lived TLSs in fault-tolerant quantum computation.
The superconducting Josephson phase qubit device was fabricated by a NbN/AlN-based technology with the goal to carry out the spectroscopy of parasitic quantum two-level systems (TLSs) in the AlN tunnel barrier by combining qubit spectroscopy with mechanical strain tuning. So far all existing results on TLS spectroscopy have been obtained on Al-based Josephson qubits and thus only TLSs in amorphous aluminum oxide barriers were studied. Understanding the physics of TLS and TLS-induced decoherence requires a study of individual TLSs in tunnel barriers made from different materials. The layout of the NbN/AlN device was optimized to improve the magnetic flux coupling between the flux bias coil and the qubit loop and to minimize the unwanted coupling to the dc-readout SQUID. The area of the SiO insulation under wiring layer was made as small as possible in order to decrease the number of TLSs which can contribute to the suppression of the coherence time. The NbN/AlN Josephson phase qubit was tested in a 3He/4He dilution refrigerator at a temperature of about 60 mK by measuring Rabi oscillations and the energy relaxation time TD. Rabi oscillations had a mean decay time of about of 3-5 ns. We performed systematic studies of TD by varying the power and duration of a resonant microwave pulse. We observe a large enhancement of the qubit's relaxation time for longer microwave pulses. We explain this effect by microwave induced suppression of spontaneous qubit emission.