Abstract
Superconducting qubits are a leading candidate for quantum computing but display temporal fluctuations in their energy relaxation times T1. This introduces instabilities in multi-qubit device performance. Furthermore, autocorrelation in these time fluctuations introduces challenges for obtaining representative measures of T1 for process optimization and device screening. These T1 fluctuations are often attributed to time varying coupling of the qubit to defects, putative two level systems (TLSs). In this work, we develop a technique to probe the spectral and temporal dynamics of T1 in single junction transmons by repeated T1 measurements in the frequency vicinity of the bare qubit transition, via the AC-Stark effect. Across 10 qubits, we observe strong correlations between the mean T1 averaged over approximately nine months and a snapshot of an equally weighted T1 average over the Stark shifted frequency range. These observations are suggestive of an ergodic-like spectral diffusion of TLSs dominating T1, and offer a promising path to more rapid T1 characterization for device screening and process optimization.
Similar content being viewed by others
Introduction
Superconducting qubits are a leading platform for quantum computing1,2. This has been driven, in part, by improvements in coherence times over five orders of magnitude since the realization of coherent dynamics in a Cooper-pair box3. However, further improving coherence times remains crucial for enhancing the scope of noisy superconducting quantum processors as well as the long-term challenge of building a fault tolerant quantum computer. Recent advances4,5,6,7 in two-qubit gate control have placed their fidelities at the cusp of their coherence limit, implying that improvements in coherence could directly drive gate fidelities past the fault tolerant threshold. In this context, coherence stability and its impact on multi-qubit device performance is also an important theme, since superconducting qubits have been shown to display large and correlated temporal fluctuations (i.e., 1/fα) in their energy relaxation times T18,9,10,11,12,13,14. This places additional challenges for benchmarking the coherence properties of these devices13, and also for error mitigation strategies such as zero noise extrapolation12.
The fluctuations of qubit T1 are often attributed to resonant couplings with two-level systems (TLSs) that have been historically studied in the context of amorphous solids15,16 and their low temperature properties. More recently, TLSs have attracted renewed interest due to their effect on the coherence properties of superconducting quantum circuits11,13,14,17,18,19,20, and are attributed to defects in amorphous materials at surfaces, interfaces, and the Josephson junction tunnel barrier. Frequency resolved measurements of T1 in flux and stress tunable devices11,19,20,21 have also displayed fluctuations, suggesting an environment of TLSs with varying coupling strengths around the qubit frequency. The variability of T1 over time is explained11,16, at least in part, by temporal fluctuations in this frequency environment, associated with the spectral diffusion of the TLSs15,22.
Furthermore, two-qubit gates that involve frequency excursions5,11,23 can also interact with TLSs near the qubit frequency leading to additional incoherent error. The fluctuations in TLS peak positions, therefore, can also introduce fluctuations in two-qubit fidelity. Spectroscopy of defect TLS is, therefore, central to understanding the short and long time T1 and gate fidelity of qubits.
Single Josephson junction transmons with fixed frequency couplings represent a successful device architecture achieving networks of over 60 qubits1 with all microwave control and state of the art device coherence. The single junction configuration offers advantages such as reduced sensitivity to flux noise, while preserving the transmon charge insensitivity and also reducing system complexity with fewer control inputs. However, there is little TLS spectroscopy of single junction transmons because of the limited tunability, despite the central importance of understanding the TLS environment both for device and process characterization.
In this work, we introduce an all-microwave technique for the fast spectroscopy of TLSs in single junction transmon qubits that requires no additional hardware resources. In contrast to flux-based approaches to TLS spectroscopy, we employ off-resonant microwave tones to drive AC-Stark shifts of the fundamental qubit transition and spectrally resolve qubit relaxation times. Dips in relaxation times serve as a probe of the frequency location of a strongly coupled TLS. We use repeated frequency sweeps to probe the time dynamics of the relaxation probabilities including tracking the spectral diffusion of strongly coupled TLS. Across 10 qubits, we observe strong correlations between the long time mean, averaged over several months \({\langle {T}_{1}\rangle }_{T}\), and the short time mean, averaged around the local qubit frequency \({\langle {T}_{1}\rangle }_{\omega ,t}\).
This strong correlation suggests a quasi-ergodic behavior of the TLS spectral diffusion in the nearby frequency neighborhood of the qubit. In contrast, there is lower correlation between \({\langle {T}_{1}\rangle }_{T}\) and T1 measured over a single day. The \({\langle {T}_{1}\rangle }_{\omega ,t}\) can provide, therefore, a more rapid estimate of long-time behavior.
Results
Device and spectroscopy technique
The experiments reported in this letter were performed on ibmq_almaden, a 20 qubit processor based off single junction transmons and fixed couplings. The device topology is shown in Fig. 1a, and qubit frequencies are around ~5 GHz. Figure 1b depicts the characteristic spread of the qubit T1s and their mean, from ~250 measurements over 9 months. The base plate (to which the device was mounted) temperature of the dilution refrigerator was typically ~13 mK excepting several temperature excursions to ~1 K, which were not observed to have any significant effects on the long time T1 time series or distributions of T1 values discussed in this work, discussed later. Several qubits on the device display mean T1s exceeding 100 μs. However, the large spread in individual qubit T1s highlights the challenge for rapid benchmarking of device coherence, since any single T1 measurement can disagree substantially from its long-time mean.
We study the spectral dynamics of these T1 times by employing off-resonant microwave tones24 to induce an effective frequency shift Δωq in single junction transmons by the AC Stark effect. This has been employed previously for coherent state transfer between coupled qubits that are Stark shifted into resonance25. In this work, shifting the qubit frequency into resonance with a defect TLS induces a faster relaxation time, which in turn is used to detect the frequency location of the TLS26, as depicted in Fig. 2a. The Stark shift can be described analytically by a Duffing oscillator model27,28
where δq is the qubit anharmonicity, Ωs is the drive amplitude and Δqs = ωq − ωs is the detuning between the qubit frequency and the Stark tone.
As seen from the expression above, the magnitude and sign of the Stark shift can be manipulated by the detuning and the drive amplitude of the Stark tone, Fig. 2c. Very large frequency shifts can be obtained by driving close to the transmon transitions, but this typically leads to undesired excitations/leakage out the two-state manifold. In this work, we obtain Stark shifts of 10’s of MHz, with modest drive amplitudes and a fixed detuning Δqs of ±50 MHz. The frequency shifts are experimentally measured using a modified Ramsey sequence29, schematically shown in Fig. 2b, and display good agreement with the quadratic dependence of the perturbative model in the low-drive limit. A representative case is shown in Fig. 2d.
We focus on the spectrally resolved T1 measurements in Fig. 3 that we use as a probe of defect TLS transition frequencies. However, instead of measuring the entire T1 decay, we use the excited state probability, P1, after a fixed delay time as a measure of T1. This speeds up the spectral scans significantly. Our experiments are performed at a repetition rate of 1 kHz, but our scheme can be further accelerated with reset techniques30, which can be crucial for probing faster TLS dynamics. For an effective frequency sweep, we run an amplitude sweep with off-resonant pulses at fixed detuning (±50 MHz) and duration (delay time of 50 μs), after exciting the qubit with an initial π pulse. The pulsed Stark sequence enables faster spectroscopy by circumventing the need to re-calibrate the π, π/2 pulses at every frequency. The off-resonant pulses have Gaussian-square envelopes with a 2σ rise-fall profile, where σ = 10 ns. This pulse sequence is shown in Fig. 2b. The amplitude points in the sweep are then related to Stark shifts by Ramsey sequences. Figure 3 shows representative data of such a sweep on qubit 19 (Q19) with distinctive dips in P1 that we attribute to strongly coupled TLS at their transition frequencies. T1 measurements at Stark tone amplitudes corresponding to high/low P1 points, as seen in the bottom panel of Fig. 3, explicitly show the substantial variation in T1 as a function of frequency and the consistent tracking of T1 with P1.
Variations in P1 can potentially be caused by sources other than TLS. In our experiments, P1 is spectrally resolved to ~± 25 MHz around the individual qubit frequencies. The narrow frequency range combined with measuring non-neighbor sets of qubits simultaneously avoids strong P1 suppression from resonances with neighboring qubits, the coupling bus or common low-Q parasitic microwave modes. Control experiments show that time insensitive features in the P1 fingerprint are robust to choice of the Stark tone detuning, ruling out a power dependence for the power range used in this work. Finally, while a recent report31 modeled their broadband T1 scatter as arising from quasi-particle fluctuations, this is not sufficient to explain the sharp frequency-dependent P1 features depicted, for instance in Fig. 3. Furthermore, recent experiments on our qubits suggest a quasi-particle limit to T1 that exceeds several milliseconds32.
TLS dynamics and correlations of P 1(ω, t) and 〈T 1〉T
We repeat the line traces of Fig. 3 for both positive and negative 50 MHz detuning, approximately once every 3–4 h, extended over hundreds of hours for all the qubits. A representative example of the cumulative scans is shown in Fig. 4 for Q15. Spectroscopy of the other qubits is shown in the supplemental information S1. The TLS dynamics around the qubit frequency are qualitatively similar to previous TLS spectroscopy using flux or stress tunable devices16.
In the case of Q15, Fig. 4, there are prominent dips in relaxation probability around positive 1 MHz, negative 5–10 MHz, and negative 15–20 MHz. The spectral diffusion of the positions of the T1 dips can vary between order of 1 to 10 MHz over the 272 h of measurement providing a qualitative measure of linewidths. A more quantitative discussion of linewidths can be found in supplemental information S2. The background is covered by an ensemble of smaller dips of relaxation, Fig. 3, that also dynamically evolve, with features that are larger than the sampling noise in the measurement.
As discussed previously, T1 fluctuations introduce uncertainty in the coherence benchmarking, stability of multi-qubit circuit performance and process optimization of superconducting qubit devices. In this context of better estimator, we examine if the long-time averages (T ~ 9 months) \({\langle {T}_{1}\rangle }_{T}\) and \({\langle {P}_{1}\rangle }_{T}\) are correlated with the frequency neighborhood of the qubit \({\langle {T}_{1}\rangle }_{\omega ,t}\) and \({\langle {P}_{1}\rangle }_{\omega ,t}\), respectively. The averaged relaxation probabilities and T1s are defined as
where definitions of variables can be found in Table 1.
We compare \({\langle {P}_{1}\rangle }_{\omega ,t}\) to \({\langle {P}_{1}\rangle }_{T}\) from the daily T1 measurements over \({T}_{\max } \sim\) 9 months evaluated at τ = 53 μs, shown in Fig. 1. The \({\langle {P}_{1}\rangle }_{\omega ,t}\) are calculated for a T1 delay time of τ = 50 μs for 10 qubits in the device for the first time slice and a cutoff frequency Δω/2π = 5 MHz. A qualitatively close agreement for all 10 qubits is observed, see Fig. 5a.
A \({\langle {T}_{1}\rangle }_{\omega ,t}\) can also be estimated for each \({\langle {P}_{1}\rangle }_{\omega ,t}\) at τ = 50 μs by assuming an exponential decay. The approximate equivalence of \({\langle {T}_{1}\rangle }_{\omega ,t}\) and \({\langle {T}_{1}\rangle }_{T}\) is seen in the scatter plot of Fig. 5a inset. A near 1:1 relationship is observed when this approach is applied more broadly across many IBM devices, see supplemental information S3. Furthermore, the poorer correlation between \({\langle {T}_{1}\rangle }_{T}\) and a single instance of T1 measurements, is also shown by larger scatter, as seen in Fig. 5a inset.
To quantify with a single value the correlation between \({\langle {T}_{1}\rangle }_{T}\) or \({\langle {P}_{1}\rangle }_{T}\) and their estimators for many qubits, we use a Pearson R measure across the ten odd-labeled qubits,
where d is the number of qubits in the device or analysis, 10 in this case, and X is the observable P1 or T1. The Pearson correlation is a normalized covariance between two variables reflecting a linear correlation from 1 to −1, where R = 1 (−1) represents a 100% positive (negative) correlation and R = 0 indicates no correlation. Strong R correlation can therefore signal the existence of a potential linear mapping between the estimator and \({\langle {T}_{1}\rangle }_{T}\), in particular, possibly one that is 1:1 or a scaling factor that will reliably estimate \({\langle {T}_{1}\rangle }_{T}\).
For a single frequency sweep that takes ~20 min, we obtain 0.76 < R(ti) < 0.84 correlation between \({\langle {T}_{1}\rangle }_{T}\) and \({\langle {T}_{1}\rangle }_{\omega ,t}\) for 0.5 MHz < Δω < 5 MHz. Using the P1 values without assuming an exponential dependence leads to stronger correlations of 0.87 < R(ti) < 0.91. Both of these are substantially stronger than the correlation found between the representative instance of T1 and \({\langle {T}_{1}\rangle }_{T}\), which was R = 0.29. We note this instance of R can have a large spread, as seen by simulations of Gaussian-distributed fluctuations in supplemental information S4.
A better estimate of the \({\langle {T}_{1}\rangle }_{T}\) for each qubit, Qk, in the device can be obtained from a moving average of multiple, N, measurements. We show the evolution of \({\langle R\rangle }_{{T}_{0\to N}}\) using a moving average of the T1(Ti) measurements, \({\langle {T}_{1}\rangle }_{{T}_{0\to N}}\), for each qubit, Fig. 5b. The \({\langle R\rangle }_{{T}_{0\to N}}\) exceeds R ~ 0.8 (i.e., strong correlation) after ~10 measurements, corresponding to a time exceeding 100 h. Approximately 10 independent measurements is sufficient for fluctuations with magnitude \(\sim 0.2{\langle {T}_{1}\rangle }_{T}\) to obtain a strong correlation, R ~ 0.8, between an estimator (e.g., \({\langle {T}_{1}\rangle }_{{T}_{0}\to N}\)) and \({\langle {T}_{1}\rangle }_{T}\). The details of R dependence on fluctuation magnitude and number of measurements in the moving average are discussed more completely in supplemental information S4.
Autocorrelation between T1(Ti) and T1(Ti−1) measurements is an underlying challenge to fast estimation of \({\langle {T}_{1}\rangle }_{T}\). Evidence of autocorrelation can be seen for example in long-term drifts in the average and short-term correlations between T1, inset of Fig. 5b. On shorter time scales, our experimental data shows evidence of stronger autocorrelation frustrating faster accurate estimation of \({\langle {T}_{1}\rangle }_{T}\) and that the fastest R ~ 0.8 can be obtained on order of 1–2 days, see supplemental information S5 and S6. We conclude that \({\langle {T}_{1}\rangle }_{\omega ,t}\) shows promise as a method for faster estimation of \({\langle {T}_{1}\rangle }_{T}\) than repeated T1(ω = ωq) measurements at only the qubit frequency. Extending the \({\langle {T}_{1}\rangle }_{\omega ,t}\) estimator to a set of many qubits, {Qk}, in a device result in larger R, in the same time, compared to relying only on T1(ωq) measurements for each qubit. The R value simply being a quantitative single value expression of the high correlation between each \({\langle {T}_{1}\rangle }_{\omega ,t}\) and \({\langle {T}_{1}\rangle }_{T}\) across the entire set of qubits.
It is important to note that our calculations of \({\langle {T}_{1}\rangle }_{\omega ,t}\) employ an equal weighting of P1 associated with every frequency bin and the same choice of Δω for every qubit. However, it is not a priori clear that equal weighting is a representative choice over the Δω range. For example, how evenly does the spectral diffusion of each TLS contribute to the T1 of the qubit? The strong correlation of \({\langle {T}_{1}\rangle }_{\omega ,t}\) with \({\langle {T}_{1}\rangle }_{T}\) with equal weighting suggests that an ergodic-like sampling of the TLSs near the qubit frequency is a reasonable first approximation. The ergodic behavior of the T1 estimators is examined more completely in supplemental information S7 and supplemental information S8. Central to the question of assigning a T1 estimate to any qubit, we observe that \({\langle {T}_{1}\rangle }_{T}\) behaves ergodically for all the qubits despite short-term 1/fα correlated behavior (i.e., a constant mean \({\langle {T}_{1}\rangle }_{T}\) can be identified). Assignment of any T1 estimate could alternatively be made impossible in the presence of drift, which is not observed in these qubits, see supplemental information S9 and supplemental information S7 for further details about weak stationarity and ergodicity. Furthermore, the strong correlation of \({\langle {T}_{1}\rangle }_{T}\) to \({\langle {T}_{1}\rangle }_{\omega ,t}\) using only the P1(ω, τ, t) spectrum around the qubit is consistent with a leading hypothesis that the \({\langle {T}_{1}\rangle }_{T}\) is dominated by TLS behavior rather than other stochastic or static contributions.
Correlation dependence on frequency and measurement time
A natural question about the estimator \({\langle {T}_{1}\rangle }_{\omega ,t}\) is, what are the optimal parameter choices for frequency range Δω, n autocorrelated samples and the spacing in time, Δt = ti − ti−1, to obtain sufficiently weakly autocorrelated measurements and a fast, accurate measure of \({\langle {T}_{1}\rangle }_{T}\). Since the optimum choices are presently not known a priori, we evaluate and plot \({\langle R\rangle }_{{t}_{0\to n}}\) versus Δω and ti in Fig. 5c to guide future application of this approach. Equal frequency bin weighting of P1 is used. While this order of magnitude choice of Δω produces a reasonably good first approximation for correlation across the entire range, the plot displays several unexplained features (e.g., non-monotonic dependence on Δω) indicating the unsurprising insufficiency of these two globally applied parameters (i.e., Δω and t) alone to weight the frequency contribution of all the qubits and approach R ~ 1. Additional sensitivity analysis in supplemental information S8 also examines correlation between frequencies and highlights that individual qubits have different sensitivity to the range sampled, Δω. We see that a wide span of Δω produces high \({\langle R\rangle }_{{t}_{0\to n}}\), comparable or better than R(Ti) from a single T1(ωq) measurement. We further show that not only is there a strong R correlation (e.g., linear dependence) but that \({\langle {T}_{1}\rangle }_{\omega ,t}\) approaches 1:1 quantitative agreement with \({\langle {T}_{1}\rangle }_{T}\). The degree to which a T1 estimator, from sampling the nearby frequency space, is quasi-ergodic and would converge to 1:1 agreement is addressed in much more detail in supplemental information S8 and supplemental information S3.
Discussion
Implications for process characterization
The strong correlation between \({\langle {T}_{1}\rangle }_{\omega ,t}\) and \({\langle {T}_{1}\rangle }_{T}\) suggests that long-time T1 averages might be estimated relatively rapidly using spectroscopy. This is in contrast to overcoming correlation times in T1 at a single ωq to obtain a representative \({\langle {T}_{1}\rangle }_{T}\) for the qubit.
Identification of better choices of Δω and n in this study were made with pre-knowledge of what \({\langle {T}_{1}\rangle }_{T}\) was. These parameters will have to be chosen without this pre-characterization for future implementation of this method. Encouragingly, the R dependence on both these parameters appears to be relatively weak suggesting that a heuristic choice for a single Δω and n might be sufficient to obtain useful estimates (i.e., R > 0.8) of \({\langle {T}_{1}\rangle }_{T}\) for new processes when using this simple equal weighting approach until improved choices can be formulated (i.e., different frequency spans for each qubit and or weighted averaging over frequency).
More specifically we observe that \({{{\mathcal{O}}}}\)(10) independent measurements is sufficient to obtain an R ~ 0.8 or higher, see supplemental information S4. We conjecture that one can obtain 10 approximately independent samples, S, in a single scan by sampling at frequency spacings, χ, that are greater than the autocorrelation frequency width (i.e., a frequency spacing where correlation drops below ~ 0.2). In this work, we found the correlation to become weak for \({{{\mathcal{O}}}}\)(1 MHz), see supplemental information S8. Then by this heuristic, a single spectroscopy scan would require a Δω = \(\frac{(S-1)}{2}\chi\), where S = 10 for the target of R ~ 0.8. We assume one of the measurements is done at the qubit frequency, T1(ωq), so for a χ ~ 1 MHz, a scan from ± 4.5 MHz would be suggested by such a heuristic. Extra n measurements can be obtained by waiting longer than the autocorrelation time. The autocorrelation width, furthermore, can be evaluated in the same scan as that used for the \({\langle {T}_{1}\rangle }_{T}\) estimate as long as a sufficiently wide range is sampled. Alternatively, a second scan can be taken if the initial Δω guess was too small.
Empirically we see diminishing gains in using ever larger Δω. Further research is needed to guide better limits on Δω beyond the operational observation that \(S \sim {{{\mathcal{O}}}}(10)\) produces a quasi-ergodic result for qubits with \({\langle {T}_{1}\rangle }_{T}\) in the range of 10–200 μs, see supplemental information S8 for more details on quasi-ergodicity. Since we do find ~ 1:1 agreement using a relatively small Δω ~ 10 MHz for the ~9 month time series and we observe that the distribution of T1(ωq, Ti) produces a constant standard deviation, see supplemental information S9, rather than growing (e.g., proportional to a random walk \(\propto \sqrt{t}\)), we speculate that optimal Δω is bounded rather than growing indefinitely from spectral diffusion processes. Notably, Klauder et al. calculate that dipole-coupled ensembles that are proposed for TLS spectral diffusion22, will produce a truncated linewidth33.
Remarks on technique, correlations, and ergodicity
In this work, we probe the temporal and spectral dynamics of superconducting qubit relaxation times. We study these dynamics in high coherence, single-junction transmons by developing a technique for energy relaxation spectroscopy of defect TLSs via the AC Stark effect. Our technique requires no additional hardware resources and can be easily sped up further by integration with reset schemes. Autocorrelation of T1 frustrates rapid characterization of the long-time average \({\langle {T}_{1}\rangle }_{T}\) and therefore accurate characterization of devices. Our analysis of the dynamics identifies a strong correlation between \({\langle {T}_{1}\rangle }_{T}\) and its short time average over the local frequency span, \({\langle {T}_{1}\rangle }_{\omega ,t}\). The strong correlation of \({\langle {T}_{1}\rangle }_{T}\) with \({\langle {T}_{1}\rangle }_{\omega ,t}\) is also consistent with a TLS dominated T1 that quasi-ergodically samples the qubit local frequency neighborhood in contrast to static or uncorrelated stochastic processes. This work opens up several new promising directions for rapid process characterization and evaluation of device stability.
Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
References
Zhang, E. J. et al. High-performance superconducting quantum processors via laser annealing of transmon qubits. Sci. Adv. 8, eabi6690 (2022).
Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019).
Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-cooper-pair box. Nature 398, 786–788 (1999).
Hong, S. S. et al. Demonstration of a parametrically activated entangling gate protected from flux noise. Phys. Rev. A 101, 012302 (2020).
Kandala, A. et al. Demonstration of a high-fidelity CNOT for fixed-frequency transmons with engineered zz suppression. Phys. Rev. Lett. 127, 130501 (2021).
Hashim, A. et al. Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor. Phys. Rev. X 11, 041039 (2021).
Foxen, B. et al. Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms. Phys. Rev. Lett. 125, 120504 (2020).
Müller, C., Lisenfeld, J., Shnirman, A. & Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Phys. Rev. B 92, 035442 (2015).
Paladino, E., Galperin, Y. M., Falci, G. & Altshuler, B. L. \(\frac{1}{f}\) noise: Implications for solid-state quantum information. Rev. Mod. Phys. 86, 361–418 (2014).
Weissman, M. B. \(\frac{1}{f}\) noise and other slow, nonexponential kinetics in condensed matter. Rev. Mod. Phys. 60, 537–571 (1988).
Klimov, P. et al. Fluctuations of energy-relaxation times in superconducting qubits. Phys. Rev. Lett. 121, 090502 (2018).
Kandala, A. et al. Error mitigation extends the computational reach of a noisy quantum processor. Nature 567, 491–495 (2019).
Burnett, J. J. et al. Decoherence benchmarking of superconducting qubits. npj Quantum Inf. 5, 1–8 (2019).
Schlör, S. et al. Correlating decoherence in transmon qubits: low frequency noise by single fluctuators. Phys. Rev. Lett. 123, 190502 (2019).
Phillips, W. Tunneling states in amorphous solids. J. Low. Temp. Phys. 7, 351–360 (1972).
Müller, C., Cole, J. H. & Lisenfeld, J. Towards understanding two-level-systems in amorphous solids—insights from quantum circuits. Rep. Prog. Phys. 82, 124501 (2019).
Martinis, J. M. et al. Decoherence in Josephson qubits from dielectric loss. Phys. Rev. Lett. 95, 210503 (2005).
Grabovskij, G. J., Peichl, T., Lisenfeld, J., Weiss, G. & Ustinov, A. V. Strain tuning of individual atomic tunneling systems detected by a superconducting qubit. Science 338, 232–234 (2012).
Barends, R. et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013).
Lisenfeld, J. et al. Electric field spectroscopy of material defects in transmon qubits. npj Quantum Inf. 5, 1–6 (2019).
Abdurakhimov, L. V. et al. Driven-state relaxation of a coupled qubit-defect system in spin-locking measurements. Phys. Rev. B 102, 100502 (2020).
Black, J. L. & Halperin, B. I. Spectral diffusion, phonon echoes, and saturation recovery in glasses at low temperatures. Phys. Rev. B 16, 2879–2895 (1977).
Stehlik, J. et al. Tunable coupling architecture for fixed-frequency transmons. Phys. Rev. Lett. 127, 080505 (2021).
Gambetta, J. et al. Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006).
Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).
Simmonds, R. W., Lang, K. M., Hite, D. A., Pappas, D. P. & Martinis, J. M. Decoherence in Josephson qubits from junction resonances. Phys. Rev. Lett. 93, 077003 (2004).
Magesan, E. & Gambetta, J. M. Effective hamiltonian models of the cross-resonance gate. Phys. Rev. A 101, 052308 (2020).
Schneider, A. et al. Local sensing with the multilevel ac stark effect. Phys. Rev. A 97, 062334 (2018).
Ramsey, N. F. A molecular beam resonance method with separated oscillating fields. Phys. Rev. 78, 695–699 (1950).
Egger, D. J. et al. Pulsed reset protocol for fixed-frequency superconducting qubits. Phys. Rev. Appl. 10, 044030 (2018).
Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nat. Commun. 7, 1–9 (2016).
Kurter, C. et al. Quasiparticle tunneling as a probe of Josephson junction barrier and capacitor material in superconducting qubits. npj Quantum Inf. 8, 31 (2022).
Klauder, J. R. & Anderson, P. W. Spectral diffusion decay in spin resonance experiments. Phys. Rev. 125, 912–932 (1962).
Acknowledgements
We acknowledge technical support on the ibmq_almaden device from the IBM Quantum deployment team. Additional insightful discussions, suggestions and assistance came from Nick Bronn, Andrew Cross, Oliver Dial, Doug McClure, Easwar Magesan, Hasan Nayfeh, James Raferty, Martin Sandberg, Srikanth Srinivasan, Neereja Sundaresan, Jerry Tersoff, Ben Fearon, Karthik Balakrishnan, James Hannon, and Jerry Chow. M.C. also acknowledges support from Princeton Plasma Physics Laboratory through the Department of Energy Laboratory Directed Research and Development program and contract number DE-AC02-09CH11466 to complete parts of the analysis and manuscript.
Author information
Authors and Affiliations
Contributions
S.R. and A.K. developed the technique with contributions from M.C., I.L., and P.J. M.C. and S.R. performed the experiments. M.C., S.R., and A.K. analyzed the data. M.C., S.R., and A.K. wrote the manuscript with feedback from the other authors.
Corresponding authors
Ethics declarations
Competing interests
The authors declare that elements of this work will be included in patents filed by the International Business Machines Corporation with the US Patent and Trademark office. The authors declare no other financial or non/financial competing interests in relation to this published work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Carroll, M., Rosenblatt, S., Jurcevic, P. et al. Dynamics of superconducting qubit relaxation times. npj Quantum Inf 8, 132 (2022). https://doi.org/10.1038/s41534-022-00643-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41534-022-00643-y
- Springer Nature Limited
This article is cited by
-
Wiring surface loss of a superconducting transmon qubit
Scientific Reports (2024)
-
Markovian noise modelling and parameter extraction framework for quantum devices
Scientific Reports (2024)
-
Scalable error mitigation for noisy quantum circuits produces competitive expectation values
Nature Physics (2023)
-
Evidence for the utility of quantum computing before fault tolerance
Nature (2023)
-
Enhancing the coherence of superconducting quantum bits with electric fields
npj Quantum Information (2023)