Sub-MHz SWAP spectroscopy of two-level systems in superconducting qubits

arXiv:2610.11125 · quant-ph · Submitted 2026-10-08 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Sub-MHz SWAP spectroscopy of two-level systems in superconducting qubits".

Mira: The gist: High-sensitivity SWAP spectroscopy enables the detection of Rabi chevrons at qubit-TLS coupling rates typically associated with the incoherent regime,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're looking at this paper today, "Sub-MHz SWAP spectroscopy of two-level systems in superconducting qubits." It’s from Minguzzi and Clai Owens and others. This paper is about finding ways to see two-level systems, or TLS defects, that we usually think are too weakly coupled to measure coherently.

Mira: Yeah, it tackles a problem where we can only reliably see the most strongly coupled TLS defects with standard Rabi spectroscopy. This work is trying to extend that coherent detection down to much lower coupling rates.

Lev: From an experimental standpoint, I’m curious if this actually means we can pull more information out of these defects than before. If they are so weakly coupled that we usually just see incoherent decay, can this technique find something new?

Kai: Exactly. The core idea here is using a specific pulse sequence to get better frequency resolution and longer interaction times without needing those long flux pulses we usually have to calibrate for. They’ve managed to get detection down to swap rates as low as zero point one MHz, which is about ten times lower than what we've reported before <ref:2610.11125#pg1,swap rates as low as 0.1 MHz>.

Mira: That level of sensitivity, that zero point one MHz step size, is quite significant when you think about the timescale of these defects <ref:2610.11125#pg1>. They find that even at these low coupling rates, the median TLS energy-relaxation time they measure is around ten microseconds <ref:2610.11125#pg2>.

Lev: Ten microseconds sounds much longer than we've seen for these types of defects in similar systems where we were talking about strongly coupled ones. That suggests a different kind of defect physics might be involved here.

Kai: Right, and this isn't just about seeing a slower decay; they are using the dressed-state picture to model it. They fit the coherent swap oscillations to extract that TLS energy-relaxation time directly from the data they collect.

Mira: The way they describe it is interesting because they find that for these sub-MHz coupling strengths, the exponential fit only captures the initial decay on a timescale of about one over two times g, which is just a few microseconds <ref:2610.11125#pg1>.

Lev: So what does that mean when you look at real hardware? If the coherent oscillation only lasts a few microseconds before it transitions into that faster exponential decay, how do you use that to distinguish between different types of defects?

Kai: They use this modeling to extract parameters like an oscillation frequency, omega osc, which they found is around zero point three two MHz for one resonance. That frequency is tied directly to the coupling strength between the qubit and the TLS, g, where g corresponds to a Rabi splitting of about zero point three two MHz.

Title and authors: Mira: And they use that same model to describe how noise affects those oscillations, specifically how low-frequency ones cause dephasing by making that oscillation frequency fluctuate over time.

Lev: That fluctuating frequency due to noise is what really matters for coherence, right? If the gap frequency omega osc is fluctuating because of one/f noise, it adds pure dephasing to the system <ref:2610.11125#pg1>.

Kai: Right, and they use the dressed-state model to show how this gap frequency stays far below the thermal energy scale at twenty mK, which is around four hundred MHz. That means the noise acting on that gap is effectively classical in terms of its impact on the coherence.

Mira: They also identify a rate, v, which quantifies that excess decoherence of the dressed gap beyond just energy relaxation. This rate comes from transitions between dressed states and non-Markovian dephasing from those low-frequency one/f noises they mentioned <ref:2610.11125#pg1>.

Lev: So they're saying this specific noise coupling to the low-frequency flux noise is actually protected by this dressed gap structure, which is a key point for understanding how we can suppress decoherence in dual-rail architectures or spin-locked driven qubits.

Kai: They show that the linear coupling to that low-frequency flux noise gets suppressed by the dressed gap, which acts as a shield against it, and they mention this protection is analogous to what you see in other architectures like transmon dual-rail systems.

Mira: The implication is that TLS defects that we previously categorized as incoherent might actually be able to cross into the coherent regime if we tune the qubit parameters correctly. That's a big statement about how tunable these things are.

Lev: If they can tune them into coherence, then characterizing these defects isn't just about finding where they fail; it’s about understanding how to make them work in our quantum computers.

Kai: So to wrap up the paper "Sub-MHz SWAP spectroscopy of two-level systems in superconducting qubits," we see that high-sensitivity SWAP spectroscopy can detect Rabi chevrons at coupling rates as low as zero point one MHz, yielding a median TLS energy-relaxation time of ten microseconds.

Mira: The key finding is that the dressed-state picture allows them to map these measured dynamics to physical quantities, giving us a way to understand the underlying physics of these weakly coupled TLS defects.

Lev: For running this on real hardware, the results suggest that for seventy-seven of the eighty-eight resolved TLS defects, this rate v is actually less than one/T* two which is a good sign for maintaining qubit coherence.

Kai: So what we have here is a method that extends coherent detection to these lower coupling regimes and provides a way to use noise protection mechanisms to understand how these defects behave. The paper "Sub-MHz SWAP spectroscopy of two-level systems in superconducting qubits" opens up new ways to probe the behavior of TLS defects.

The paper's summary: Kai: So to recap, this paper is about using a really sensitive SWAP spectroscopy technique to find TLS defects that we usually think are too weakly coupled to see coherently, pushing detection down to rates as low as zero point one MHz.

Mira: Right, and what's interesting is how they handle the physics underneath those numbers. They use this dressed-state picture because it lets them map the measured oscillations directly onto physical coupling strengths and relaxation times.

Kai: Exactly, because that mapping shows them that even in these weaker coupling regimes, they can pull out things like a median TLS energy-relaxation time of about ten microseconds. That’s a lot longer than what we usually see for these kinds of defects.

Mira: And the way they model the decay is telling; for those weak couplings, the exponential part only describes the very first few microseconds before something else happens. They extract an oscillation frequency, like zero point three two MHz in one case, which is directly related to that coupling strength g.

Kai: So it’s not just finding a slow decay; they are using that modeling to figure out the actual interaction strength between the qubit and the TLS. That tells us how strongly they are actually linked.

Mira: And beyond just measuring that link, they use this dressed-state model to show how low-frequency noise—that one/f noise we always worry about—actually affects the coherence of that coupling gap.

Kai: Because they found this gap frequency stays well below the thermal energy at twenty millikelvin, so the noise acting on it is behaving in a way that’s more manageable, even if it's not perfectly quiet.

Mira: They quantify this extra noise effect with a rate v, and they show that because of this gap structure, the linear coupling to low-frequency flux noise gets suppressed. That’s a neat physical mechanism for protecting the coherence in these systems.

Kai: It suggests that these TLS defects we’ve been classifying as "incoherent" might actually be on the edge of being coherent, and tuning can push them over that line.

Mira: That's a big implication because if you can tune them into coherence, then characterizing these defects isn't just about finding where they fail; it’s about understanding how to make them work in our quantum computers.

Kai: So the next thing we need to look at is what this means for actually building those qubits. Does this technique actually help us design better hardware?

The paper's improvements: Tom: So we’re looking at what the authors are suggesting they should do next with this SWAP spectroscopy work today. It’s about taking these findings and turning them into better hardware or better characterization tools for these defects.

Kai: The paper points out that to really get the most out of this, we need to resolve coherent dynamics with frequency precision that's even lower, like below one megahertz over longer time scales.

Mira: That’s right, and they suggest focusing on strain tuning and biasing the qubit right near that flux-insensitive sweet spot. They want to reduce dephasing noise that just blurs out those slow chevron oscillations.

Kai: It means if you want to see those subtle interactions in real hardware, you need better ways to control the qubit parameters to minimize that noise floor.

Mira: And they think the tools they introduced, like this high-sensitivity SWAP spectroscopy sequence, are going to be really important when we try to characterize these defects on much larger device volumes.

Kai: So it sounds like the next big step is tying this detection method into a practical tuning strategy for noise reduction.

Mira: Exactly, and they want to make sure that as we scale up the number of qubits, we don't lose the ability to see these subtle coherent effects anymore.

Conclusion: Kai: So we're wrapping up "Sub-MHz SWAP spectroscopy of two-level systems in superconducting qubits." Basically, this paper shows that we can use high sensitivity to find coherent interactions between qubits and defects even when those defects are usually considered too weak to measure coherently.

Mira: It’s a solid piece of work because they don't just report a slow decay; they use the dressed-state picture to explain the physics behind those measured rates, which gives us real insight into how these TLS defects behave under certain conditions.

Lev: From an error correction view, knowing that these defects have a measurable relaxation time of about ten microseconds is useful because it tells us exactly how long we have before we need to worry about decoherence affecting our logic gates.

Kai: That's right, and they’ve managed to show that the qubit Ramsey rate is often higher than the decoherence rate for most of these detected defects, which means this technique could be a useful tool for maintaining qubit quality.

Mira: They also establish a physical mechanism—that dressed gap—that protects the coherence against low-frequency noise, which is super important because it’s analogous to protection we see in other architectures like dual-rail systems.

Lev: If that protection holds up, it means we might be able to design qubits where these specific types of TLS defects don't immediately destroy our quantum information.

Kai: So the main implication is that TLS defects classified as incoherent might actually be tunable into a coherent regime if we can find the right control settings for the qubit.

Mira: It changes how we classify these materials, moving them from just "bad" to potentially "useful" if you can tune them correctly.

Lev: But they did flag a limitation: this method needs very high frequency precision and longer time windows, which means it’s not something you can do easily on every single chip right now.

Kai: Exactly, so the next challenge is taking these findings and figuring out how to make this technique practical for larger chips or more complex noise environments.

Mira: We'll keep an eye on how they suggest tuning and biasing the qubit because that seems like the most promising path forward for actually seeing these coherent dynamics in a lab setting.

Joaquin Minguzzi, John Clai Owens, Oskar Painter, Matthew H. Matheny, Loren J. Swenson

Amazon Center for Quantum Computing · Institute for Quantum Information and Matter, California Institute of Technology

quant-ph

Submitted: 2026-10-08

Updated: 2026-10-08

Comments: 12 pages, 8 figures, 1 table. Includes Supplemental Material

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 76/100

The gist: The gist: High-sensitivity SWAP spectroscopy enables the detection of Rabi chevrons at qubit-TLS coupling rates typically associated with the incoherent regime, extending coherent detection to swap

Key concepts

SWAP Spectroscopy
A measurement technique used to probe the interaction between a qubit and a two-level system (TLS). It involves applying specific microwave pulses to induce coherent energy exchange, allowing researchers to measure coupling strengths and relaxation dynamics. This method is highly sensitive for detecting subtle interactions.
Rabi Chevron Frequencies
These are characteristic frequencies observed in the SWAP spectroscopy signal that correspond to the coupling strength between the qubit and a TLS. The measured frequencies directly relate to how strongly these two systems interact, providing a quantitative measure of their coupling regime.
Dressed-State Picture
A theoretical model describing how a qubit and a TLS hybridize into new states called 'dressed states.' This picture explains the observed relaxation dynamics by mapping the physical interactions onto energy gaps and decoherence rates, helping to understand why TLS exhibit specific decay patterns.

Terminology

Summary

The gist: High-sensitivity SWAP spectroscopy enables the detection of Rabi chevrons at qubit-TLS coupling rates typically associated with the incoherent regime, extending coherent detection to swap rates of ∼ 0.1 MHz where the median TLS energy-relaxation time is 10 µs.

Detection Method and Sequence

The researchers introduced a sequence with fast flux pulses only at state preparation and readout, switched off during the energy-relaxation delay for finer frequency resolution and longer interaction times. This fast-flux-assisted (FFA) pulse sequence enables SWAP spectroscopy with a 0.1 MHz frequency step and delay times up to 1 ms. The DC flux sets the spectroscopy frequency, while two short FF pulses bring the qubit to its flux-insensitive sweet spot for state preparation and readout. By switching the FF completely off during the T1 delay, they eliminate the need to calibrate long flux pulses and reduce flux noise to a level set by the DC source alone.

Key Findings on Coherent TLS Detection

The study detected 118 coherent TLSs across 5 aluminum-on-silicon chips, with their relaxation dynamics described by the dressed-state picture. They resolved coherent qubit-TLS swap oscillations at rates as low as 0.1 MHz in the regime previously associated with weakly coupled TLSs. The measured Rabi chevron frequencies were 3.6065 GHz and 3.6284 GHz, corresponding to coupling strengths of 2g/(2π) = 0.32 and 0.15 MHz respectively.

TLS Relaxation Dynamics

The relaxation dynamics are described by the dressed-state picture. For the detected TLS resonances, the P1 decay is nonexponential, and an exponential fit captures only the initial decay on a timescale of ∼ 1/(2g), which is a few microseconds for sub-MHz coupling strengths. The fitted parameters yielded an oscillation frequency ωosc/2π = 0.32 ± 0.01 MHz, a swap coherence time Tosc = 9 ± 3 µs, and a relaxation time Trelax = 30±3 µs. The resulting TLS energy-relaxation time TTLS 1 was found to be 16 ± 3 µs at one resonance, which is an order of magnitude slower than strongly coupled TLS defects.

Dressed-State Model and Noise Suppression

The dressed-state model maps the fitted parameters to physical quantities, where the qubit and TLS hybridize into dressed states ±⟩ separated by ωosc = p(2g) squared + δω squared. The gap frequency ωosc/2π lies far below kBT /h ≈ 400 MHz at T = 20 mK, meaning the noise at the gap is effectively classical. The dressed-gap decoherence rate Γv quantifies the excess decoherence of the dressed gap beyond energy relaxation. This rate is composed of Markovian transitions between dressed states and non-Markovian dephasing from low-frequency 1/f noise.

Noise Coupling and Protection

The linear coupling to low-frequency flux noise is suppressed by the dressed gap, which protects the coherence against 1/f noise. The quadratic coupling term, arising from the qubit's flux noise, adds a term exp(-Γf t/2) to the decay envelope. This mechanism is analogous to that in spin-locked driven qubits and transmon dual-rail architectures where a dressed gap protects coherence against low-frequency noise.

Conclusion on Coherent Regime

The work demonstrates that high-sensitivity SWAP spectroscopy enables the detection of Rabi chevrons at qubit-TLS coupling rates typically associated with the incoherent regime. They extend coherent detection to swap rates of ∼ 0.1 MHz, where the median TLS energy-relaxation time is 10 µs. This long swap coherence times can be understood within the dressed-state picture, suggesting that TLS defects classified as incoherent could be made to cross into the coherent regime through tuning.

Future Directions

Characterizing these TLS defects requires resolving coherent dynamics with frequency precision below 1 MHz over delay times from microseconds to milliseconds. Future work should focus on strain tuning and biasing the qubit near its flux-insensitive sweet spot to reduce dephasing noise that obscures slow chevron oscillations. The tools introduced will become important as TLS characterization scales to large device volumes.

Summary of Key Parameters

The analysis extracted the dressed gap 2g and the TLS relaxation time TTLS 1 for each detected Rabi chevron. The coupling regime selected longer-lived defects, with a median TTLS 1 of approximately 10 µs. The relationship between the measured rate Γv and the predicted qubit Ramsey rate 1/T∗ 2 is tested, showing that Γv < 1/T∗ 2 for 77 of the 88 resolved TLSs.

Device Group Summary

The study characterized 16 flux-tunable transmon qubits on 5 aluminum-on-silicon chips, grouping them into four device groups based on their fabrication process. The device groups showed variations in qubit TQ 1 and TLS relaxation times, with some qubits being Purcell limited. The analysis of the predicted qubit Ramsey rate versus the measured dressed-gap decoherence rate shows a monotone device gradient across the four groups.

Noise Amplitude Calibration

The flux noise amplitude AΦ was calibrated using independent Ramsey measurements at three different qubit T∗ 2 anchors: 4.2, 8.2, and 16 µΦ0. The median implied amplitude from the analysis is 33 µΦ0, which is high compared to reported values. This calibration anchors the predicted qubit Ramsey rate against the measured dressed-gap decoherence rate.

Final Conclusion

The paper concludes that high-sensitivity SWAP spectroscopy enables the detection of Rabi chevrons at coupling rates typically associated with the incoherent regime. They extend coherent detection to swap rates of ∼ 0.1 MHz, where the median TLS energy-relaxation time is 10 µs. The long swap coherence times can be understood within the dressed-state picture, suggesting that TLS defects classified as incoherent could be made to cross into the coherent regime through tuning.

Device Group Table Summary

The 118 Rabi chevrons were grouped into four device groups based on their process, with Device 2 pooling two nominally identical chips. The table summarizes the number of chevrons in each group and the corresponding TLS relaxation times TTLS 1.

Device Group Summary Table

The table S3 summarizes the device groups contributing the 118 Rabi chevrons of Fig. 4, in the order used as columns in Figs. S3 and S4. It lists the device process, qubit type, TLS count, and resolved Γv.

Improvements for AI systems

  1. Improve qubit characterization by resolving coherent TLS dynamics at sub-MHz rates, enabling detection of coherent TLSs with a median energy-relaxation time of 10 µs. This allows for precise determination of defect properties previously only accessible in the strongly coupled regime, moving beyond incoherent TLSs characterization.

  2. Develop ultra-sensitive quantum sensing capabilities by utilizing the Fast-Flux-Assisted (FFA) pulse sequence to enable SWAP spectroscopy with a 0.1 MHz frequency step and delay times up to 1 ms, allowing for coherent detection of TLS exchange at rates as low as 0.1 MHz, an order of magnitude lower than previously reported.

  3. Enhance noise mitigation in superconducting circuits by leveraging the dressed-state picture to understand long swap coherence times, where the dressed gap protects them from low-frequency 1/f noise, providing a theoretical basis for suppressing decoherence in dual-rail architectures and spin-locked driven qubits.

  4. Improve defect identification by employing time-domain sampling via 51 logarithmically spaced delay times spanning 10−1 to 103 µs combined with the Lomb–Scargle analysis to capture the full dynamics of P1(τ) and avoid misinterpreting oscillatory decay as purely incoherent.

  5. Refine qubit control fidelity by implementing pulse sequences that use net zero shaping for fast flux pulses, which are shaped to be net zero, carrying reduced spectral weight at ∼kHz frequencies and thereby suppressing slow transients in the flux control line.

Sources

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