Quasiparticle-induced transitions in a fluxonium qubit

Benjamin Byrd; Gianluigi Catelani; Ivan V. Pechenezhskiy; Kesavan Manivannan; Maksim Litskevich; Pavel D. Kurilovich; Vladislav D. Kurilovich

Quasiparticle-induced transitions in a fluxonium qubit

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Quasiparticle-induced transitions in a fluxonium qubit are governed by the superconducting gap difference between the junction leads, not by an imbalance in quasiparticle densities.

desk verdict Careful, novel fluxonium injection experiment in which gap asymmetry plausibly resolves the apparent QP-density imbalance, though the thermal-QP assumption and one unquantified ratio keep it from being fully airtight. read the letter →

arxiv 2607.21329 v2 pith:WXCU4ZS7 submitted 2026-07-23 quant-ph

Maksim Litskevich , Kesavan Manivannan , Benjamin Byrd , Pavel D. Kurilovich , Vladislav D. Kurilovich , Gianluigi Catelani , Ivan V. Pechenezhskiy This is my paper · ORCID

classification quant-ph

keywords fluxoniumqubitquasiparticle-induceddecoherencesuperconductinggapasymmetryquasiparticletunnelinginjectionJosephsonjunctionarrayenergyrelaxationtransmon

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Fluxonium qubits are hard to protect from quasiparticles because, unlike transmons, they are insensitive to offset charge, so charge-parity detection is impossible. This paper measures quasiparticle-induced excitation and de-excitation rates under controlled on-chip injection and finds that the de-excitation rate as a function of magnetic flux has two comparable peaks, at the integer and half-integer flux quantum. The standard assumptions—equal superconducting gaps in the two junction leads and a narrow quasiparticle energy distribution—cannot explain this flux dependence. The authors' central claim is that the gap difference δΔ between the leads suppresses quasiparticle tunneling near the half-integer flux point, where the qubit transition energy is small; once δΔ is included, a one-parameter fit with equal quasiparticle densities in the small junction and the array reproduces the full flux dependence and yields x_qp = 3.6×10^-6. If correct, this resolves a long-standing apparent disparity between quasiparticle-density bounds for the small junction versus the junction array and suggests that gap engineering can suppress quasiparticle decoherence in fluxonium.

What carries the argument

The central object is the quasiparticle tunneling structure factor S±(ω) for a Josephson junction with unequal superconducting gaps ΔL and ΔH in its two leads. It enters the transition-rate formula together with flux-dependent matrix elements of sin(φ/2), cos(φ/2), and φ/2, which weight the small-junction and array contributions. The key mechanism is the combination of the gap difference δΔ = ΔH − ΔL with the energy width of the quasiparticle distribution: for de-excitation near the half-integer flux quantum, the condition k_BT_qp ≲ δΔ − ℏω01 leaves too few quasiparticle states available, suppressing the rate. The paper separately measures δΔ from a resonant peak in the |0⟩→|2⟩ rate when ℏω0

What would settle it

Measure the quasiparticle-induced transition rates with a readout that resolves states |3⟩ and higher: if the excess excitation rate near the half-integer flux quantum persists after separating leakage states, the leakage explanation fails and the thermal-Boltzmann-plus-gap-difference model would need revision; conversely, if the |0⟩→|1⟩ excitation rate drops to the predicted value, the model is confirmed. A more direct test of the δΔ mechanism would be to vary the lead-thickness asymmetry on co-fabricated devices and check that the half-integer-flux peak height tracks δΔ − ℏω01.

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Extended reading notes

Core claim

The central finding is that the superconducting gap difference δΔ between the two leads of a Josephson junction, which arises naturally when the aluminum films have different thicknesses, is essential for modeling quasiparticle-induced transitions in fluxonium. When the qubit transition energy ℏω01 is small compared with δΔ—which happens near the half-integer flux quantum—the gap difference strongly suppresses the quasiparticle-induced transition rate, making the half-integer-flux peak comparable to the integer-flux peak rather than several times larger. With δΔ/h = 1.72 GHz independently determined from a resonantly enhanced |0⟩→|2⟩ transition, and an effective quasiparticle temperature k_B

Load-bearing premise

The central fit assumes the injected quasiparticles follow a thermal Boltzmann energy distribution with a single effective temperature for both junction leads (Eq. 4), and that the quasiparticle density is the same in the small junction and the array; if the distribution is genuinely athermal, the same data can be reproduced by a different model, as the paper's own Appendix K2 demonstrates.

Editorial extensions

If this is right

Previous bounds on quasiparticle densities in fluxonia that assumed δΔ = 0 overestimated the array's sensitivity near the half-integer flux quantum; accounting for δΔ makes the inferred bound less tight, so the reported x_array ≪ x_small disparity may be an artifact of the model.
Gap engineering, already demonstrated in transmons, should also suppress quasiparticle-induced decoherence in fluxonium qubits.
A single quasiparticle density shared by the small junction and the junction array, x_qp = 3.6×10^-6, reproduces the full flux dependence of the measured de-excitation rate, and this value is consistent with the independently inferred transmon density of 3.0×10^-6.
The measured quasiparticle-induced excitation rate exceeds the model prediction near the half-integer flux quantum; the paper attributes this to leakage into higher qubit states misidentified as |1⟩ during readout, which motivates readout schemes that resolve those states.
The fluxonium results underscore that all relevant energy scales—ℏω01, δΔ, and δE_qp—must be retained when analyzing quasiparticle-induced relaxation in low-frequency qubits.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own Appendix K2 shows that an athermal quasiparticle distribution with different chemical potentials per lead can also reproduce the same data; a clean test would be to measure the quasiparticle distribution width directly, for example by probing transitions out of higher fluxonium states after injection.
The resonant |0⟩→|2⟩ enhancement when ℏω02 = δΔ offers a new spectroscopic probe of junction gap asymmetry that could be applied to other fluxonium devices without destructive fabrication measurements.
Because δΔ depends on the thickness of the aluminum films, fabricating junctions with a controlled lead-thickness asymmetry could be used as a deliberate engineering knob to suppress quasiparticle-induced transitions at the half-integer flux point; the paper demonstrates the effect but does not perform such a systematic test.
Re-analyzing historical fluxonium T1 data with δΔ ≠ 0 and a finite quasiparticle energy width might change inferred quasiparticle-density bounds for devices where the two junction leads have different thicknesses.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is a well-executed experiment with a plausible central claim—gap asymmetry δΔ, not unequal quasiparticle densities, explains why the HFQ peak in ΔΓ↓ is not three to four times the IFQ peak. The controlled on-chip injection plus quasi-instantaneous rate extraction is genuinely new for fluxonium, and the measurement of a resonant ΔΓ02 peak at ω02/2π≈1.72 GHz is a nice independent handle on δΔ. I came away believing the main conclusion is probably right.

What the paper does well: it isolates QP-induced rates by subtracting background and fitting short-time dynamics rather than doing a standard T1; it separately extracts T_qp from a co-fabricated transmon; it shows the simplified equal-gap model (Appendix H) gives x_array << x_small and then demonstrates that accounting for δΔ removes that apparent imbalance. The four-qubit comparison in the appendices gives the analysis some breadth. The treatment of the apparent rate inversion is honest: they do not claim to resolve it quantitatively, and they flag leakage as the likely cause while testing an athermal alternative.

Soft spots, in proportion. The stress-test note is right that the flux dependence of ΔΓ↓ alone cannot distinguish δΔ + equal densities from δΔ = 0 + unequal densities. It is also right that the load-bearing thermal-Boltzmann T_qp comes from the transmon, not from a direct measurement of the fluxonium QP distribution. But the paper does not merely assert this—the finite ΔΓ↑ and the independent ΔΓ02 resonance provide some support, and the athermal model in Appendix K2 is rejected on physical timescale grounds. That rejection is reasonable, not airtight. A skeptic can still demand a direct measurement of the QP energy distribution or a leakage-resolved readout. The x_array/x_small = 1.2 result is presented without uncertainty, which is a smaller but real gap. And no data or code are released, so the extraction procedure cannot be independently checked. All of these are addressable; none looks fatal to the δΔ explanation.

Who this is for: people working on quasiparticle loss in fluxonium and on gap engineering generally. It deserves a serious referee—I would send it out. My own verdict would be conditional: accept after the authors provide error bars on the density ratio and either quantify leakage with a higher-state readout or soften the claim on the excitation-rate comparison.

Referee Report

3 major / 5 minor

Summary. The paper reports measurements of quasiparticle (QP) induced excitation and de-excitation rates in a fluxonium qubit under controlled on-chip QP injection. The authors isolate QP-induced rates by measuring quasi-instantaneous transition rates with and without injection, and map their dependence on external flux. The central claim is that a superconducting gap difference δΔ between the two leads of each Josephson junction, estimated independently from film thickness and from a resonant enhancement of the |0⟩→|2⟩ transition, plays an essential role in QP-induced transitions: near the half-integer flux quantum (HFQ), where the qubit frequency is small compared with δΔ, the gap difference suppresses the de-excitation rate. After including δΔ and assuming equal QP densities in the small junction and the array, a one-parameter fit reproduces the external-flux dependence of the measured de-excitation rate ΔΓ↓, yielding x_qp = 3.6×10^-6, consistent with an independent transmon estimate. The measured excitation rate ΔΓ↑ is only qualitatively reproduced; the discrepancy is attributed to leakage to higher qubit states that are misidentified during readout. An alternative athermal QP distribution model (Appendix K2) is shown to also reproduce the data, but the authors argue it is inconsistent with the transmon-inferred QP temperature and with relaxation-time expectations.

Significance. If the central claim holds, the work resolves a long-standing puzzle in fluxonium research: the apparent order-of-magnitude disparity between QP density bounds in the small junction and the junction array could be an artifact of neglecting gap asymmetry. It also demonstrates that gap engineering can suppress QP-induced decoherence in fluxonium, extending similar results in transmon qubits. The experimental methodology — controlled injection with quasi-instantaneous rate extraction and background subtraction — is a valuable contribution, and the independent determination of δΔ from the |0⟩→|2⟩ resonance is a particularly clean result. The paper is thorough, with extensive appendices, and the theoretical framework is carefully connected to prior work. However, the uniqueness of the δΔ interpretation is not fully established, because the same ΔΓ↓ data can be fit by a δΔ=0 model with unequal densities, and the alternative athermal model reproduces both ΔΓ↓ and ΔΓ↑. The central claim is therefore plausible and well supported but not uniquely determined by the presented data.

major comments (3)

[Sec. IV C and Appendix H, Table III, Fig. 9] The rejection of the δΔ=0, x_array≠x_small simplified model is not based on a quantitative statistical comparison of the fits to ΔΓ↓. The simplified model (Appendix H, Fig. 9) and the δΔ≠0 model (Fig. 4c) appear visually similar, and Table III reports different fitted densities but no fit-quality metrics (e.g., chi-square, AIC, or residuals). Since the central claim is that δΔ is 'necessary' to model the flux dependence, the paper should provide a direct comparison of goodness-of-fit for the two models on the ΔΓ↓ data. Without this, the claim that δΔ, rather than unequal densities, is essential is underdetermined by the de-excitation data alone.
[Sec. IV A and Appendix K2] The load-bearing step that rules out δΔ=0 is the argument that δE_qp≪ℏω01 is violated, based on the finite ΔΓ↑ and the transmon detailed-balance estimate k_B T_qp/h = 1.2 GHz. However, Appendix K2 presents an alternative narrow athermal distribution (δE_qp/h = 0.20 GHz, δμ/δΔ = 0.81) that reproduces both ΔΓ↓ and ΔΓ↑ with δΔ fixed and equal densities. The authors reject this alternative using the transmon-inferred width and relaxation-time estimates, but neither directly measures the QP energy distribution in the fluxonium array. To make the 'essential role of δΔ' claim conclusive, the paper should either provide a direct experimental constraint on the fluxonium QP distribution or weaken the wording from 'essential/necessary' to 'consistent with' and acknowledge that the data do not uniquely distinguish the thermal equal-density model with δΔ≠0 from the athermal model with δΔ≠0.
[Sec. IV D and Appendix K1] The quantitative discrepancy in ΔΓ↑ is attributed to leakage to higher qubit states that are misidentified as |1⟩. This explanation is plausible, and the three-level analysis in Appendix J shows that including |2⟩ does not resolve the inversion. However, no quantitative model of the apparent ΔΓ↑ under leakage is presented; the paper states that such a description 'would require additional parameters... beyond the scope of the present work.' Since the finite ΔΓ↑ is part of the evidence against δE_qp≪ℏω01, and since the leakage hypothesis is not directly verified, this is an acknowledged limitation of the excitation-rate analysis. The paper should state more prominently that the leakage scenario is a hypothesis, not a tested correction, and that the central conclusions rest on the ΔΓ↓ data.

minor comments (5)

[Fig. 4(c) caption] The caption says the red dotted curve is the prediction for ΔΓ↑, but the curve is computed without leakage corrections; consider adding 'in the two-level model' or 'neglecting leakage to higher states' for clarity.
[Table III] The third column reports x_qp from the δΔ≠0 model, but for Q1 the main-text one-parameter fit gives 3.6×10^-6 while Table III gives 3.1×10^-6 from a two-parameter fit with T_qp free. The difference should be noted in the table caption or text to avoid confusion.
[Sec. IV A] The transmon injection response that yields k_B T_qp/h = 1.2 GHz is stated in the main text; please specify explicitly that this measurement uses the same injection parameters (V_inj = 5.0 Δ_Al/e, t_inj = 4 μs) as the data in Fig. 4, or note the difference if not.
[Appendix K2, Eq. (K1)] The text equates δE_qp/h with the Boltzmann temperature T_qp of the athermal model, but the distribution also has a chemical potential offset. Clarify how δE_qp is defined for this model, especially because the comparison to the transmon width δE_qp/h ≈ 1.2 GHz assumes a common definition.
[Sec. V] The sentence 'This similarity deserves a comment' is informal; consider rewording to 'This equality is notable' or similar.

Circularity Check

1 steps flagged · score 2.0 of 10

No constructional circularity in the central fit; a minor model-selection caveat in the rejection of the athermal alternative keeps the score low.

other [Sec. IV A and Sec. IV D (with Appendix K 2, Eqs. (4) and (K1))]
"Using the detailed-balance relation ∆Γtr↑/∆Γtr↓ = e^{−ℏωtr01/kBTqp}, we estimate the effective QP temperature to be kBTqp/h≈1.2 GHz. ... This interpretation is also inconsistent with the broader width of the QP energy distribution δE_qp/h≈1.2 GHz inferred from the injection response of the transmon qubit."

The transmon-derived width δE_qp≈1.2 GHz is obtained by interpreting the transmon rate ratio through the thermal detailed-balance relation and the thermal Boltzmann form of Eq. (4). The alternative model being rejected in Appendix K2 is explicitly non-thermal, introducing chemical-potential offsets δμ (Eq. K1) that change the detailed-balance ratio. Using a thermal-model-derived width to rule out a non-thermal model presupposes the very thermal form the alternative challenges; the measured transmon ratio alone does not force δE_qp≈1.2 GHz when δμ≠0. This is an auxiliary model-selection argument, not a fitted parameter renamed as a prediction: the main ΔΓ↓ fit uses δΔ fixed by the independent ΔΓ02 resonance, and the no-adjustable-parameter ΔΓ↑ prediction visibly disagrees with data.

full rationale

The paper's central derivation is not circular by construction. The only free parameter in the main Sec. IV C fit is the common QP density x_qp, and it is used to fit the de-excitation rate ΔΓ↓; it is not relabeled as a prediction. The two decisive inputs, δΔ/h=1.72 GHz and k_BT_qp/h=1.2 GHz, are fixed by separate measurements: δΔ comes from the thickness estimate and the position of the ΔΓ02 resonance, and T_qp comes from the co-fabricated transmon detailed-balance ratio. The theoretical ΔΓ↑ curve contains no adjustable parameters and is not forced to match the data; in fact it visibly fails, which is evidence that the model is not being reverse-engineered to its target. The simplified δΔ=0 model can also fit ΔΓ↓, but the paper does not hide this; it explicitly discusses Appendix H and rejects that model using the finite ΔΓ↑ and the transmon temperature. The appendix K2 athermal alternative is likewise acknowledged. The circularity concern is limited to the rejection of that alternative: the transmon width used to reject it is itself inferred under the thermal-Boltzmann assumption, so the argument is somewhat question-begging. However, this step is auxiliary and does not determine the central δΔ conclusion, which has independent support. Accordingly, the paper is scored 2: no significant constructional circularity, with a minor caveat in the model-selection argument.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its load-bearing parameters are the fitted x_qp and the fitted x_array/x_small ratio, plus the assumed Boltzmann/QP-density constraints; the independent measurements of δΔ and T_qp keep the central fit from being a pure parameter sweep.

free parameters (3)

x_qp (common reduced quasiparticle density) = 3.6×10^-6 for Q1 one-parameter fit; Table III lists 3.1×10^-6 for the two-parameter fit
The single free parameter in the main fit to ΔΓ↓(Φ_ext) under the assumed equal densities and fixed δΔ, T_qp.
x_array/x_small ratio = 1.2
Second fit parameter when the equal-density constraint is relaxed; reported without uncertainty, and the text uses it to claim no appreciable imbalance.
T_qp (effective QP temperature) for Q2–Q4 = k_B T_qp/h = 1.2–2.1 GHz across Q1–Q4 in Appendix I
For Q1, T_qp is independently determined from the transmon; for Q2–Q4 it is a free fit parameter together with x_qp.

assumptions (4)

standard math The quasiparticle-induced transition-rate model of Eqs. (2)–(3), with BCS density of states and coherence factors, is correct for both the small junction and the array.
This is the established microscopic model imported from Catelani et al. [21] and Glazman–Catelani [30]; the paper derives only the simplified array limit in Appendix B.
domain assumption The injected quasiparticle distribution is Boltzmann with a single effective temperature T_qp, Eq. (4), on both the low- and high-gap sides.
Introduced in Sec. IV A to relax δE_qp ≪ ℏω01; the same data can be fit by an athermal two-chemical-potential distribution (Appendix K 2), so the Boltzmann form is a load-bearing modeling choice.
ad hoc to paper Equal quasiparticle densities in the small junction and the array, x_array = x_small, is imposed in the central one-parameter fit.
Sec. IV C imposes this constraint for the main fit; the paper then tests it with a second parameter and finds x_array/x_small ≈ 1.2, but the central conclusion is reached under the constraint.
domain assumption The ΔΓ02 peak at ω02/2π ≈ 1.72 GHz is the quasiparticle resonance ℏω02 = δΔ, and δΔ is also estimated from the film-thickness relation Δ(t) = Δ_bulk + a/t.
Sec. IV B and Appendix J 2 use this to set δΔ/h = 1.72 GHz; the thickness estimate (1.8 GHz) provides an independent check, but the identification assumes the model's resonant structure.

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Cite this review

Pith. "Pith review of Quasiparticle-induced transitions in a fluxonium qubit." pith.science (2026). https://pith.science/paper/WXCU4ZS7

@misc{pith2026260721329,
  author       = {Pith},
  title        = {Pith review of: Quasiparticle-induced transitions in a fluxonium qubit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WXCU4ZS7}},
  note         = {Machine review of arXiv:2607.21329}
}

read the original abstract

Quasiparticles are a prominent decoherence source in superconducting qubits, but their effects are notoriously difficult to isolate in fluxonium. Unlike the transmon, fluxonium is insensitive to offset charge, precluding charge-parity detection of quasiparticle tunneling. We address this challenge by measuring the excitation and de-excitation rates in a fluxonium qubit under controlled on-chip quasiparticle injection and isolating the quasiparticle-induced contribution by subtracting the background transition rates. We show that to accurately model the external magnetic flux dependence of the quasiparticle-induced transition rates, it is necessary to account for the superconducting gap asymmetry across the Josephson junctions. A comparison between theory and experiment constrains the relative quasiparticle densities in the small junction and the junction array and helps explain previously reported discrepancies between the bounds on the quasiparticle densities inferred for these two circuit elements.