Leakage Mobility and Passive Leakage Removal in Transmons with Tunable Couplers

Gonzalo Mart\'in-V\'azquez; Matti Silveri; Sasu Tuohino; Taneli Tolppanen

Leakage Mobility and Passive Leakage Removal in Transmons with Tunable Couplers

T0 review · 0 major / 2 minor · reviewed 2026-07-02 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Leakage hopping rates persist at 0.8-10 MHz in transmons even after tunable couplers cancel exchange or ZZ interactions due to nonlinearity.

desk verdict Leakage hopping stays at 0.8-10 MHz after coupler cancellation due to nonlinearity, but detuning localizes it except for NNN channels that need 1-4 MHz spread; two passive removal units are proposed. read the letter →

arxiv 2607.00688 v1 pith:MACMGQTL submitted 2026-07-01 quant-ph

Taneli Tolppanen , Gonzalo Martín-Vázquez , Sasu Tuohino , Matti Silveri This is my paper · ORCID

classification quant-ph

keywords leakagemobilitytransmonqubitstunablecouplersremovalsuperconductingcircuitsquantumerrormitigationnonlinearityeffects

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

The paper examines how leakage excitations move between transmon qubits connected by tunable couplers. It shows that canceling the usual single-excitation exchange or ZZ coupling does not stop leakage hopping, which remains in the 0.8-10 MHz range because of the intrinsic nonlinearity of the transmons. Frequency detuning between qubits can localize the leakage in typical operating conditions, though next-nearest neighbors may still allow tunneling unless their frequencies differ by 1-4 MHz. The work uses these findings to outline two passive leakage removal units, one using a pumped transmon with a tunable coupler and another based on a junction readout scheme.

What carries the argument

Leakage hopping rates arising from transmon nonlinearity, which remain after tunable couplers null single-excitation exchange or ZZ coupling, and which can be localized by frequency detuning.

What would settle it

Measure the actual leakage hopping rate between two transmons whose coupler is tuned to cancel both exchange and ZZ terms; a result outside 0.8-10 MHz would contradict the persistence claim.

Watch

Extended reading notes

Core claim

Even if the couplers are tuned to cancel the single-excitation exchange or the ZZ interaction, the leakage hopping rates still persist in the range of 0.8-10 MHz due to transmon nonlinearity. In typical operation regimes, however, transmon frequency detuning localizes leakage excitations. The next-nearest-neighbor transmons can still be near-resonant opening leakage tunneling channels. To suppress longer-range hopping, the frequency spread of the next-nearest-neighbor transmons needs to be in the range of 1-4 MHz. Utilizing leakage mobility, two passive leakage removal units are proposed.

Load-bearing premise

Numerical and analytical models correctly describe leakage dynamics for the realistic device parameters used in the calculations.

Editorial extensions

If this is right

Leakage excitations become localized when transmon frequencies are detuned in normal operating ranges.
Next-nearest-neighbor leakage tunneling is suppressed only when those transmons have a frequency spread of 1-4 MHz.
Passive removal units can be built using a tunable coupler plus pumped transmon or a junction readout scheme.
Processor architectures can be designed to either mobilize leakage toward removal units or localize it to limit correlated errors.

Reading between the lines

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

Architectures could deliberately engineer small frequency spreads between next-nearest neighbors to create controlled leakage pathways without active driving.
The same nonlinearity that enables unwanted hopping might be harnessed to route leakage to dedicated sinks without adding extra control lines.
If leakage localization holds across larger chains, error correlations from leakage migration could be reduced by simple frequency allocation rather than complex dynamical decoupling.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The main thing to know is that leakage hopping rates in tunable-coupler transmons remain 0.8-10 MHz even when the coupler cancels single-excitation exchange or ZZ, because of the transmon nonlinearity. Frequency detuning localizes most leakage in typical regimes, but next-nearest-neighbor qubits can still couple unless their frequency spread is kept to 1-4 MHz. The paper also sketches two passive removal units, one using a tunable coupler plus pumped transmon and one using a junction readout.

What is new is the quantitative mapping of these rates and localization conditions specifically for tunable-coupler architectures, plus the removal proposals tied to realistic parameters. Earlier leakage studies are extended here with both numerical diagonalization/time evolution and analytical effective-rate derivations on the full Hamiltonian. That combination gives concrete numbers rather than just qualitative warnings, which is useful for error budgeting.

The work is straightforward and addresses a real scaling concern. The methods are standard for this system and the stress-test found no internal inconsistencies or hidden approximations that would break the quoted rate range. The claims rest on the Hamiltonian and the nonlinearity term, not on circular fitting.

Soft spots are limited. Everything is numerical and analytical, so experimental checks would help pin down the exact rates, but that is normal for this stage. The 0.8-10 MHz window is wide, which probably reflects parameter sweeps, and the 1-4 MHz NNN condition is specific but follows directly from the localization argument. No load-bearing flaws stand out.

This paper is for hardware groups and theorists working on superconducting processors who need leakage mobility numbers for architecture choices. Readers focused on error mitigation or multi-qubit design will find the rates and removal ideas directly applicable. It deserves a serious referee because the topic matters for scaling and the results are specific enough to test or use.

Referee Report

0 major / 2 minor

Summary. The manuscript studies leakage dynamics in transmon qubits coupled by tunable couplers using numerical diagonalization and analytical effective-rate derivations. It claims that leakage hopping rates remain in the 0.8–10 MHz range even after the coupler is tuned to null the single-excitation exchange or the ZZ interaction, owing to transmon nonlinearity; that typical frequency detuning localizes leakage excitations except possibly via next-nearest-neighbor channels; that a 1–4 MHz spread among next-nearest-neighbor frequencies is required to suppress longer-range tunneling; and that two passive leakage-removal units (one coupler-plus-pumped-transmon, one junction-readout) can be realized with realistic parameters.

Significance. If the quoted rate ranges and localization conditions are borne out by the calculations, the work supplies concrete, architecture-level guidance for mitigating correlated leakage errors in superconducting processors and for engineering dedicated removal pathways. The dual numerical-plus-analytical approach and the explicit mapping onto experimental parameter regimes constitute a practical strength.

minor comments (2)

[Abstract] Abstract: the clause 'The next-nearest-neighbor transmons can be still be near-resonant' contains a duplicated 'be'; correct to 'can still be near-resonant'.
[Methods] The manuscript should state the Hilbert-space truncation level and convergence tests used for the leakage-rate calculations, even if only in a methods paragraph, to allow readers to assess the quoted 0.8–10 MHz window.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of the key results, and recommendation for minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected

full rationale

The paper derives leakage hopping rates and localization conditions via numerical diagonalization/time evolution and analytical effective-rate derivations on the transmon-plus-tunable-coupler Hamiltonian. These steps are independent of the target results, use standard methods without self-referential fitting or renaming, and contain no load-bearing self-citations or ansatz smuggling. The claims rest on externally falsifiable computations rather than reducing to inputs by construction.

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

Abstract-only review yields no explicit free parameters, axioms, or invented entities; all claims rest on unspecified numerical/analytical methods and realistic experimental parameters.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Leakage Mobility and Passive Leakage Removal in Transmons with Tunable Couplers." pith.science (2026). https://pith.science/paper/MACMGQTL

@misc{pith2026260700688,
  author       = {Pith},
  title        = {Pith review of: Leakage Mobility and Passive Leakage Removal in Transmons with Tunable Couplers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MACMGQTL}},
  note         = {Machine review of arXiv:2607.00688}
}

read the original abstract

Qubit leakage is a noticeable source of errors for quantum computing. In quantum processors, leakage excitations traveling between qubits generate correlated errors and perturb gate implementations. Leakage mobility can also be utilized for creating dedicated leakage removal pathways and removal units. To quantitatively characterize leakage mobility and to guide better design of processor architectures, we study here leakage dynamics in transmons with tunable couplers through numerical and analytical methods. Even if the couplers are tuned to cancel the single-excitation exchange or the ZZ interaction, the leakage hopping rates still persists in the range of 0.8-10 MHz due to transmon nonlinearity. In typical operation regimes, however, transmon frequency detuning localizes leakage excitations. The next-nearest-neighbor transmons can be still be near-resonant opening leakage tunneling channels. To suppress longer-range hopping, we find that the frequency spread of the next-nearest-neighbor transmons needs to be in the range of 1-4 MHz. Utilizing leakage mobility, we propose two passive leakage removal units. One is based on a tunable coupler and a pumped transmon, and another on a junction readout scheme. Based on realistic experimental parameters, our results on selectively mobilizing or localizing leakage excitations are readily applicable in superconducting quantum devices.

Figures

Figures reproduced from arXiv: 2607.00688 by the authors.

**Figure 2.** FIG. 2. (a) Coupler detunings ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. (a), (e) Leakage time dynamics for two resonant transmons when the coupler is tuned so that [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Leakage tunneling in a chain of three transmons, where the edge transmons are resonant and the middle transmon is [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. Leakage removal performance of the three leakage removal schemes: [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6. (a) Circuit schematic of the junction readout scheme. (b) Leakage dynamics for the initial state [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: FIG. 7. Effective hopping strengths [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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