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

Leakage Mobility and Passive Leakage Removal in Transmons with Tunable Couplers

Taneli Tolppanen , Gonzalo Mart\'in-V\'azquez , Sasu Tuohino , Matti Silveri This is my paper

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classification quant-ph
keywords leakage mobilitytransmon qubitstunable couplersleakage removalsuperconducting circuitsquantum error mitigationnonlinearity effects
0
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The pith

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

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

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.

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.

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.

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.

Where Pith is reading between the lines

These are 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.

Load-bearing premise

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

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.

Figures

Figures reproduced from arXiv: 2607.00688 by Gonzalo Mart\'in-V\'azquez, Matti Silveri, Sasu Tuohino, Taneli Tolppanen.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematics of the coupled transmon systems: Two [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Coupler detunings ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. 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 ↗
Figure 4
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] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Leakage removal performance of the three leakage removal schemes: [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
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] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Effective hopping strengths [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

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)
  1. [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'.
  2. [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

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.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 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.

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Reference graph

Works this paper leans on

53 extracted references · 53 canonical work pages

  1. [1]

    K. C. Miao, M. McEwen, J. Atalaya, D. Kafri, L. P. Pryadko, A. Bengtsson, A. Opremcak, K. J. Satzinger, Z. Chen, P. V. Klimov,et al., Overcoming leakage in quantum error correction, Nat. Phys.19, 1780 (2023)

    work page 2023

  2. [2]

    B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys.87, 307 (2015)

    work page 2015

  3. [3]

    Motzoi, J

    F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Simple pulses for elimination of leakage in weakly nonlinear qubits, Phys. Rev. Lett.103, 110501 (2009)

    work page 2009

  4. [4]

    Hyypp¨ a, A

    E. Hyypp¨ a, A. Veps¨ al¨ ainen, M. Papiˇ c, C. F. Chan, S. Inel, A. Landra, W. Liu, J. Luus, F. Marxer, C. Ockeloen- Korppi, S. Orbell, B. Tarasinski, and J. Heinsoo, Reducing leakage of single-qubit gates for superconducting quantum processors using analytical control pulse envelopes, PRX Quantum5, 030353 (2024)

    work page 2024

  5. [5]

    B. M. Varbanov, F. Battistel, B. M. Tarasinski, V. P. Ostroukh, T. E. O’Brien, L. DiCarlo, and B. M. Terhal, Leakage detection for a transmon-based surface code, npj Quantum Inf.6, 102 (2020)

    work page 2020

  6. [6]

    J. F. Marques, H. Ali, B. M. Varbanov, M. Finkel, H. M. Veen, S. L. M. van der Meer, S. Valles-Sanclemente, N. Muthusubramanian, M. Beekman, N. Haider, B. M. Terhal, and L. DiCarlo, All-microwave leakage reduction units for quantum error correction with superconducting transmon qubits, Phys. Rev. Lett.130, 250602 (2023)

    work page 2023

  7. [7]

    Marxer, J

    F. Marxer, J. Mro˙ zek, J. Andersson, L. Abdurakhimov, J. Adam, V. Bergholm, R. Beriwal, C. F. Chan, S. Dahl, S. R. Das,et al., Above 99.9% Fidelity Single-Qubit Gates, Two-Qubit Gates, and Readout in a Single Superconduct- ing Quantum Device, PRX Quantum7, 020333 (2026)

    work page 2026

  8. [8]

    A. G. Fowler, Coping with qubit leakage in topological codes, Phys. Rev. A88, 042308 (2013)

    work page 2013

  9. [9]

    J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wil- helm, Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator, Phys. Rev. A 83, 012308 (2011)

    work page 2011

  10. [10]

    Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Camp- bell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Nee- ley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, Measuring and suppressing quantum state leakage in a superconducti...

    work page 2016

  11. [11]

    M. A. Rol, F. Battistel, F. K. Malinowski, C. C. Bultink, B. M. Tarasinski, R. Vollmer, N. Haider, N. Muthusubra- manian, A. Bruno, B. M. Terhal, and L. DiCarlo, Fast, high-fidelity conditional-phase gate exploiting leakage in- terference in weakly anharmonic superconducting qubits, Phys. Rev. Lett.123, 120502 (2019)

    work page 2019

  12. [12]

    Camps, O

    J. Camps, O. Crawford, G. P. Geh´ er, A. V. Gramolin, M. P. Stafford, and M. Turner, Leakage Mobility in Su- perconducting Qubits as a Leakage Reduction Unit, Phys. Scr.101, 115107 (2026)

    work page 2026

  13. [13]

    Y. Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, et al., Qubit architecture with high coherence and fast tunable coupling, Phys. Rev. Lett.113, 220502 (2014)

    work page 2014

  14. [14]

    F. Yan, P. Krantz, Y. Sung, M. Kjaergaard, D. L. Camp- bell, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Tunable coupling scheme for implementing high-fidelity two-qubit gates, Phys. Rev. Appl.10, 054062 (2018)

    work page 2018

  15. [15]

    X. Li, T. Cai, H. Yan, Z. Wang, X. Pan, Y. Ma, W. Cai, J. Han, Z. Hua, X. Han, Y. Wu, H. Zhang, H. Wang, Y. Song, L. Duan, and L. Sun, Tunable coupler for realiz- ing a controlled-phase gate with dynamically decoupled regime in a superconducting circuit, Phys. Rev. Appl.14, 024070 (2020)

    work page 2020

  16. [16]

    Y. Sung, L. Ding, J. Braum¨ uller, A. Veps¨ al¨ ainen, B. Kan- nan, M. Kjaergaard, A. Greene, G. O. Samach, C. Mc- Nally, D. Kim,et al., Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler, Phys. Rev. X11, 021058 (2021)

    work page 2021

  17. [17]

    Marxer, A

    F. Marxer, A. Veps¨ al¨ ainen, S. W. Jolin, J. Tuorila, A. Lan- dra, C. Ockeloen-Korppi, W. Liu, O. Ahonen, A. Auer, et al., Long-distance transmon coupler with CZ-gate fi- delity above 99.8%, PRX Quantum4, 010314 (2023)

    work page 2023

  18. [18]

    Kjaergaard, M

    M. Kjaergaard, M. E. Schwartz, J. Braum¨ uller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Supercon- ducting Qubits: Current State of Play, Ann. Rev. Cond. Matt. Phys.11, 369 (2020)

    work page 2020

  19. [19]

    L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim,et al., High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler, Phys. Rev. X13, 031035 (2023). 21

    work page 2023

  20. [20]

    Zhang, C

    H. Zhang, C. Ding, D. Weiss, Z. Huang, Y. Ma, C. Guinn, S. Sussman, S. P. Chitta, D. Chen, A. A. Houck, J. Koch, and D. I. Schuster, Tunable inductive coupler for high- fidelity gates between fluxonium qubits, PRX Quantum 5, 020326 (2024)

    work page 2024

  21. [21]

    E. L. Rosenfeld, C. T. Hann, D. I. Schuster, M. H. Ma- theny, and A. A. Clerk, High-Fidelity Two-Qubit Gates between Fluxonium Qubits with a Resonator Coupler, PRX Quantum5, 040317 (2024)

    work page 2024

  22. [22]

    Mundada, G

    P. Mundada, G. Zhang, T. Hazard, and A. Houck, Sup- pression of qubit crosstalk in a tunable coupling super- conducting circuit, Phys. Rev. Appl.12, 054023 (2019)

    work page 2019

  23. [23]

    J. J. Wesdorp, E. Hyypp¨ a, J. Andersson, J. Adam, R. Beri- wal, V. Bergholm, S. Dahl, S. D. Fasciati, A. G. Friero, Z. Gao,et al., Mitigating crosstalk errors for simulta- neous single-qubit gates on a superconducting quantum processor, arXiv:2603.11018 (2026)

    work page arXiv 2026

  24. [24]

    A. H. Karamlou, I. T. Rosen, S. E. Muschinske, C. N. Barrett, A. Di Paolo, L. Ding, P. M. Harrington, M. Hays, R. Das, D. K. Kim, B. M. Niedzielski, M. Schuldt, K. Serniak, M. E. Schwartz, J. L. Yoder, S. Gustavs- son, Y. Yanay, J. A. Grover, and W. D. Oliver, Probing entanglement in a 2D hard-core Bose–Hubbard lattice, Nature629, 561 (2024)

    work page 2024

  25. [25]

    A. A. Chapple, O. Benhayoune-Khadraoui, S. Richer, and A. Blais, Balanced cross-Kerr coupling for superconduct- ing qubit readout, Phys. Rev. Lett.135, 256002 (2025)

    work page 2025

  26. [26]

    Beaulieu, J.-Z

    G. Beaulieu, J.-Z. Chen, M. Scigliuzzo, O. Benhayoune- Khadraoui, A. A. Chapple, P. A. Spring, A. Blais, and P. Scarlino, Fast, high-fidelity transmon readout with intrinsic purcell protection via nonperturbative cross-kerr coupling, arXiv:2601.04975 (2026)

    work page arXiv 2026

  27. [27]

    Wang, F.-M

    C. Wang, F.-M. Liu, H. Chen, Y.-F. Du, C. Ying, J.-W. Wang, Y.-H. Huo, C.-Z. Peng, X. Zhu, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, Longitudinal and nonlinear coupling for high-fidelity readout of a superconducting qubit, Phys. Rev. Lett.135, 060803 (2025)

    work page 2025

  28. [28]

    Stehlik, D

    J. Stehlik, D. M. Zajac, D. L. Underwood, T. Phung, J. Blair, S. Carnevale, D. Klaus, G. A. Keefe, A. Carniol, M. Kumph, M. Steffen, and O. E. Dial, Tunable coupling architecture for fixed-frequency transmon superconduct- ing qubits, Phys. Rev. Lett.127, 080505 (2021)

    work page 2021

  29. [29]

    E. A. Sete, A. Q. Chen, R. Manenti, S. Kulshreshtha, and S. Poletto, Floating tunable coupler for scalable quantum computing architectures, Phys. Rev. Appl.15, 064063 (2021)

    work page 2021

  30. [30]

    Magesan and J

    E. Magesan and J. M. Gambetta, Effective hamiltonian models of the cross-resonance gate, Phys. Rev. A101, 052308 (2020)

    work page 2020

  31. [31]

    Kandala, K

    A. Kandala, K. X. Wei, S. Srinivasan, E. Magesan, S. Carnevale, G. A. Keefe, D. Klaus, O. Dial, and D. C. McKay, Demonstration of a high-fidelity CNOT gate for fixed-frequency transmons with engineered ZZ suppres- sion, Phys. Rev. Lett.127, 130501 (2021)

    work page 2021

  32. [32]

    Mart´ ın-V´ azquez, T

    G. Mart´ ın-V´ azquez, T. Tolppanen, and M. Silveri, Passive leakage removal unit based on a disordered transmon array, Phys. Rev. A112, 032408 (2025)

    work page 2025

  33. [33]

    Mart´ ın-V´ azquez, T

    G. Mart´ ın-V´ azquez, T. Tolppanen, and M. Silveri, Phase transitions induced by standard and feedback measure- ments in transmon arrays, Phys. Rev. B109, 214308 (2024)

    work page 2024

  34. [34]

    Mercurio, Y.-T

    A. Mercurio, Y.-T. Huang, L.-X. Cai, Y.-N. Chen, V. Savona, and F. Nori, QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems, Quantum9, 1866 (2025)

    work page 2025

  35. [35]

    Bravyi, D

    S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Ann. Phys.326, 2793 (2011)

    work page 2011

  36. [36]

    Espin´ os, I

    H. Espin´ os, I. Panadero, J. J. Garc´ ıa-Ripoll, and E. Tor- rontegui, Quantum control of tunable-coupling transmons using dynamical invariants of motion, Quantum Sci. Tech- nol.8, 025017 (2023)

    work page 2023

  37. [37]

    Chu and F

    J. Chu and F. Yan, Coupler-assisted controlled-phase gate with enhanced adiabaticity, Phys. Rev. Appl.16, 054020 (2021)

    work page 2021

  38. [38]

    Vall´ es-Sanclemente, T

    S. Vall´ es-Sanclemente, T. H. F. Vroomans, T. R. van Ab- swoude, T. Stavenga, F. Brulleman, S. L. M. van der Meer, Y. Xin, A. Lawrence, V. Singh, M. A. Rol, and L. DiCarlo, Optimizing the frequency positioning of tunable couplers in a circuit QED processor to mitigate spectator effects on quantum operations, Phys. Rev. Lett.136, 200801 (2026)

    work page 2026

  39. [39]

    L. Chen, S. P. Fors, Z. Yan, A. Ali, T. Abad, A. Osman, E. Moschandreou, B. Lienhard, S. Kosen, H.-X. Li,et al., Fast unconditional reset and leakage reduction in fixed- frequency transmon qubits, arXiv:2409.16748 (2024)

    work page arXiv 2024

  40. [40]

    X. Yang, J. Chu, Z. Guo, W. Huang, Y. Liang, J. Liu, J. Qiu, X. Sun, Z. Tao, J. Zhang,et al., Coupler-Assisted Leakage Reduction for Scalable Quantum Error Correc- tion with Superconducting Qubits, Phys. Rev. Lett.133, 170601 (2024)

    work page 2024

  41. [41]

    Blais, A

    A. Blais, A. L. Grimsmo, S. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys.93, 025005 (2021)

    work page 2021

  42. [42]

    D. Sank, Z. Chen, M. Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Mutus, M. Neeley,et al., Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation, Phys. Rev. Lett.117, 190503 (2016)

    work page 2016

  43. [43]

    Shillito, A

    R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. Lewis, G. Vidal, and A. Blais, Dynam- ics of transmon ionization, Phys. Rev. Appl.18, 034031 (2022)

    work page 2022

  44. [44]

    Cohen, A

    J. Cohen, A. Petrescu, R. Shillito, and A. Blais, Rem- iniscence of classical chaos in driven transmons, PRX Quantum4, 020312 (2023)

    work page 2023

  45. [45]

    Khezri, A

    M. Khezri, A. Opremcak, Z. Chen, K. C. Miao, M. McEwen, A. Bengtsson, T. White, O. Naaman, D. Sank, A. N. Korotkov, Y. Chen, and V. Smelyanskiy, Measurement-induced state transitions in a superconduct- ing qubit: Within the rotating-wave approximation, Phys. Rev. Appl.20, 054008 (2023)

    work page 2023

  46. [46]

    M. F. Dumas, B. Groleau-Par´ e, A. McDonald, M. H. Mu˜ noz-Arias, C. Lled´ o, B. D’Anjou, and A. Blais, Measurement-induced transmon ionization, Phys. Rev. X14, 041023 (2024)

    work page 2024

  47. [47]

    Thorbeck, A

    T. Thorbeck, A. McDonald, O. Lanes, J. Blair, G. Keefe, A. A. Stabile, B. Royer, L. C. G. Govia, and A. Blais, High-fidelity gates in a transmon using bath engineering for passive leakage reset, arXiv:2411.04101 (2024)

    work page arXiv 2024

  48. [48]

    C. C. Bultinket al., Protecting quantum entanglement from leakage and qubit errors via repetitive parity mea- surements, Sci. Adv.6, eaay3050 (2020)

    work page 2020

  49. [49]

    McEwenet al., Removing leakage-induced correlated errors in superconducting quantum error correction, Nat

    M. McEwenet al., Removing leakage-induced correlated errors in superconducting quantum error correction, Nat. Commun.12, 1761 (2021)

    work page 2021

  50. [50]

    Y. Xin, S. L. M. van der Meer, M. Serra-Peralta, T. H. F. 22 Vroomans, M. Finkel, H. M. Veen, M. W. Beekman, and L. DiCarlo, Improved error correction with leakage reduc- tion units built into qubit measurement in a supercon- ducting quantum processor, arXiv:2511.17460 (2025)

    work page arXiv 2025

  51. [51]

    Lacroix, L

    N. Lacroix, L. Hofele, A. Remm, O. Benhayoune- Khadraoui, A. McDonald, R. Shillito, S. Lazar, C. Hellings, F. Swiadek, D. Colao-Zanuz,et al., Fast flux- activated leakage reduction for superconducting quantum circuits, Phys. Rev. Lett.134, 120601 (2025)

    work page 2025

  52. [52]

    M. D. Reed, B. R. Johnson, A. A. Houck, L. DiCarlo, J. M. Chow, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, Fast reset and suppressing spontaneous emission of a su- perconducting qubit, App. Phys. Lett.96, 203110 (2010)

    work page 2010

  53. [53]

    Y. Zhou, Z. Zhang, Z. Yin, S. Huai, X. Gu, X. Xu, J. All- cock, F. Liu,et al., Rapid and unconditional parametric reset protocol for tunable superconducting qubits, Nat. Commun.12, 5924 (2021)

    work page 2021