Pith. sign in

REVIEW 2 major objections 4 minor 69 references

A general periodic flux drive can jointly optimize a fluxonium qubit's relaxation and dephasing lifetimes, pushing dephasing past 7 ms while establishing a fundamental ceiling on relaxation.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

Optimized arbitrary periodic flux waveforms yield Pareto-optimal T1/Tphi trade-offs and an upper bound on T1 for superconducting fluxonium qubits.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection Useful and novel Pareto-front engineering framework for fluxonium DSSs, but the advertised fundamental bound (Theorem 1, T_UB^(2)) is not proven as stated—a repair or downgrade is needed. the 2 major comments →

arxiv 2601.19209 v2 pith:ZH6NXQYQ submitted 2026-01-27 quant-ph

Pareto Front Engineering of Dynamical Sweet Spots in Superconducting Qubits

Zhen Yang , Shan Jin , Yajie Hao , Guangwei Deng , Xiu-Hao Deng , Re-Bing Wu , Xiaoting Wang This is my paper
classification quant-ph
keywords fluxonium qubitsdynamical sweet spotsPareto-front optimizationFloquet theoryflux noisedielectric losscoherence timesquantum gates
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 argues that the old trade-off between energy relaxation and pure dephasing at dynamical sweet spots (transition frequencies made first-order insensitive to low-frequency flux noise) can be broken by treating the periodic flux waveform as fully tunable. It builds a T1–Tφ Pareto front for fluxonium qubits under 1/f flux noise plus dielectric loss, and finds dephasing times up to 7398 µs — three to five times longer than existing dynamical-sweet-spot schemes — while keeping relaxation times above 500 µs. The same analysis produces Theorem 1, claiming that no periodic drive can make relaxation arbitrarily slow: T1 has a universal upper bound, and a closed-form version holds at a dynamical sweet spot. If these results hold up, they give experimenters both a practical design method and a fundamental benchmark for how much coherence can be squeezed from flux modulation.

Core claim

Under the most general periodic flux drive, formulated as an arbitrary Fourier series in the external flux, the paper shows that a multi-objective search over drive waveforms maps out a Pareto front between the relaxation rate γ1 and the pure-dephasing rate γz. Points on this front are dynamical sweet spots, where first-order sensitivity to low-frequency flux noise vanishes; a segment is a double-DSS, also insensitive to AC flux amplitude. The headline numerical claim is a dephasing lifetime of 7398 µs at a point where T1 remains 553 µs, and the structural claim is Theorem 1: T1 ≤ T_UB^(1) for every periodic drive, with the stronger closed-form T1 ≤ T_UB^(2) at a DSS (Eqs. (18)–(19)). The th

What carries the argument

The engine is the Floquet decomposition of the qubit's noise sensitivity. The coupling σz(t) is expanded in harmonics with weights g_z^(k) and g_±^(k), so that the dephasing and relaxation rates become weighted sums of the noise spectral density at the Bohr frequencies kωd and kωd ∓ Ω. The waveform enters through the Fourier coefficients p_n of the periodic flux drive, turning coherence engineering into a population-based multi-objective optimization problem with a normalization constraint on the g-weights. That constraint is what creates the trade-off and what ultimately feeds the upper-bound theorem.

Load-bearing premise

All quantitative claims rest on the assumed 1/f flux-noise plus dielectric-loss spectrum of Eq. (12) inside a second-order time-convolutionless Floquet master equation; if that model misses real device behavior the coherence gains and the T1 bound do not transfer, and the proof of Theorem 1 currently relies on an inequality in the supplement whose constant appears incorrect.

What would settle it

Calibrate Af and Ad on a fluxonium device, hold it at one of the reported Pareto points, and measure T1 and Tφ: if T1 exceeds the universal T_UB^(1) of Eq. (18), or if Tφ does not reach the predicted 3–5x improvement, the central claims fail. Independently, checking the inequality in Supplemental Eq. (S2) numerically for the relevant frequency range would settle whether the proof of Theorem 1 is valid as written.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Any periodic flux waveform, not just single- or two-tone drives, is subject to a fundamental ceiling on energy relaxation; the DSS version of Theorem 1 gives a closed-form benchmark for device design.
  • The optimized waveforms deliver Tφ three to five times longer than previous dynamical-sweet-spot strategies while T1 stays in the hundreds of microseconds, so the gains do not come at the cost of relaxation.
  • The double-DSS bands are first-order insensitive to both DC and AC flux, giving experimenters operating regions that should be stable against slow drifts in either bias.
  • Fast control is compatible with the long coherence times: an X gate in 10 ns and a √iSWAP gate in 28 ns reach simulated open-system fidelities of 99.9993% and 99.995% at the optimized points.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the universal bound survives scrutiny, further T1 improvement at a dynamical sweet spot must come from reducing noise amplitudes Af and Ad or changing materials, not from smarter waveforms — a testable consequence of the theorem.
  • The double-DSS criterion Σk p_k g_z^(k) ≈ 0 offers a cheap experimental check: measure how the transition frequency shifts with AC drive amplitude in any single- or two-tone device, without running the full Pareto optimization.
  • The n=5 Fourier-truncation results in the supplement show lower Tφ than n=4, which the authors attribute to incomplete convergence; running the same search with more generations would reveal whether the true Pareto front extends beyond 7398 µs or whether the headline value is a truncation artifact.
  • The closed-form DSS bound T_UB^(2) could be inverted before optimization to choose drive frequencies that permit the largest possible T1, a design step the paper does not explicitly exploit.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper develops a multi-objective optimization framework for fluxonium qubits under general periodic flux modulation, treating the Fourier coefficients of the drive as tunable parameters and optimizing the energy relaxation rate γ1 and pure dephasing rate γz with evolutionary algorithms. It reports a Pareto front with Tφ up to 7398 μs while maintaining T1 above 500 μs, identifies single- and double-DSS operating regions, and demonstrates high-fidelity X and √iSWAP gates under open-system dynamics. The paper also states Theorem 1, claiming a universal upper bound on T1 for arbitrary periodic drives and a closed-form, modulation-independent DSS upper bound. The proof is relegated to the Supplemental Material.

Significance. If the result holds, the Pareto-front method would be a practical design tool for coherence optimization, and Theorem 1 would establish a fundamental limit on T1 under periodic flux modulation. The manuscript contains substantial numerical work: explicit device and noise parameters, convergence checks for Floquet truncation (Fig. S3), aggregation of several multi-objective algorithms, and comparison rows reproducing earlier DSS results. The main advertised fundamental-limit claim, however, rests on a proof gap in the Supplement that must be repaired before the theorem can be accepted.

major comments (2)
  1. [Supplemental §IX, Eq. (S16)–(S17); main Eq. (19)] The transition from Eq. (S16) to Eq. (S17) replaces |1−Σ| in the denominator of Eq. (S7) by |1−U| with U=π²Δ²/(3ω_d²). This is valid only if U≤1. The proof establishes only Σ≤U; if U>1, the required inequality |1−Σ|≥|1−U| is false, e.g. for U=3.29 and Σ=0.5 one has 0.5<2.29. The allowed drive range ω_d∈[0.5Ω_ge,1.5Ω_ge] in §III.A does not exclude U>1 (for ω_d=Ω_ge/2 and Δ≈Ω_ge, U≈13.2). Consequently Theorem 1's closed-form DSS bound T_UB^(2) is not rigorously established. The theorem needs an explicit condition such as 3ω_d²≥π²Δ², or a different argument that also works when U>1; otherwise the claim of a modulation-independent fundamental limit should be qualified accordingly.
  2. [Main Eq. (18) and §III.B] The universal bound T_UB^(1) has denominator Σ_k|g_+^k|², so it does not by itself exclude arbitrarily long T1: if the filter weights vanish, the bound diverges. The text in §III.B says that a lower bound on S̃(ω) 'imposes an upper bound on T1', but a useful upper bound also requires a lower bound on the filter weights. For DSSs this is exactly what the argument leading to Eq. (S17) is supposed to supply, so the gap described above affects the advertised conclusion that the relaxation rate cannot be reduced arbitrarily close to zero. Please clarify the logical role of the DSS condition and state explicitly what additional assumption is needed.
minor comments (4)
  1. [Supplemental Eq. (S2)] AM–GM applied to the two terms of S̃(ω) gives 2/√π A_f(A_d|ω|)^{1/2}, not 2√π A_f(A_d|ω|)^{1/2}. The final T_UB^(1) in Eq. (S6)/(18) is unchanged after carrying the corrected constant, but the displayed inequality is false as written.
  2. [Supplemental Eq. (S20); main Eq. (20)] Using the definition g_z^k = (1/(2T))∫ Tr[σ_z τ_z(t)] e^{ikω_d t}dt in Eq. (10), the first-order perturbation result is δΩ/δA = 2Σ_k p_k g_z^k, not Σ_k p_k g_z^k. The factor 2 does not change the threshold-based double-DSS criterion, but the displayed formula should be corrected for consistency.
  3. [§III.A and Fig. S2] The PF is obtained from heuristic evolutionary algorithms with a fixed 2000-iteration stopping rule, and Fig. S2 shows that the n=5 PF is less complete than n=4. The wording 'maximal values' and 'optimal working points' should be softened to 'approximate Pareto front' unless a convergence certificate or a more systematic multi-start study is provided.
  4. [References] References [67] and [68] duplicate Refs. [60] and [62]. Please consolidate to avoid duplicate entries.

Circularity Check

0 steps flagged

No significant circularity: coherence times are optimization outputs, not fitted inputs; the Theorem 1 proof gap is a correctness issue, not a circular reduction.

full rationale

The paper's central derivation is self-contained within a stated Floquet-plus-noise model. The optimized Fourier coefficients p_n are free parameters; the reported T1 and Tphi values are computed from the decoherence rates (Eqs. (13)-(14)) evaluated at those optimized parameters, so the coherence times are outputs of the optimization, not fitted inputs or hidden calibration constants. The normalization condition in Eq. (17) is a mathematical identity used in the proof, not an imported target. The upper bound T_UB^(1) follows from a lower bound on the noise spectral density and is not constructed from the numerical coherence times; the closed-form T_UB^(2) is intended as an analytic consequence of that bound plus a bound on the Floquet filter weights. The skeptic-identified flaw in the proof of Theorem 1 (Supplemental Eqs. (S16) to (S17) replacing |1-Sigma| by |1-U| requires U <= 1, a condition not stated in the theorem) is an error in an inequality, which is a correctness risk rather than a circularity: the conclusion is not an input to its own derivation. No load-bearing self-citation or imported uniqueness theorem is present. The references to earlier DSS work ([40,43]) are external, independently published baselines, and the only co-author self-citation ([69]) is not load-bearing in the derivation. Reusing the same noise model both to define the optimization objectives and to report final coherence times is ordinary design optimization under an explicit model, not a 'prediction' obtained from a fitted subset of the same data. Therefore no circular step is exhibited.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper does not introduce new physical entities. Its quantitative claims rest on the Floquet master-equation noise model, the two-level approximation, and the supplied free parameters of the optimized waveform. The main added content is computational parameter selection; the 'fundamental bound' depends on the noise model and on a proof that currently contains an algebraic error.

free parameters (4)
  • Fourier coefficients p_0..p_4 of periodic flux waveform = DSS-1/DSS-2/DSS-3 sets in Supplement Table I
    Trainable parameters optimized to minimize γ1 and γz; their optimized values determine the reported coherence times and Pareto front.
  • Drive frequency ω_d = 0.99–1.13 Ω_ge for the three working points
    Chosen as part of the optimization in the range [0.5Ω_ge,1.5Ω_ge]; it directly enters the Floquet rates and the upper-bound formulas.
  • Fourier truncation order n = n=4
    Selected because 'n=4 yields the most complete PF'; n=5 was discarded due to incomplete convergence (Supplement Fig. S2), so the reported PF depends on this hand choice.
  • DSS and double-DSS numerical thresholds = |g_z^0|<10^-4; |Σ p_k g_z^k|<0.1
    Hand-chosen criteria used to declare DSS and double-DSS regions; changing thresholds changes the size of the claimed robust operating bands.
axioms (4)
  • domain assumption Second-order time-convolutionless (TCL) Floquet master equation and secular rate expressions (Eq. (8)–(13))
    The entire decoherence model, and therefore the optimization objectives and Theorem 1, relies on this open-system approximation and its Markovian limits.
  • domain assumption Two-level qubit-subspace truncation of fluxonium to {|g>,|e>} (Eq. (3))
    The effective Hamiltonian and all Pauli-operator expressions assume the higher fluxonium levels can be neglected; anharmonicity is only mentioned as a future practical consideration.
  • domain assumption 1/f flux noise plus dielectric-loss spectral density with 1 Hz and 3 GHz cutoffs (Eq. (12))
    The quantitative PF, coherence-time comparisons, and upper-bound constants are computed under this specific noise model; a different spectrum would change the results.
  • domain assumption First-order perturbation equivalence ∂Ω/∂φ_dc ∝ |g_z^0| as established in Ref. [40]
    Used to identify single-DSS points on the PF and to justify minimizing γz as a proxy for reaching DSS; the same structure is extended by perturbation theory to double-DSS in Supplement Section X.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Pareto Front Engineering of Dynamical Sweet Spots in Superconducting Qubits." pith.science (2026). https://pith.science/paper/ZH6NXQYQ

@misc{pith2026260119209,
  author       = {Pith},
  title        = {Pith review of: Pareto Front Engineering of Dynamical Sweet Spots in Superconducting Qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZH6NXQYQ}},
  note         = {Machine review of arXiv:2601.19209}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Operating superconducting qubits at dynamical sweet spots (DSSs) suppresses decoherence from low-frequency flux noise. A key open question is how long coherence can be extended under this strategy and what fundamental limits constrain it. Here we introduce a fully parameterized, multi-objective periodic-flux modulation framework that simultaneously optimizes energy relaxation $T_1$ and pure dephasing $T_\phi$, thereby quantifying the tradeoff between them. For fluxonium qubits with realistic noise spectra, our method enhances $T_\phi$ by a factor of 3-5 compared with existing DSS strategies while maintaining $T_1$ in the hundred-microsecond range. We further prove that, although DSSs eliminate first-order sensitivity to low-frequency noise, relaxation rate cannot be reduced arbitrarily close to zero, establishing an upper bound on achievable $T_1$. At the optimized working points, we identify double-DSS regions that are insensitive to both DC and AC flux, providing robust operating bands for experiments. As applications, we design single- and two-qubit control protocols at these operating points and numerically demonstrate high-fidelity gate operations. These results establish a general and useful framework for Pareto-front engineering of DSSs that substantially improves coherence and gate performance in superconducting qubits.

Figures

Figures reproduced from arXiv: 2601.19209 by Guangwei Deng, Re-Bing Wu, Shan Jin, Xiaoting Wang, Xiu-Hao Deng, Yajie Hao, Zhen Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Aggregated PF with Fourier truncation [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a). Control setup for implementing a single-qubit gate in the fluxonium system. (b). The circuit diagram of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a). Schematic of the two-qubit gate implementation between two fluxonium qubits. (b). The circuit diagram of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

69 extracted references · 3 linked inside Pith

  1. [1]

    Nakamura, Y

    Y. Nakamura, Y. A. Pashkin, and J. Tsai, nature398, 786 (1999)

    1999

  2. [2]

    J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, Science285, 1036 (1999)

    1999

  3. [3]

    Wallraff, D

    A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Nature431, 162 (2004)

    2004

  4. [4]

    Blais, R.-S

    A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A69, 062320 (2004)

    2004

  5. [5]

    Schuster, A

    D. Schuster, A. A. Houck, J. Schreier, A. Wallraff, J. Gambetta, A. Blais, L. Frunzio, J. Majer, B. John- son, M. Devoret,et al., Nature445, 515 (2007)

    2007

  6. [7]

    A. A. Houck, H. E. T¨ ureci, and J. Koch, Nature Physics 8, 292 (2012)

    2012

  7. [8]

    Riste, M

    D. Riste, M. Dukalski, C. Watson, G. De Lange, M. Tiggelman, Y. M. Blanter, K. W. Lehnert, R. Schouten, and L. DiCarlo, Nature502, 350 (2013)

    2013

  8. [9]

    Gong, M.-C

    M. Gong, M.-C. Chen, Y. Zheng, S. Wang, C. Zha, H. Deng, Z. Yan, H. Rong, Y. Wu, S. Li, F. Chen, Y. Zhao, F. Liang, J. Lin, Y. Xu, C. Guo, L. Sun, J. Clark, H. Wang, C. Peng, C.-Y. Lu, X. Zhu, and J.-W. Pan, Phys. Rev. Lett.122, 110501 (2019)

    2019

  9. [10]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell,et al., Nature574, 505 (2019)

    2019

  10. [11]

    Blais, A

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

    2021

  11. [12]

    Wu, W.-S

    Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen, X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan, M. Gong, C. Guo, C. Guo, S. Guo, L. Han, L. Hong, H.-L. Huang, Y.-H. Huo, L. Li, N. Li, S. Li, Y. Li, F. Liang, C. Lin, J. Lin, H. Qian, D. Qiao, H. Rong, H. Su, L. Sun, L. Wang, S. Wang, D. Wu, Y. Xu, K. Yan, W. Yang, Y. Yang, Y. Ye, J. Yin, C. Ying, J. Yu, C. Zh...

    2021

  12. [13]

    Z. Ni, S. Li, X. Deng, Y. Cai, L. Zhang, W. Wang, Z.- B. Yang, H. Yu, F. Yan, S. Liu,et al., Nature616, 56 (2023)

    2023

  13. [14]

    Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. Van Den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zale- tel, K. Temme,et al., Nature618, 500 (2023)

    2023

  14. [15]

    Bravyi, A

    S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, Nature627, 778 (2024)

    2024

  15. [16]

    Nature638, 920 (2025)

    2025

  16. [17]

    Putterman, K

    H. Putterman, K. Noh, C. T. Hann, G. S. MacCabe, S. Aghaeimeibodi, R. N. Patel, M. Lee, W. M. Jones, H. Moradinejad, R. Rodriguez,et al., Nature638, 927 (2025)

    2025

  17. [18]

    V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Science326, 113 (2009). 10

    2009

  18. [20]

    L. B. Nguyen, G. Koolstra, Y. Kim, A. Morvan, T. Chis- tolini, S. Singh, K. N. Nesterov, C. J¨ unger, L. Chen, Z. Pedramrazi, B. K. Mitchell, J. M. Kreikebaum, S. Puri, D. I. Santiago, and I. Siddiqi, PRX Quantum 3, 037001 (2022)

    2022

  19. [21]

    B. M. Terhal, Rev. Mod. Phys.87, 307 (2015)

    2015

  20. [22]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Phys. Rev. A86, 032324 (2012)

    2012

  21. [23]

    Preskill, Quantum2, 79 (2018)

    J. Preskill, Quantum2, 79 (2018)

    2018

  22. [24]

    Temme, S

    K. Temme, S. Bravyi, and J. M. Gambetta, Phys. Rev. Lett.119, 180509 (2017)

    2017

  23. [25]

    Yoshihara, K

    F. Yoshihara, K. Harrabi, A. O. Niskanen, Y. Nakamura, and J. S. Tsai, Phys. Rev. Lett.97, 167001 (2006)

    2006

  24. [26]

    J. M. Martinis, K. B. Cooper, R. McDermott, M. Steffen, M. Ansmann, K. D. Osborn, K. Cicak, S. Oh, D. P. Pap- pas, R. W. Simmonds, and C. C. Yu, Phys. Rev. Lett. 95, 210503 (2005)

    2005

  25. [27]

    Ithier, E

    G. Ithier, E. Collin, P. Joyez, P. J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Sch¨ on, Phys. Rev. B72, 134519 (2005)

    2005

  26. [28]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A76, 042319 (2007)

    2007

  27. [29]

    L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Manucharyan, Phys. Rev. X9, 041041 (2019)

    2019

  28. [30]

    Zhang, S

    H. Zhang, S. Chakram, T. Roy, N. Earnest, Y. Lu, Z. Huang, D. K. Weiss, J. Koch, and D. I. Schuster, Phys. Rev. X11, 011010 (2021)

    2021

  29. [31]

    E. A. Sete, M. J. Reagor, N. Didier, and C. T. Rigetti, Phys. Rev. Appl.8, 024004 (2017)

    2017

  30. [32]

    Viola, E

    L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett.82, 2417 (1999)

    1999

  31. [33]

    Khodjasteh and D

    K. Khodjasteh and D. A. Lidar, Phys. Rev. Lett.95, 180501 (2005)

    2005

  32. [34]

    Cywi´ nski, R

    L. Cywi´ nski, R. M. Lutchyn, C. P. Nave, and S. Das Sarma, Phys. Rev. B77, 174509 (2008)

    2008

  33. [35]

    G. S. Uhrig, Phys. Rev. Lett.98, 100504 (2007)

    2007

  34. [36]

    Pokharel, N

    B. Pokharel, N. Anand, B. Fortman, and D. A. Lidar, Phys. Rev. Lett.121, 220502 (2018)

    2018

  35. [37]

    C. Wang, C. Axline, Y. Y. Gao, T. Brecht, Y. Chu, L. Frunzio, M. H. Devoret, and R. J. Schoelkopf, Applied Physics Letters107, 162601 (2015)

    2015

  36. [38]

    Didier, E

    N. Didier, E. A. Sete, J. Combes, and M. P. da Silva, Phys. Rev. Appl.12, 054015 (2019)

    2019

  37. [39]

    J. A. Valery, S. Chowdhury, G. Jones, and N. Didier, PRX Quantum3, 020337 (2022)

    2022

  38. [40]

    Huang, P

    Z. Huang, P. S. Mundada, A. Gyenis, D. I. Schuster, A. A. Houck, and J. Koch, Phys. Rev. Appl.15, 034065 (2021)

    2021

  39. [41]

    P. S. Mundada, A. Gyenis, Z. Huang, J. Koch, and A. A. Houck, Phys. Rev. Appl.14, 054033 (2020)

    2020

  40. [42]

    Gandon, C

    A. Gandon, C. Le Calonnec, R. Shillito, A. Petrescu, and A. Blais, Phys. Rev. Appl.17, 064006 (2022)

    2022

  41. [43]

    Cheng, Y.-C

    J.-M. Cheng, Y.-C. Zhang, X.-F. Zhou, and Z.-W. Zhou, New Journal of Physics24, 123034 (2022)

    2022

  42. [44]

    Lauwens, K

    J. Lauwens, K. Moors, and B. Sor´ ee, Optimization of floquet fluxonium qubits with commensurable two-tone drives (2025), arXiv:2506.06002 [cond-mat.mes-hall]

    arXiv 2025

  43. [45]

    Frees, S

    A. Frees, S. Mehl, J. K. Gamble, M. Friesen, and S. Cop- persmith, npj Quantum Information5, 73 (2019)

    2019

  44. [46]

    Guo, S.-B

    Q. Guo, S.-B. Zheng, J. Wang, C. Song, P. Zhang, K. Li, W. Liu, H. Deng, K. Huang, D. Zheng,et al., Physical review letters121, 130501 (2018)

    2018

  45. [47]

    Pirkkalainen, S

    J.-M. Pirkkalainen, S. Cho, J. Li, G. Paraoanu, P. Hako- nen, and M. Sillanp¨ a¨ a, Nature494, 211 (2013)

    2013

  46. [48]

    D. D. Brise˜ no-Colunga, B. Bhandari, D. Das, L. B. Nguyen, Y. Kim, D. I. Santiago, I. Siddiqi, A. N. Jordan, and J. Dressel, Dynamical sweet and sour re- gions in bichromatically driven floquet qubits (2025), arXiv:2505.22606 [quant-ph]

    Pith/arXiv arXiv 2025

  47. [49]

    V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Science326, 113 (2009)

    2009

  48. [50]

    Kohler, T

    S. Kohler, T. Dittrich, and P. H¨ anggi, Phys. Rev. E55, 300 (1997)

    1997

  49. [51]

    Creffield, Phys

    C. Creffield, Phys. Rev. B67, 165301 (2003)

    2003

  50. [52]

    Su´ arez and M

    G. Su´ arez and M. Horodecki, Making non-markovian master equations accessible with approximate environ- ments (2025), arXiv:2506.22346 [quant-ph]

    Pith/arXiv arXiv 2025

  51. [53]

    V. E. Manucharyan, N. A. Masluk, A. Kamal, J. Koch, L. I. Glazman, and M. H. Devoret, Phys. Rev. B85, 024521 (2012)

    2012

  52. [54]

    P. V. Klimov, J. Kelly, Z. Chen, M. Neeley, A. Megrant, B. Burkett, R. Barends, K. Arya, B. Chiaro, Y. Chen, A. Dunsworth, A. Fowler, B. Foxen, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, E. Lucero, J. Y. Mutus, O. Naaman, C. Neill, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, S. Boixo, R. Babbush, V. N. Smelyanski...

    2018

  53. [55]

    Groszkowski, A

    P. Groszkowski, A. Di Paolo, A. L. Grimsmo, A. Blais, D. I. Schuster, A. A. Houck, and J. Koch, New Journal of Physics20, 043053 (2018)

    2018

  54. [56]

    A. Kou, W. C. Smith, U. Vool, R. T. Brierley, H. Meier, L. Frunzio, S. M. Girvin, L. I. Glazman, and M. H. De- voret, Phys. Rev. X7, 031037 (2017)

    2017

  55. [57]

    K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, IEEE Transactions on Evolutionary Computation6, 182 (2002)

    2002

  56. [58]

    Zitzler, M

    E. Zitzler, M. Laumanns, and L. Thiele, TIK report103 (2001)

    2001

  57. [59]

    K. Li, R. Chen, G. Fu, and X. Yao, IEEE Transactions on Evolutionary Computation23, 303 (2018)

    2018

  58. [60]

    Zitzler and S

    E. Zitzler and S. K¨ unzli, inParallel Problem Solving from Nature - PPSN VIII(Springer Berlin Heidelberg, Berlin, Heidelberg, 2004) pp. 832–842

    2004

  59. [61]

    Bader and E

    J. Bader and E. Zitzler, Evolutionary computation19, 45 (2011)

    2011

  60. [62]

    Zhang and H

    Q. Zhang and H. Li, Trans. Evol. Comp11, 712–731 (2007)

    2007

  61. [63]

    S.-Z. Zhao, P. N. Suganthan, and Q. Zhang, IEEE Trans- actions on Evolutionary Computation16, 442 (2012)

    2012

  62. [64]

    ColaLab, Emoc: Evolutionary multi-objective optimiza- tion in c++

  63. [65]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, Applied Physics Reviews6, 021318 (2019)

    2019

  64. [66]

    K. N. Nesterov, C. Wang, V. E. Manucharyan, and M. G. Vavilov, Phys. Rev. Appl.18, 034063 (2022)

    2022

  65. [67]

    Zitzler and S

    E. Zitzler and S. K¨ unzli, inProc. of the 8th Interna- tional Conference on Parallel Problem Solving from Na- ture (PPSN VIII)(2004) pp. 832–842. 11

    2004

  66. [68]

    Zhang and H

    Q. Zhang and H. Li, IEEE Transactions on Evolutionary Computation11, 712 (2007)

    2007

  67. [69]

    Y. Song, J. Li, Y.-J. Hai, Q. Guo, and X.-H. Deng, Phys. Rev. A105, 012616 (2022)

    2022

  68. [70]

    Didier, Flux control of superconducting qubits at dy- namical sweet spots (2019), arXiv:1912.09416 [quant-ph]

    N. Didier, Flux control of superconducting qubits at dy- namical sweet spots (2019), arXiv:1912.09416 [quant-ph]

    Pith/arXiv arXiv 2019

  69. [71]

    Thibodeau, A

    M. Thibodeau, A. Kou, and B. K. Clark, PRX Quantum 5, 040314 (2024). Supplemental Material for Pareto-Front Engineering of Dynamical Sweet Spots in Superconducting Qubits VI. P ARETO FRONTS The PFs obtained with four different selection strategies are shown in Fig. S1; these correspond to Fig. 1(a) in the main text. In regionC 1, SPEA2 and tDEA achieve th...

    2024

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.