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Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Flux-modulating a coupler turns a plasmon exchange into sub-100 ns CZ gates on fluxonium qubits, with intrinsic error below 10^-4.

desk verdict A competent parametric-bSWAP proposal for fluxoniums—real value in the g_eff analysis and collision-free windows, but the sub-1e-4 error claim lacks a convergence check. read the letter →

arxiv 2509.04762 v3 pith:EFBCW5PW submitted 2025-09-05 quant-ph

Peng Zhao , Peng Xu , Zheng-Yuan Xue This is my paper
classification quant-ph PACS 03.67.Lx85.25.Cp85.25.Hv
keywords fluxoniumparametricdrivebSWAPinteractioncontrolled-Zgateplasmontransitiontunablecouplersuperconductingqubits
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 have strong-anharmonicity spectra with several accessible plasmon transitions, but their computational transition has a tiny dipole moment, so entangling gates must run through non-computational states. This paper proposes driving a tunable transmon coupler with a flux modulation at the sum frequency of the two fluxoniums' |1>→|2> plasmon transitions. That parametrically switches on a bSWAP-type exchange |11>↔|22>, letting the system accumulate a conditional phase on the computational subspace. For two concrete circuit parameter sets, numerical optimization yields CZ gates shorter than 100 ns with intrinsic error below 10^-4, and with realistic ~10-microsecond coherence the expected error approaches 10^-3. The strategy is presented as a path to crosstalk- and frequency-crowding-tolerant gates in a scalable fluxonium processor.

What carries the argument

The load-bearing mechanism is the parametric bSWAP interaction: a transmon coupler whose frequency is modulated at the sum of two fluxoniums' |1>→|2> plasmon frequencies converts the static, off-resonant plasmon-plasmon coupling into a resonant two-plasmon exchange |11> ↔ |22>. The effective Hamiltonian after Schrieffer-Wolff elimination is that of Eq. (8), with activated coupling g_eff = δΦ (∂g_p/∂Φ_ext,c), so gate speed is set by how strongly the plasmon interaction responds to flux bias. This interaction is what turns a fast exchange between non-computational states into a conditional phase on the computational subspace.

What would settle it

A direct device test: drive the coupler at the predicted |11> ↔ |22> resonance and measure the population transferred into |202> versus time and drive amplitude. If the Rabi frequency does not track g_eff from Eq. (9), or if simulating the coupler in a full charge basis pushes the CZ error above 10^-4, the central claim fails.

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Extended reading notes

Core claim

The central claim is that flux-modulating the coupler at the sum frequency of two selected fluxonium plasmon transitions activates a resonant bSWAP interaction |11> ↔ |22> that can serve as the engine of a fast CZ gate. The paper derives an effective coupling strength g_eff proportional to δΦ ∂g_p/∂Φ_ext,c, and numerically shows that for the |1>→|2> plasmons the target transition remains cleanly separated from significant spurious transitions even when the activated coupling exceeds 5–15 MHz. For both a dynamic-bias and a static-bias operating point, optimized flat-top cosine drives give CZ gate lengths in the 30–100 ns range with intrinsic gate errors below 10^-4. Residual intrinsic error i

Load-bearing premise

The sub-10^-4 error numbers assume the transmon coupler can be treated as a low-anharmonicity oscillator truncated to a few Fock levels even while it is driven hard in a strongly non-dispersive regime, and that parasitic fluxonium array modes stay out of the gate dynamics.

Editorial extensions

If this is right

  • Sub-100 ns CZ gates on fluxonium are achievable with a single-tone flux drive on a coupler, with intrinsic error below 10^-4, without driving the qubits directly.
  • Activated bSWAP couplings exceeding 5–15 MHz are accessible without significant frequency collisions, which is larger than typical parametric coupling strengths in transmon systems.
  • With ~10 µs coherence times, the expected gate error approaches 10^-3, comparable to state-of-the-art experimental fluxonium gates.
  • The same parametric mechanism extends to other bSWAP transitions, such as |00> ↔ |33> and |10> ↔ |23>, and to native multi-controlled phase gates.
  • Both a dynamic-bias and a static-bias operating mode can be used, giving system designers a choice between parameter flexibility and reduced control complexity.

Reading between the lines

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

  • If the |11> ↔ |22> transition stays collision-free at even larger drive amplitudes, parametric coupler modulation could become a microwave-free, frequency-flexible way to allocate two-qubit gates across a dense fluxonium lattice, relaxing global frequency-allocation constraints.
  • The paper's leakage analysis suggests that synchronizing oscillation periods of multiple off-resonant transitions is a promising but rapidly harder route; a concrete multi-transition synchronization protocol would be a natural testable extension.
  • The robustness of the sub-10^-4 error claim could be tested by repeating the numerical gate simulation with a full charge-basis coupler model instead of a truncated anharmonic oscillator; survival of the low error would materially strengthen the central claim.
  • Similar parametric bSWAP gating could transfer to other multi-level superconducting qubits, but only if they share fluxonium's combination of strong anharmonicity and weak computational-state dipole moment.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes and numerically analyzes a scheme for fast CZ gates between fluxonium qubits by parametrically modulating the frequency of a tunable transmon coupler. The drive activates a bSWAP-type interaction between the |11> and |22> plasmon states, accumulating a conditional phase on the computational subspace. The central claim is that sub-100 ns CZ gates with intrinsic error below 10^-4 are achievable in two operational configurations (dynamic flux-bias and static-bias), with decoherence-limited errors of order 10^-3 for ~10 μs plasmon coherence times. The analytic model in Sec. II uses a Schrieffer-Wolff transformation to derive an effective coupling g_eff; the numerical analysis in Secs. III–IV uses a truncated circuit Hamiltonian built from circuit parameters taken from prior experimental and architecture work.

Significance. If the numerical claim is robust, this is a useful addition to the fluxonium control toolbox. The scheme offers potential advantages in crosstalk reduction and frequency allocation, and the paper provides a fairly complete qualitative taxonomy of spurious transitions and leakage channels. The derived g_eff is obtained from circuit parameters rather than fitted to the target gate error, and the transition frequencies are cross-checked against Floquet numerics in Fig. 5. The main concern is whether the quoted sub-10^-4 intrinsic error is an artifact of Hilbert-space truncation in a strongly driven, non-dispersive operating regime; this must be resolved before the central claim can be accepted at face value.

major comments (3)
  1. [Appendix C, Sec. IV] The central claim of intrinsic errors below 10^-4 rests on numerical simulation in which each fluxonium is truncated to its five lowest levels and the transmon coupler is modeled as an anharmonic oscillator (Eq. A4). No Fock-space cutoff or convergence check for the coupler is reported. This is load-bearing because the operating regime is strongly non-dispersive (Table III gives J_ck/2π = 300–500 MHz against coupler–plasmon detunings of roughly 1.7–2.4 GHz) and driven with δΦ/Φ0 = 0.045–0.075. Figure 8 shows transient coupler-excited states (|121>, |211>) during the gate, and Appendix B.2 itself states that the Fock/anharmonic description 'may break down' for highly excited coupler states, with some transitions requiring a charge-basis treatment. Omitted high coupler levels could add leakage or phase error exceeding 10^-4. Please add a systematic convergence study in coupler cutoff and/o
  2. [Sec. II, Eqs. (8)–(9); Sec. III B] The analytic model is derived under the dispersive condition |Δ_p,k| >> g_p,ck and to first order in the modulation amplitude δΦ, but the gate operating points are explicitly in the strongly non-dispersive regime (see the text near Fig. 3 and Table III). The authors acknowledge that sideband transitions and higher-order corrections are omitted. While the numerical gate simulations in Sec. IV use the full truncated Hamiltonian rather than Eq. (8), the identification of the |11>↔|22> resonance and the chosen parameter ranges come from this approximate model. Please quantify the uncertainty in g_eff and in the resonance condition when higher-order Schrieffer–Wolff terms and δΦ^2 corrections are included, or benchmark the gate error against a simulation that includes them.
  3. [Appendix B.2, Sec. V] The gate-error claims are computed for the symmetric SQUID case d=0, where the parametric drive only produces a squeezing term. For a general device geometry (d≠0), Eq. (B4) contains a single-photon coupler drive ~(a_c + a_c^†) that can cause transmon ionization, which the authors identify as 'another limiting factor' for fast high-fidelity gates. The abstract and conclusion do not carry this qualification. Please state this assumption prominently and, if the claim is intended to cover realistic devices, estimate the effect of the d≠0 terms on the gate error.
minor comments (5)
  1. [Fig. 3 caption] Typo: 'and and the drive amplitude'.
  2. [Sec. IV B] Duplicate state label in the text: '|211⟩,|211⟩' should likely be '|211⟩,|112⟩' or similar.
  3. [Fig. 7 caption] The caption states the gray lines assume T22_1 = T22_2 = 5 μs, while the text in Sec. IV A says 'on the order of ~10 μs'. Please reconcile.
  4. [Fig. 10 caption] Typo: 'trasnitions' should be 'transitions'.
  5. [Appendix C, Eq. (C3)] Notation U_cz and U_CZ is used inconsistently; use a single symbol for the ideal CZ unitary.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the sub-10^-4 CZ error is obtained from direct numerical simulation with externally sourced circuit parameters; the few self-citations are not load-bearing.

full rationale

The paper's derivation chain is self-contained and does not reduce to its inputs. (i) From the circuit Hamiltonian (1) with parameters taken from the independent experiment Ref. [16] (Table I), the authors derive the truncated two-plasmon + anharmonic-oscillator model (2), eliminate the coupler via a standard Schrieffer-Wolff transformation to obtain the static coupling g_p (5), then expand g_p to first order in the flux modulation to obtain the parametric bSWAP strength g_eff (9); this is a direct chain-rule derivation. (ii) The |11>->|22> transition and g_eff are verified by direct numerical integration and Floquet extraction (Figs. 3-5), with the approximate model compared rather than fitted. (iii) The CZ gate error (Fig. 7) comes from numerical integration of the full circuit Hamiltonian in the truncated space, with only the standard control parameters (drive amplitude and frequency) optimized to minimize leakage and conditional-phase error. No parameter is fitted to the target error, and the reported error is set by residual off-resonant transitions (|101>->|121>, |211>, |112>, Fig. 8) that the two control parameters cannot zero, so the 'sub-10^-4 intrinsic error' is a genuine simulation outcome rather than a construction. The self-citations (Refs. [19], [34], [60], and [71] with author overlap) provide the architecture concept, the state-shift metric, and the optimization recipe; they are methodological, not uniqueness theorems, and the platform is externally anchored by Ref. [16]'s experimental parameters, so they are not load-bearing. The manuscript itself flags the relevant limitations: Sec. II admits the approximate model omits sideband transitions; Appendix B states the Fock/anharmonic coupler description 'may break down' for highly excited states (black-square chevron, Fig. 9) and warns of transmon ionization under strong drive; Appendix C truncates each fluxonium to its five lowest levels with no convergence check; the Conclusion notes parasitic array modes. These are correctness/robustness risks — the central error claim rests on an untested Fock-space truncation in a strongly driven, non-dispersive regime — but they concern whether the simulation faithfully models the device, not whether the result is equivalent to its inputs. No circular reduction is present.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central derivation rests on the circuits' dispersive and weak-modulation assumptions, which are only approximately met in the high-performance regime studied. The reported error also depends on assumed coherence times for the doubly excited plasmon level; with 5-10 microseconds the estimated error is about 10^-3, not 10^-4.

free parameters (4)
  • Parametric drive amplitude delta_Phi/Phi0 = 0.045 (Jck=500 MHz), 0.075 (300 MHz); optimized in 0.02-0.14 depending on gate length (Fig. 11)
    Chosen control pulse amplitude; the reported gate error is achieved at these optimized values. Not a physical constant fitted to data, but central to the protocol.
  • Parametric drive frequency omega_p/2pi = About 10.77-10.85 GHz, optimized per gate length (Fig. 11)
    Optimized jointly with amplitude to minimize leakage and conditional-phase error; determines which transition is activated.
  • Second parameter configuration for static bias = J_c0=J_c1=300 MHz, J_01=80 MHz, E_Jc/2pi=40 GHz
    Reduced coupling and higher coupler Josephson energy, selected by hand to realize a static-bias operating point rather than taken from a measured device.
  • Assumed coherence times for |22> state = T_22^1 = T_22^2 = 5 microseconds (Fig. 7 estimate); about 10 microseconds in discussion
    The decoherence error estimate in Eq. (C4) assumes these values based on typical current devices, not measured for this specific gate.
assumptions (6)
  • standard math Schrieffer-Wolff transformation valid to second order in g/Delta
    Used to eliminate coupler degrees of freedom in Eqs. (A8)-(A9); validity requires the dispersive condition, which is only marginally satisfied for the chosen parameters.
  • standard math Rotating-wave approximation neglects fast-oscillating terms
    Used to derive Eq. (8); standard but requires clear time-scale separation between resonant and off-resonant processes.
  • domain assumption First-order expansion in modulation amplitude delta_Phi
    Eqs. (7)-(9) assume delta_Phi much less than 1; the largest drive used, 0.075 Phi0, is small but not asymptotically so.
  • domain assumption Fluxonium biased at half-flux-quantum sweet spot
    Stated in Sec. II; determines the spectrum and the effective decoupling of the computational transition from the coupler.
  • ad hoc to paper Transmon coupler treated as anharmonic oscillator with few Fock levels
    Used throughout the numerical gate simulations (Appendix C); the authors note this approximation breaks down for high coupler excitation (Appendix B).
  • ad hoc to paper Fluxonium truncated to lowest five levels
    Simulations retain five levels per fluxonium; higher levels and parasitic array modes are neglected (Appendix C, Sec. V).

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Pith. "Pith review of Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction." pith.science (2026). https://pith.science/paper/EFBCW5PW

@misc{pith2026250904762,
  author       = {Pith},
  title        = {Pith review of: Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EFBCW5PW}},
  note         = {Machine review of arXiv:2509.04762}
}
abstract

In superconducting quantum processors, exploring diverse control methods could offer essential versatility and redundancy to mitigate challenges such as frequency crowding, spurious couplings, control crosstalk, and fabrication variability, thus leading to better system-level performance. Here we introduce a control strategy for fast entangling gates in a scalable fluxonium architecture, utilizing parametric modulation of the plasmon interaction. In this architecture, fluxoniums are coupled via a tunable coupler, whose transition frequency is flux-modulated to control the inter-fluxonium plasmon interaction. A bSWAP-type interaction is activated by parametrically driving the coupler at the sum frequency of the plasmon transitions of the two fluxoniums, resulting in the simultaneous excitation or de-excitation of both plasmon modes. This strategy therefore allow the transitions between computational states and non-computational plasmon states, enabling the accumulation of conditional phases on the computational subspace and facilitating the realization of controlled-phase gates. By focusing on a specific case of these bSWAP-type interactions, we show that a simple drive pulse enables sub-100ns CZ gates with an error below $10^{-4}$. Given its operational flexibility and extensibility, this approach could potentially offer a foundational framework for developing scalable fluxonium-based quantum processors.

Figures

Figures reproduced from arXiv: 2509.04762 by the authors.

Figure 1
Figure 1. FIG. 1: (a) A two-dimensional (2D) square qubit lattice comprising [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Coupler-mediated interactions for the plasmon tran [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Population within the computational (qubit) subspace as a function of parametric drive frequency and evolution time, for the coupled [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: FIG. 5: Population in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: (a) A typical control pulse (flat-top cosine) for implement [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Gate errors (a, c) and leakage (b, d) of the parametric CZ [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Typical system dynamics of CZ gates with and without sig [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Identical to Fig [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: A schematic illustrating parametric-activated state tran [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: The optimized gate parameters (i.e., modulation amplitudes [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

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Reference graph

Works this paper leans on

85 extracted references · 57 canonical work pages · cited by 1 Pith paper

  1. [1]

    3(a), Figure 9 reveals the specific state tran- sitions responsible for the chevron patterns observed across the 3-13 GHz frequency range

    The analysis of the spurious transition Similar to Fig. 3(a), Figure 9 reveals the specific state tran- sitions responsible for the chevron patterns observed across the 3-13 GHz frequency range. Corresponding detailed illus- trations of the two main transition types, i.e., bSW AP-type plasmon transitions and blue sideband transitions, are pro- vided for a...

  2. [2]

    As illustrated in Fig

    Effective coupler drive Here we provide further details regarding the effective drive experienced by the transmon coupler. As illustrated in Fig. 9, the parametric drive can induce transitions within the coupler states or transitions that involve coupler excitation, such as |000⟩ → |020⟩. To elucidate the physical mechanism un- derlying these transitions,...

  3. [3]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schus- ter, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the cooper pair box, Phys. Rev. A76, 042319 (2007)

    2007

  4. [4]

    V . E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-pair circuit free of charge offsets, Science326, 113 (2009)

    2009

  5. [5]

    Brink, J

    M. Brink, J. M. Chow, J. Hertzberg, E. Magesan, and Sami Rosenblatt, Device challenges for near term superconducting quantum processors: frequency collisions, 2018 IEEE Int. Elec- tron Devices Meeting (IEDM), (2018)

    2018

  6. [6]

    Neill, P

    Yu Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, A. Megrant, J. Y . Mutus, P. J. J. O’Malley, C. M. Quin- tana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, Michael R. Geller, A. N. Cleland, and John M. Martinis, Qubit Archi- tecture with High Coherence and Fast Tunable ...

    work page 2014

  7. [7]

    Kelly, R

    J. Kelly, R. Barends, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, J. Y . Mutus, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wen- 13 ner, A. N. Cleland, and John M. Martinis, State preservation by repetitive error detection in a superconducting q...

    work page 2015

  8. [8]

    M ¨uller, J

    C. M ¨uller, J. H. Cole, and J. Lisenfeld, Towards understanding two-level-systems in amorphous solids: insights from quantum circuits, Rep. Prog. Phys.82, 124501 (2019)

    work page 2019

Show all 85 references
  1. [9]

    Mundada, G

    P. Mundada, G. Zhang, T. Hazard, and A. Houck, Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Cir- cuit, Phys. Rev. Appl.12, 054023 (2019)

    2019

  2. [10]

    Barends, J

    R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, Y . Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Supe...

    2014

  3. [11]

    J. M. Kreikebaum, K. P. O’Brien, A. Morvan, and I. Siddiqi, Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits, Supercond. Sci. Technol.33, 06LT02 (2020)

    2020

  4. [12]

    J. B. Hertzberg, E. J. Zhang, S. Rosenblatt, E. Magesan, J. A. Smolin, J.-B. Yau, V . P. Adiga, M. Sandberg, M. Brink, Je. M. Chow, and J. S. Orcutt, Laser-annealing Josephson junc- tions for yielding scaled-up superconducting quantum proces- sors, npj Quantum Inf.7, 129 (2021)

    2021

  5. [13]

    D. P. Pappas, M. Field, C. J. Kopas, J. A. Howard, X. Wang, E. Lachman, J. Oh, L. Zhou, A. Gold, G. M. Stiehl, K. Ya- davalli, E. A. Sete, A. Bestwick, M. J. Kramer, and J. Y . Mutus, Alternating-bias assisted annealing of amorphous oxide tunnel junctions, Commun Mater5, 150 (2024)

    2024

  6. [14]

    K. N. Nesterov, I. V . Pechenezhskiy, C. Wang, V . E. Manucharyan, and M. G. Vavilov, Microwave-activated controlled-z gate for fixed-frequency fluxonium qubits, Phys. Rev. A98, 030301 (2018)

    2018

  7. [15]

    Ficheux, L

    Q. Ficheux, L. B. Nguyen, A. Somoroff, H. Xiong, K. N. Nes- terov, M. G. Vavilov, and V . E. Manucharyan, Fast logic with slow qubits: Microwave-activated controlled-z gate on low- frequency fluxoniums, Phys. Rev. X11, 021026 (2021)

    2021

  8. [16]

    Xiong, Q

    H. Xiong, Q. Ficheux, A. Somoroff, L. B. Nguyen, E. Dogan, D. Rosenstock, C. Wang, K. N. Nesterov, M. G. Vavilov, and V . E. Manucharyan, Arbitrary controlled-phase gate on fluxo- nium qubits using differential ac stark shifts, Phys. Rev. Res.4, 023040 (2022)

    2022

  9. [17]

    I. A. Simakov, G. S. Mazhorin, I. N. Moskalenko, N. N. Abramov, A. A. Grigorev, D. O. Moskalev, A. A. Pishchimova, N. S. Smirnov, E. V . Zikiy, I. A. Rodionov, and I. S. Besedin, Coupler Microwave-Activated Controlled-Phase Gate on Flux- onium Qubits, PRX Quantum4, 040321 (2023)

    2023

  10. [18]

    L. Ding, M. Hays, Y . Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High-fidelity, frequency-flexible...

    2023

  11. [19]

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

    2024

  12. [20]

    Xiong, J

    H. Xiong, J. Wang, J. Song, J. Yang, Z. Bao, Y . Li, Z.-Y . Mi, H. Zhang, H.-F. Yu, Y . Song, and L. Duan, Scalable Low- overhead Superconducting Non-local Coupler with Exponen- tially Enhanced Connectivity, arXiv:2502.18902

    arXiv

  13. [21]

    P. Zhao, G. Zhao, S. Li, C. Zha, and M. Gong, Scalable fluxo- nium qubit architecture with tunable interactions between non- computational levels, arXiv:2504.09888

    arXiv

  14. [22]

    Singh, E

    S. Singh, E. Y . Huang, J. Hu, F. Yilmaz, M. F. S. Zwanenburg, P. Kumaravadivel, S. Wang, T. V . Stefanski, and C. K. Ander- sen, Fast microwave-driven two-qubit gates between fluxonium qubits with a transmon coupler, arXiv:2504.13718

  15. [23]

    G. Zhu, D. G. Ferguson, V . E. Manucharyan, and J. Koch, Circuit QED with fluxonium qubits: Theory of the dispersive regime, Phys. Rev. B87, 024510 (2013)

    2013

  16. [24]

    Y .-H. Lin, L. B. Nguyen, N. Grabon, J. S. Miguel, N. Pankra- tova, and V . E. Manucharyan, Demonstration of Protection of a Superconducting Qubit from Energy Decay, Phys. Rev. Lett. 120, 150503 (2018)

    2018

  17. [25]

    L. B. Nguyen, G. Koolstra, Y . Kim, A. Morvan, T. Chistolini, 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, Blueprint for a high-performance fluxonium quantum processor, PRX Quantum3, 03...

    2022

  18. [26]

    T. V . Stefanski, F. Yilmaz, E. Y . Huang, M. F. S. Zwanen- burg, S. Singh, S. Wang, L. J. Splitthoff, and C. K. Ander- sen, Improved fluxonium readout through dynamic flux pulsing, arXiv:2411.13437

    arXiv

  19. [27]

    Bothara, S

    G. Bothara, S. Das, K. V . Salunkhe, M. Chand, J. Deshmukh, M. P. Patankar, and R. Vijay, High-fidelity QND readout and measurement back-action in a tantalum-based high-coherence fluxonium qubit, APL Quantum2, 026103 (2025)

    2025

  20. [28]

    Watanabe, K

    S. Watanabe, K. Hida, K. Matsuura, and Y . Nakamura, Nonde- molition fluorescence readout and high-fidelity unconditional reset of a fluxonium qubit via dissipation engineering, Phys. Rev. A112, 012624 (2025)

    2025

  21. [29]

    V . E. Manucharyan, J. Koch, M. Brink, L. I. Glazman, and M. H. Devoret, Coherent oscillations between classically separable quantum states of a superconducting loop, arXiv:0910.3039

    arXiv

  22. [30]

    Zhang, S

    H. Zhang, S. Chakram, T. Roy, N. Earnest, Y . Lu, Z. Huang, D. K. Weiss, J. Koch, and D. I. Schuster, Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit, Phys. Rev. X11, 011010 (2021)

    2021

  23. [31]

    T. Wang, F. Wu, F. Wang, X. Ma, G. Zhang, J. Chen, H. Deng, R. Gao, R. Hu, L. Ma, Z. Song, T. Xia, M. Ying, H. Zhan, H.-H. Zhao, and C. Deng, Efficient Initialization of Fluxonium Qubits based on Auxiliary Energy Levels, Phys. Rev. Lett.132, 230601 (2024)

    2024

  24. [32]

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

    2019

  25. [33]

    Somoroff, Q

    A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. Kuzmin, and V . E. Manucharyan, Millisecond coherence in a supercon- ducting qubit, Phys. Rev. Lett.130, 267001 (2023)

    2023

  26. [34]

    F. Wang, K. Lu, H. Zhan, L. Ma, F. Wu, H. Sun, H. Deng, Y . Bai, F. Bao, X. Chang, R. Gao, X. Gao, G. Gong, L. Hu, R. Hu, H. Ji, X. Ma, L. Mao, Z. Song, C. Tang, H. Wang, T. Wang, Z. Wang, T. Xia, H. Xu, Z. Zhan, G. Zhang, T. Zhou, M. Zhu, Q. Zhu, S. Zhu, X. Zhu, Y . Shi, H.-H...

    2025

  27. [35]

    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 correc- tion, Nature Physics19, 1780 (2023)

    2023

  28. [36]

    P. Zhao, P. Xu, and Z.-Y . Xue, Scalable native multi-qubit gates for fluxonium architectures with tunable plasmon interactions, arXiv:2507.18984

  29. [37]

    Bertet, C

    P. Bertet, C. J. P. M. Harmans, and J. E. Mooij, Parametric coupling for superconducting qubits, Phys. Rev. B73, 064512 (2006). 14

    2006

  30. [38]

    A. O. Niskanen, K. Harrabi, F. Yoshihara, Y . Nakamura, S. Lloyd, and J. S. Tsai, Quantum Coherent Tunable Coupling of Superconducting Qubits, Science316, 723 (2007)

    2007

  31. [39]

    M. Roth, M. Ganzhorn, N. Moll, S. Filipp, G. Salis, and S. Schmidt, Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconduct- ing qubits, Phys. Rev. A96, 062323 (2017)

    2017

  32. [40]

    Poletto, J

    S. Poletto, J. M. Gambetta, S. T. Merkel, J. A. Smolin, J. M. Chow, A. D. C ´orcoles, G. A. Keefe, M. B. Rothwell, J. R. Rozen, D. W. Abraham, C. Rigetti, and M. Steffen, Entangle- ment of Two Superconducting Qubits in a Waveguide Cavity via Monochromatic Two-Photon Excitation...

    2012

  33. [41]

    Kapit, Universal two-qubit interactions, measurement, and cooling for quantum simulation and computing, Phys

    E. Kapit, Universal two-qubit interactions, measurement, and cooling for quantum simulation and computing, Phys. Rev. A 92, 012302 (2015)

    2015

  34. [42]

    P. Zhao, X. Tan, H. Yu, S.-L. Zhu, and Y . Yu, Simultaneously exciting two atoms with photon-mediated Raman interactions, Phys. Rev. A95, 063848 (2017)

    2017

  35. [43]

    K. N. Nesterov, Q. Ficheux, V . E. Manucharyan, and M. G. Vavilov, Proposal for entangling gates on fluxonium qubits via a two-photon transition, PRX Quantum2, 020345 (2021)

    2021

  36. [44]

    D. C. McKay, S. Filipp, A. Mezzacapo, E. Magesan, J. M. Chow, and J. M. Gambetta, Universal Gate for Fixed-Frequency Qubits via a Tunable Bus, Phys. Rev. Appl.6, 064007 (2016)

    2016

  37. [45]

    X. Y . Han, T. Q. Cai, X. G. Li, Y . K. Wu, Y . W. Ma, Y . L. Ma, J. H. Wang, H. Y . Zhang, Y . P. Song, and L. M. Duan, Error analysis in suppression of unwanted qubit interactions for a parametric gate in a tunable superconducting circuit, Phys. Rev. A102, 022619 (2020)

    2020

  38. [46]

    S. Li, D. Fan, M. Gong, Y . Ye, X. Chen, Y . Wu, H. Guan, H. Deng, H. Rong, H.-L. Huang, C. Zha, K. Yan, S. Guo, H. Qian, H. Zhang, F. Chen, Q. Zhu, Y . Zhao, S. Wang, C. Ying, S. Cao, J. Yu, F. Liang, Y . Xu, J. Lin, C. Guo, L. Sun, N. Li, L. Han, C.-Z. Peng, X. Zhu, and J.-W...

    2022

  39. [47]

    Ganzhorn, G

    M. Ganzhorn, G. Salis, D. J. Egger, A. Fuhrer, M. Mergenthaler, C. M ¨uller, P. M ¨uller, S. Paredes, M. Pechal, M. Werninghaus and S. Filipp, Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quan- tum computing platform, P...

    2020

  40. [48]

    Bravyi, D

    S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer-Wolff transformation for quantum many-body systems, Ann. Phys. 326, 2973 (2011)

    2011

  41. [49]

    Beaudoin, M

    F. Beaudoin, M. P. da Silva, Z. Dutton, and A. Blais, First-order sidebands in circuit QED using qubit frequency modulation, Phys. Rev. A86, 022305 (2012)

    2012

  42. [50]

    Petrescu, C

    A. Petrescu, C. L. Calonnec, C. Leroux, A. D. Paolo, P. Mundada, S. Sussman, A. Vrajitoarea, A. A. Houck, and A. Blais, Accurate Methods for the Analysis of Strong-Drive Ef- fects in Parametric Gates, Phys. Rev. Appl.19, 044003 (2023)

    2023

  43. [51]

    P. V . Klimov, J. Kelly, Z. Chen, M. Neeley, A. Megrant, B. Bur- kett, R. Barends, K. Arya, B. Chiaro, Y . Chen,et al., Fluctua- tions of Energy-Relaxation Times in Superconducting Qubits, Phys. Rev. Lett.121, 090502 (2018)

    2018

  44. [52]

    Z. T. Wang, P. Zhao, Z. H. Yang, Ye Tian, H. F. Yu, and S. P. Zhao, Escaping Detrimental Interactions with Microwave- Dressed Transmon Qubits, Chin. Phys. Lett.40, 070304 (2023)

    2023

  45. [53]

    R. Wang, Y . Feng, Y . Zhang, J. Ding, B. Li, F. Motzoi, Y . Gao, H. Xu, Z. Yang, W. Nuerbolati, H. Yu, W. Sun, and F. Yan, Sup- pressing spurious transitions using spectrally balanced pulse, arXiv:2502.10116

  46. [54]

    Chen, K.-H

    L. Chen, K.-H. Lee, C.-H. Liu, B. Marinelli, R. K. Naik, Z. Kang, N. Goss, H Kim, D. I. Santiago, and I. Siddiqi, Scal- able and Site-Specific Frequency Tuning of Two-Level System Defects in Superconducting Qubit Arrays, arXiv:2503.04702

    arXiv

  47. [55]

    Didier, E

    N. Didier, E. A. Sete, M. P. d. Silva, and C. Rigetti, Analytical modeling of parametrically modulated transmon qubits, Phys. Rev. A97, 022330 (2018)

    2018

  48. [56]

    G. S. Paraoanu, Microwave-induced coupling of superconduct- ing qubits , Phys. Rev. B74, 140504(R) (2006)

    2006

  49. [57]

    Rigetti and M

    C. Rigetti and M. Devoret, Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies, Phys. Rev. B81, 134507 (2010)

    2010

  50. [58]

    P. C. de Groot, J. Lisenfeld, R. N. Schouten, S. Ashhab, A. Lupas ¸cu, C. J. P. M. Harmans, and J. E. Mooij, Selective dark- ening of degenerate transitions demonstrated with two super- conducting quantum bits, Nat. Phys.6, 763 (2010)

    2010

  51. [59]

    J. M. Chow, A. D. C ´orcoles, J. M. Gambetta, C. Rigetti, B. R. Johnson, J. A. Smolin, J. R. Rozen, G. A. Keefe, M. B. Roth- well, M. B. Ketchen, and M. Steffen, Simple All-Microwave Entangling Gate for Fixed-Frequency Superconducting Qubits, Phys. Rev. Lett.107, 080502 (2011)

    2011

  52. [60]

    Malekakhlagh, E

    M. Malekakhlagh, E. Magesan, and D. C. McKay, First prin- ciples analysis of cross-resonance gate operation, Phys. Rev. A 102, 042605 (2020)

    2020

  53. [61]

    K. Heya, M. Malekakhlagh, S. Merkel, N. Kanazawa, and E. Pritchett, Floquet analysis of frequency collisions, Phys. Rev. Appl.21, 024035 (2024)

    2024

  54. [62]

    Zhao, Mitigation of quantum crosstalk in cross-resonance- based qubit architectures, Phys

    P. Zhao, Mitigation of quantum crosstalk in cross-resonance- based qubit architectures, Phys. Rev. Appl.20, 054033 (2024)

    2024

  55. [63]

    Malekakhlagh, W

    M. Malekakhlagh, W. Shanks, and H. Paik, Optimization of the resonator-induced PHASE gate for superconducting qubits, Phys. Rev. A105, 022607 (2022)

    2022

  56. [64]

    Osman, J

    A. Osman, J. Fern ´andez-Pend´as, C. Warren, S. Kosen, M. Scigliuzzo, A. F. Kockum, G. Tancredi, A. F. Roudsari, and J. Bylander, Mitigation of frequency collisions in superconduct- ing quantum processors, Phys. Rev. Res.5, 043001 (2023)

    2023

  57. [65]

    M. H. Goerz, F. Motzoi, K. B. Whaley, and C. P. Koch, Charting the circuit QED design landscape using optimal control theory, npj Quantum Inf.3, 37 (2017)

    2017

  58. [66]

    Y . Sung, L. Ding, J. Braum¨uller, A. Veps¨al¨ainen, B. Kannan, M. Kjaergaard, A. Greene, G. O. Samach, C. McNally, D. Kim, A. Melville, B. M. Niedzielski, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Realization of High- Fidelity CZ and ZZ-Free...

    2021

  59. [67]

    P. Zhao, D. Lan, P. Xu, G. Xue, M. Blank, X. Tan, H. Yu, and Y . Yu, Suppression of Static ZZ Interaction in an All-Transmon Quantum Processor, Phys. Rev. Appl.16, 024037 (2021)

    2021

  60. [68]

    J. H. Shirley, Solution of the Schr¨odinger equation with a hamil- tonian periodic in time, Phys. Rev.138, B979 (1965)

    1965

  61. [69]

    Sambe, Steady states and quasienergies of a quantum me- chanical system in an oscillating field, Phys

    H. Sambe, Steady states and quasienergies of a quantum me- chanical system in an oscillating field, Phys. Rev. A7, 2203 (1973)

    1973

  62. [70]

    Johansson, P

    J. Johansson, P. Nation, and F. Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems , Comput. Phys. Commun.183, 1760 (2012)

    2012

  63. [71]

    L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quan- tum operations, Phys. Lett. A367, 47 (2007)

    2007

  64. [72]

    C. J. Wood and J. M. Gambetta, Quantification and characteri- zation of leakage errors, Phys. Rev. A97, 032306 (2018)

    2018

  65. [73]

    Jiang, P

    L. Jiang, P. Xu, S. Wu, J. A. Sun, and F. Q. Dou, Microwave-activated two-qubit gates for fixed-coupling and fixed-frequency transmon qubits, Phys. Rev. A111, 032609 (2025)

    2025

  66. [74]

    T. Abad, A. F. Kockum, and G. Johansson, Impact of decoher- 15 ence on the delity of quantum gates leaving the computational subspace, arXiv:2302.13885

    arXiv

  67. [75]

    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 Quantum5, 020326 (2024)

    2024

  68. [76]

    W.-J. Lin, H. Cho, Y . Chen, M. G. Vavilov, C. Wang, and V . E. Manucharyan, 24 days-stable CNOT-gate on fluxonium qubits with over 99.9%fidelity, PRX Quantum6, 010349 (2025)

    2025

  69. [77]

    S. E. Economou and E. Barnes, Analytical approach to swift nonleaky entangling gates in superconducting qubits, Phys. Rev. B91, 161405(R) (2015)

    2015

  70. [78]

    Barends, C

    R. Barends, C. M. Quintana, A. G. Petukhov, Y . Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixoet al., Diabatic Gates for Frequency-Tunable Superconducting Qubits, Phys. Rev. Lett.123, 210501 (2019)

    2019

  71. [79]

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

    2024

  72. [80]

    Sorokanich, M

    S. Sorokanich, M. Hays, and N. C. Warrington, Exact and ap- proximate fluxonium array modes, Phys. Rev. B110, 125404 (2024)

    2024

  73. [81]

    Zueco, G

    D. Zueco, G. M. Reuther, S. Kohler, and P. H ¨anggi, Qubit- oscillator dynamics in the dispersive regime: Analytical the- ory beyond the rotating-wave approximation, Phys. Rev. A80, 033846 (2009)

    2009

  74. [82]

    X. You, J. A. Sauls, and J Koch, Circuit quantization in the pres- ence of time-dependent external flux, Phys. Rev. B99, 174512 (2019)

    2019

  75. [83]

    Riwar and D

    R.-P. Riwar and D. P. DiVincenzo, Circuit quantization with time-dependent magnetic fields for realistic geometries, npj Quantum Inf.8, 36 (2022)

    2022

  76. [84]

    M. Xia, C. Lled ´o, M. Capocci, J. Repicky, B. D’Anjou, I. Mondragon-Shem, R. Kaufman, J. Koch, A. Blais, and M. Ha- tridge, Exceeding the Parametric Drive Strength Threshold in Nonlinear Circuits, arXiv:2506.03456

    arXiv

  77. [85]

    M. F. Dumas, B. Groleau-Par ´e, A. McDonald, M. H. M. Arias, C. Lled ´o, B. D’Anjou, and A. Blais, Measurement-induced transmon ionization, Phys. Rev. X14, 041023 (2025)

    2025

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