Pith. sign in

REVIEW 3 major objections 6 minor 85 references

A fluxonium-transmon cross-resonance CNOT can run in 50 ns with coherent errors near 1e-5, and the three-qubit FTF layout keeps fidelity above 99.994%.

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 ↗

T0 review · deepseek-v4-flash

2026-08-04 21:28 UTC pith:W3O53CRF

load-bearing objection Solid numerical proposal for CR gates in FT/FTF systems — the coherent-only fidelities are upper bounds, but the architecture is plausible and deserves a serious referee. the 3 major comments →

arxiv 2509.07935 v3 pith:W3O53CRF submitted 2025-09-09 quant-ph

Cross-Resonant Gates in Hybrid Fluxonium-Transmon Systems

Nikola D. Dimitrov , Chen Wang , Vladimir E. Manucharyan , Maxim G. Vavilov This is my paper
classification quant-ph
keywords cross-resonance gatefluxoniumtransmonselective darkeningCNOT gatesuperconducting qubitsparity checkquantum error correction
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.

This paper claims that a fluxonium-transmon-fluxonium system can run fast, high-fidelity quantum gates without strong couplers or direct fluxonium-fluxonium coupling. The key is a cross-resonance drive on a fluxonium-control/transmon-target pair, with the two drive amplitudes tuned so the unwanted transition is left dark. In closed-system numerical simulations, 50 ns CNOT gates between a fluxonium and the transmon reach coherent errors around 1e-5, and the same gates stay above 99.994% fidelity when a second fluxonium sits nearby as a spectator. Sequences of these gates give two-fluxonium parity checks above 99.98% and a logical fluxonium-fluxonium CNOT above 99.97%, and the same transmon can read out both fluxoniums. The quoted numbers assume full qubit coherence; with realistic T1 and Tphi near 1 ms, decoherence adds roughly 5e-5 error per 50 ns gate.

Core claim

The paper's central claim is that the cross-resonance effect, previously used for fluxonium-fluxonium gates, works cleanly between a fluxonium control and a transmon target because the large frequency detuning lets the drive amplitudes be tuned so that the control-in-|0> transition is selectively darkened while the control-in-|1> transition executes a bright Rabi flip. In the three-qubit fluxonium-transmon-fluxonium system, the CX1 and CX2 gates exceed 99.994% fidelity at 50 ns, with the dominant error coming from spectator-state-dependent shifts of the transmon frequency. Applying these gates in sequence yields fluxonium-fluxonium parity checks exceeding 99.98% and a transmon-mediated logic

What carries the argument

The central mechanism is the cross-resonance drive with selective darkening: a microwave tone near the transmon frequency is applied to both the fluxonium control and the transmon target, with the ratio eta of the two drive amplitudes chosen so that the transition with the control in |0> cancels (the dark transition), while the transition with the control in |1> is a bright Rabi flip. This converts the CR interaction into a CNOT while suppressing leakage into higher states. The argument also rests on keeping all qubit couplings weak so the always-on ZZ interaction stays below the kilohertz level; the residual error floor is then set by spectator-state-dependent shifts of the dressed transmon

Load-bearing premise

The quoted fidelities assume the qubits remain fully coherent during the gate; the paper states this in Section V, and with realistic T1/Tphi near 1 ms, decoherence adds roughly 5e-5 error per 50 ns gate, the same order as the simulated coherent errors.

What would settle it

Fabricate the Table I FTF device, run the optimized 50 ns CX1 pulse, and measure process fidelity with the spectator fluxonium prepared in |0> and separately in |1>. Including a Lindblad model with T1 = Tphi = 1 ms for all qubits, the predicted total error is about 6e-5; an observed error above roughly 2e-4, or a spectator-state dependence much larger than the predicted phase error, would indicate the selective-darkening mechanism is not achieving the simulated coherent error.

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

Share X Bluesky LinkedIn Reddit HN

If this is right

  • An interleaved lattice of fluxoniums and transmons could keep fluxonium-fluxonium ZZ coupling below the kilohertz range and suppress long-range crosstalk, since gates need no direct fluxonium-fluxonium coupling.
  • The same 50 ns CR pulses serve for readout mapping, parity checks, and logical CNOTs, so one ancilla type handles multiple tasks needed for surface-code-style syndrome extraction.
  • Spectator-state-dependent transmon frequency shifts set the dominant coherent error; lowering fluxonium-transmon coupling reduces that error at the cost of higher drive amplitudes and leakage, leaving a tunable valley near 20-22 MHz coupling.
  • With 50 ns gates and current millisecond-scale coherence times, the coherent error floor is not the practical limit; the added decoherence error is comparable to the reported coherent errors.
  • The gates use only a charge drive with a simple pulse envelope, making the scheme straightforward to implement on existing experimental hardware.

Where Pith is reading between the lines

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

  • Direct experimental target: with T1 and Tphi near 1 ms, the total error budget for a 50 ns CX gate is around 6e-5, so optimizing the drive parameters with decoherence included could shift the shortest useful gate time below 50 ns.
  • The three-qubit result is extrapolated to a full lattice; that step assumes spectator-induced frequency shifts from many neighbors remain small and roughly additive, which a four- or five-fluxonium simulation could test.
  • Because the transmon both gates and reads out its neighboring fluxoniums, the architecture could reduce readout-resonator overhead relative to designs where every data qubit needs its own resonator, provided transmon readout infidelity stays below the gate error.
  • The residual spectator-dependent phase, treated here as an error, could be repurposed as a measurement handle: the phase accumulated during CX depends on the spectator state, so it might enable ancilla-free parity information in a future design.

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

3 major / 6 minor

Summary. The paper proposes a dual-species fluxonium-transmon-fluxonium (FTF) architecture in which cross-resonance (CR) pulses with selective darkening implement CNOT gates between a fluxonium control and a transmon target. The authors derive effective CR dynamics, define a four-category coherent-error budget, and numerically optimize drive parameters for two- and three-qubit Hamiltonians. Headline results are a fluxonium-transmon CNOT with coherent error on the order of 1e-5, FTF CX1/CX2 fidelities above 99.994% at 50 ns, parity checks above 99.98%, and logical fluxonium-fluxonium CNOT gates above 99.97%. All quoted fidelities are closed-system unitary process fidelities; incoherent dynamics are not simulated. The paper also discusses readout via the transmon and argues that low residual ZZ couplings make the architecture scalable to larger lattices.

Significance. If read as coherent-error benchmarks, the paper is a solid theoretical contribution. It extends the selective-darkening CR technique to highly detuned fluxonium-transmon pairs, identifies spectator-induced frequency shifts as the dominant coherent error, and supports the numerics with perturbation-theory checks (Appendix A), an explicit error budget (Appendix C), and a parameter-sensitivity study (Appendix E). The honest disclosure that decoherence is omitted is a strength, but it also means the device-level fidelity numbers in the abstract and conclusions are upper bounds on coherent error, not realistic predictions. The scalability claims likewise go beyond the simulated few-qubit model. The central derivation appears internally consistent; the main weakness is the gap between the simulated coherent quantities and the fault-tolerance-oriented conclusions.

major comments (3)
  1. [Abstract; Sec. V] All headline fidelities (FT ~1e-5 error, CX1/CX2 >99.994%, parity >99.98%, logical CNOT >99.97%) are closed-system unitary fidelities. Sec. V gives E_de ≈ 1 - exp[-t_g(1/T1 + 1/Tphi)] per qubit. For t_g = 50 ns and T1 = Tphi = 1 ms, E_de ≈ 1e-4 per qubit, i.e., roughly 2e-4 for a two-qubit gate, several times the ~6e-5 coherent error reported in Sec. III B and Fig. 6. For parity checks (2t_g) and logical gates (3t_g) the omitted contribution is proportionally larger. Thus the abstract's '99.994%' and the conclusion's 'fidelity greater than 99.994%' are coherent-error upper bounds, not device-level predictions. This is a load-bearing gap for the fault-tolerance claim. I recommend adding open-system estimates (or at least adding the E_de contributions to the quoted fidelities) and qualifying the abstract and conclusion accordingly.
  2. [Sec. II B; Sec. V] The scalability claims ('easily extrapolated', 'straightforward scaling to an interleaved lattice') are not backed by simulation beyond the three-qubit model. The numerical studies include at most one spectator qubit in a computational state, and the error budget in Eq. (24) sums over spectator states |0> and |1> only. Effects of multiple spectators, spectator leakage, simultaneous gate operation, and frequency collisions in a larger lattice are not modeled. The low-ZZ argument makes the extrapolation plausible, but it remains an unverified leap. I recommend either adding a small multi-qubit crosstalk test (e.g., 4-5 qubits with two spectators) or softening the scalability language in the abstract and conclusions.
  3. [Sec. III B 2; Appendix C] The error-budget derivation in Appendix C drops second-order error terms (e.g., Eqs. C6-C7 and C19-C20). This is acceptable at the quoted 1e-4 to 1e-5 error levels, but the main text should state clearly that Eq. (22) is a first-order decomposition and not an exact accounting. The current text presents the four terms as a complete budget. This does not affect the numerically computed fidelities, which are direct, but it is a presentation issue in a load-bearing analysis.
minor comments (6)
  1. [Eq. (16)] Edark and Eflip in Eq. (16) use Π without absolute value, while the three-qubit version in Eq. (24) correctly uses |Π|. Since the matrix elements are complex, please add absolute-value bars or state the phase convention explicitly.
  2. [Sec. IV C 1] 'Using optimized CX1 and CX2 from Sec. III A' should reference Sec. III B, where the three-qubit CX gates are defined.
  3. [Appendix E] The target parameters E_J,1 = E_J,2 = 4 GHz and E_J,T = 17 GHz stated in the text differ from Table I (3.95/4.05 GHz and 18 GHz). Clarify which parameter set underlies the stability table and main-text results.
  4. [Fig. 5(f) caption] The caption for Fig. 5(f) is hard to parse. Define f̃_T01, f_d, and the bare/dressed frequency convention in the caption or in the main text.
  5. [Sec. IV B] The sentence 'In the same regime, they also stay within a range of 1.03e-4' lacks units and a clear subject. Specify whether this is the spread in error values or in fidelity.
  6. [Eq. (25c)] E_imag is defined with a minus sign and is therefore negative. The sentence 'the entire term is always positive' should refer to E_phase as a whole, not to E_imag individually, to avoid confusion.

Circularity Check

0 steps flagged

No circularity: the reported fidelities are outputs of an explicitly defined Hamiltonian simulation with optimized drive parameters, not fits or self-referential constructions.

full rationale

The paper is self-contained on its own terms. It defines the static and drive Hamiltonians (Eqs. 1-3, 9-10, 17-18), simulates the time-ordered evolution operator, and computes process fidelity against an ideal CNOT (Eq. 15). The quoted errors (coherent errors ~1e-5 for FT; CX1/CX2 >99.994%; parity checks >99.98%; logical FF-CNOT >99.97%) are the results of numerical optimization over drive parameters (epsilon, eta, omega_d). This is standard gate calibration/pulse optimization, not a fitted parameter renamed as a prediction. The selective-darkening ratio eta is first estimated perturbatively (Eq. 13) and then optimized; the final fidelity is not an input to any equation. Prior work on selective darkening [43-48] is cited as a starting point and includes externally published and experimentally demonstrated results; it is not an unverified self-citation chain that forces the outcome. The only noteworthy caveat is explicitly disclosed in Section V: 'Our proposed gate times are short in comparison to modern fluxonium [59] and transmon [63] coherence times, and thus we do not explicitly consider incoherent dynamics.' This is a scope limitation on how the coherent-error numbers map to hardware, not a circularity: the coherent fidelities are computed directly from the model and are not equivalent to any fitted input by construction. No equation reduces to its own input, and no central claim is justified solely by a self-citation.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities. The free parameters are the chosen qubit energies, coupling strengths, pulse shape, and optimized drive parameters. The main idealizations are full coherence, finite truncation, and ideal single-qubit gates, all of which are stated or implied in the text.

free parameters (6)
  • Qubit energy parameters (EJ, EC, EL) for F1, F2, T = Table I: EJ,F1/h=3.95 GHz, EC=1.4 GHz, EL=0.9 GHz; EJ,T/h=18 GHz, EC,T=0.25 GHz
    Chosen by hand to give the desired f01 and anharmonicity values, not fitted to experimental data. The central gate dynamics depend directly on these numbers.
  • Fluxonium-transmon coupling strengths J1, J2 = J1/h = J2/h = 22 MHz
    Chosen to balance gate speed against ZZ interaction and spectator shifts. The paper sweeps J in Figs. 4-7 but does not derive an optimal value from first principles.
  • Fluxonium-fluxonium coupling I = I/h = 0
    Set to zero for the main calculations; the scalability claim relies on this coupling remaining negligible in a larger lattice.
  • Drive amplitude ratio eta (target/control) = eta_opt = 1.36e-3 for 50 ns FT gate; Eq. (13) gives 1.01e-3
    Optimized numerically to minimize total gate error; the selective darkening condition ties it to matrix elements of the charge operator.
  • Drive amplitude epsilon and drive frequency omega_d = Optimized per gate; numerical values not reported in text
    Minimized coherent error for each gate configuration. These are the main fitting parameters in the simulations.
  • Pulse rise time tr = 5 ns
    Chosen for effective adiabatic switching of the drive, not optimized. The gate error depends on this choice.
axioms (6)
  • domain assumption Circuit-QED Hamiltonians for fluxonium and transmon (Eqs. 2-3)
    The simulations assume the devices are described by these lumped-element Hamiltonians with capacitive coupling n_T * J * n_alpha and a small direct n_F1 * n_F2 term.
  • domain assumption Operation at flux sweet spot phi_ext = pi for both fluxoniums
    All fluxoniums are biased at maximal coherence flux. This is a standard experimental choice but a premise for the quoted qubit frequencies.
  • domain assumption Full qubit coherence in all quoted fidelities
    The error budgets are coherent-only; the authors provide a formula for decoherence contributions but do not include them in the headline fidelity numbers.
  • domain assumption Finite Hilbert-space truncation
    Numerical diagonalization and the error budget require truncating the infinite-level fluxonium and transmon Hilbert spaces. The cutoff is not stated in the main text.
  • standard math Rotating-wave approximation and Schrieffer-Wolff perturbation theory
    Used to derive the effective ZX, ZZ, and IX interactions in Eq. (8) and the selective darkening condition. Valid when J and drive strength are small compared to the detuning.
  • ad hoc to paper Ideal single-qubit gates and virtual Z rotations in compound gates
    The parity check and logical CNOT sequences assume perfect Hadamard and Rz rotations, isolating all error to the CR pulses. This is a deliberate but not experimentally justified simplification.

pith-pipeline@v1.3.0-alltime-deepseek · 28215 in / 12612 out tokens · 139648 ms · 2026-08-04T21:28:06.793246+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Cross-Resonant Gates in Hybrid Fluxonium-Transmon Systems." pith.science (2026). https://pith.science/paper/W3O53CRF

@misc{pith2026250907935,
  author       = {Pith},
  title        = {Pith review of: Cross-Resonant Gates in Hybrid Fluxonium-Transmon Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W3O53CRF}},
  note         = {Machine review of arXiv:2509.07935}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

We propose a scalable fluxonium-transmon-fluxonium (FTF) system that utilizes a central transmon to mediate high-fidelity gates and parity checks between two fluxonium qubits without the need for strong non-local interactions. This approach suppresses unwanted long-range interactions, which is critical for developing larger quantum processors. First, we analyze the performance of cross-resonance (CR) CNOT gates between a fluxonium and a transmon. We show that even in the presence of a spectator qubit, these gates maintain high fidelity with coherent errors on the order of $10^{-5}$. We then demonstrate that these gates, when applied sequentially, enable high-fidelity parity checks and logical fluxonium-fluxonium CNOT gates. In addition, the central transmon can facilitate the readout of the neighboring fluxoniums, consolidating multiple critical functions into a single ancilla. Our work establishes the viability of a dual-species architecture as a promising path toward fault-tolerant quantum computation.

Figures

Figures reproduced from arXiv: 2509.07935 by Chen Wang, Maxim G. Vavilov, Nikola D. Dimitrov, Vladimir E. Manucharyan.

Figure 2
Figure 2. Figure 2: FIG. 2. Fluxonium-fluxonium [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Optimized gate error as a function of (a) coupling [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a-b): Eigenstate population dynamics of initial state [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a): Categorized errors in optimized [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Categorized gate error as a function of (a) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Evolution operator diagrams for optimized (a) [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a): Grouped [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Compound fluxonium-fluxonium [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. 50 ns [PITH_FULL_IMAGE:figures/full_fig_p016_12.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

85 extracted references · 35 canonical work pages · 2 internal anchors

  1. [1]

    targeted

    CX gate realization A natural extension of the system we consider in Sec. III A is the addition of another fluxonium (F2) strongly coupled to T and either weakly coupled to or fully decoupled from F1. It follows that the Hamilto- nian in Eq. (9) acquires terms for the third qubit and its interactions such that ˆHFTF(t) = ˆHFTF + ˆHdr,(17) whereJ 2 andIare...

  2. [2]

    (f): ∆(f T

    The optimized value balances error caused by spectator state-dependent detuning after accounting for drive-induced AC-Stark shifts. (f): ∆(f T

  3. [3]

    Square markers show results from second order perturbation theory while ignoring terms with charge matrix elements<0.01

    = ˜f T 01 −f T 01 as a function ofJ/hwhere ˜f T 01 is dressed by F1(F2) in statei(j) andf T 01 is the bare value. Square markers show results from second order perturbation theory while ignoring terms with charge matrix elements<0.01. Black stars show fd −f T 01 wheref d values have been chosen by the optimizer for a gate witht g = 50 ns. single-qubit gat...

  4. [4]

    flip” and “phase

    CX error budget Given that the number of computational matrix ele- ments is now 64, individually tracking and grouping each of the 56 error transitions is especially uninsightful. In- stead, we once again construct an error budget around the matrix elements ideally equal to unity. Following this approach, we define total error on an optimized gate as E=E ...

  5. [5]

    We propose doing so using our previously described CRcnotgates between the fluxonium of interest and the transmon

    FT system In a setup where qubit T does not store computational data, it can be kept in the ground state and used for an- cillary operations, including neighboring fluxonium read- out. We propose doing so using our previously described CRcnotgates between the fluxonium of interest and the transmon. For an idealcnotgate, we expect the following evolution: ...

  6. [6]

    We now index states as|i T jFαkFβ⟩and examine the use ofCX α to perform readout of Fα

    FTF system The same approach can be extended to the FTF sys- tem. We now index states as|i T jFαkFβ⟩and examine the use ofCX α to perform readout of Fα. ACX α gate has the ideal evolution |0⟩ ⊗(c0|0⟩+c 1|1⟩)⊗ |β⟩ CXα − − − →c0|0,0, β⟩+e iθc1|1,1, β⟩. (29) Depending on the conditions for readout to qualify as successful, different probability amplitudes ca...

    work page

  7. [7]

    Process fidelity approach WithCX 1,CX 2, and local Hadamards, acnotoper- ation between Fα(control) and Fβ(target) can also be performed. When T is initialized to|0⟩, and both fluxoni- ums are in arbitrary computational states, the sequence CX αβ for a logicalcnotgate between Fα(control) and Fβ(target) is ˆUCXαβ = ˆUCXα ( ˆH⊗ ˆI⊗ ˆH) ˆUCXβ ( ˆH⊗ ˆI⊗ ˆH) ˆU...

    work page

  8. [8]

    As before, valid initial states must have the transmon set to|0⟩

    State fidelity approach An alternative approach to characterizing our fluxonium-fluxonium gate is through comparison of sim- ulated and expected final qubit states. As before, valid initial states must have the transmon set to|0⟩. For uni- form sampling of this space, we define a set of initial 20 40 60 80 tg (ns) 10 5 10 4 10 3 10 2 10 1 100 Error 00 01 ...

    work page

  9. [9]

    We will do so in the active two-qubit subspace, labeled as|i αjT ⟩, and using shorthand notationn T ij =⟨i|ˆnT |j⟩, nα ij =⟨i|ˆnα|j⟩

    Matrix elements To estimateη α|β, perturbative analysis of the relevant matrix elements⟨0 T 0αβ|ˆnα|1T 0αβ⟩and ⟨0T 0αβ|ˆnT |1T 0αβ⟩can be helpful. We will do so in the active two-qubit subspace, labeled as|i αjT ⟩, and using shorthand notationn T ij =⟨i|ˆnT |j⟩, nα ij =⟨i|ˆnα|j⟩. Starting with the result from [45], and using angular frequencies such that ...

    work page

  10. [10]

    For the latter, second order perturbation theory is sufficient due to low qubit coupling strengths

    Energy levels Dressed eigenenergies for our FTF system can be calculated either directly through numerical diagonalization or with perturbation theory. For the latter, second order perturbation theory is sufficient due to low qubit coupling strengths. For our case whereJ=J 1 =J 2 andI= 0, we only have pathways for matrix elements of ˆn 1 ˆnT and ˆn2 ˆnT ....

    work page

  11. [11]

    These error categorizations come from a decomposition ofE= 1− F coh whereF coh is cal- culated with Eq

    2-qubit system To construct acnotgate error budget, we define Ebright,E dark,andE leak. These error categorizations come from a decomposition ofE= 1− F coh whereF coh is cal- culated with Eq. (15). Explicitly, this begins with E= 1− T r(ˆU † ˆU) 20 − T r(ˆU † id ˆU) 2 20 .(C1) Leakage error is separable from the rest as Eleak = 1 5 − Tr{ˆU † ˆU} 20 ,(C2) ...

    work page

  12. [12]

    For simplicity, we will now refer to the evo- lution operatorsCX α as ˆU

    3-qubit system We derive error termsE dark andE flip for the three- qubit case, extending our novel method from the two- qubit case. For simplicity, we will now refer to the evo- lution operatorsCX α as ˆU. Starting withE= 1− F coh, we write E= 1− Tr(ˆU † ˆU) 72 − Tr(ˆU † id ˆU) 2 72 .(C14) 16 16.0 16.5 17.0 17.5 18.0 EJ, T/h (GHz) 10 6 10 5 10 4 Error er...

    work page

  13. [13]

    P. W. Shor, Polynomial-time algorithms for prime factor- ization and discrete logarithms on a quantum computer, SIAM review41, 303 (1999)

    1999

  14. [14]

    L. K. Grover, A fast quantum mechanical algorithm for database search, inProceedings of the twenty-eighth an- nual ACM symposium on Theory of computing(1996) pp. 212–219

    1996

  15. [15]

    Aspuru-Guzik, A

    A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head- Gordon, Simulated quantum computation of molecular energies, Science309, 1704 (2005)

    2005

  16. [16]

    Preskill, Quantum computing in the nisq era and be- yond, Quantum2, 79 (2018)

    J. Preskill, Quantum computing in the nisq era and be- yond, Quantum2, 79 (2018)

    2018

  17. [17]

    Gottesman, An introduction to quantum error cor- rection and fault-tolerant quantum computation, arXiv preprint arXiv:0904.2557 (2009)

    D. Gottesman, An introduction to quantum error cor- rection and fault-tolerant quantum computation, arXiv preprint arXiv:0904.2557 (2009)

    Pith/arXiv arXiv 2009

  18. [18]

    A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Physical Review A54, 1098 (1996)

    1996

  19. [19]

    A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. Sloane, Quantum error correction and orthogonal geom- etry, Physical Review Letters78, 405 (1997)

    work page 1997

  20. [20]

    A. M. Steane, Simple quantum error-correcting codes, Physical Review A54, 4741 (1996)

    1996

  21. [21]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. Bardin, R. Barends, R. Biswas, S. Boixo, F. Brandao, D. Buell, B. Burkett, Y. Chen, J. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. M. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M. Harrigan, M. Hartmann, A. Ho, M. R. Hoffmann, T. Huang, T. Humble, S. Isako...

    2019

  22. [22]

    Quantum error correction below the surface code thresh- old, Nature638, 920 (2025)

    2025

  23. [23]

    D. Gao, D. Fan, C. Zha, J. Bei, G. Cai, J. Cai, S. Cao, F. Chen, J. Chen, K. Chen,et al., Establishing a new benchmark in quantum computational advantage with 105-qubit zuchongzhi 3.0 processor, Physical Review Let- ters134, 090601 (2025)

    work page 2025

  24. [24]

    Acharya, I

    R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, M. Ans- mann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Bab- bush, D. Bacon, J. C. Bardin, J. Basso, A. Bengtsson, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, B. B. Buckley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, Y. Chen, Z. Chen, B. Chiaro, J. Cogan, R. Collins, P. C...

    work page 2023

  25. [25]

    Krinner, N

    S. Krinner, N. Lacroix, A. Remm, A. Di Paolo, E. Genois, C. Leroux, C. Hellings, S. Lazar, F. Swiadek, J. Her- rmann, G. J. Norris, C. K. Andersen, M. M¨ uller, A. Blais, C. Eichler, and A. Wallraff, Realizing repeated quantum error correction in a distance-three surface code, Nature 605, 669 (2022)

    2022

  26. [26]

    J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, F. Battistel, M. Beekman, N. Haider, W. Vlothuizen, A. Bruno, B. M. Terhal, and L. DiCarlo, Logical-qubit operations in an error-detecting surface code, Nature Physics18, 80 (2022)

    2022

  27. [27]

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

    work page 2022

  28. [28]

    Blais, R.-S

    A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Physical Review A—Atomic, Molecular, and Optical Physics69, 062320 (2004)

    2004

  29. [29]

    Blais, J

    A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Quantum- information processing with circuit quantum electrody- namics, Physical Review A—Atomic, Molecular, and Op- tical Physics75, 032329 (2007)

    2007

  30. [30]

    G. Zhu, D. G. Ferguson, V. E. Manucharyan, and J. Koch, Circuit qed with fluxonium qubits: Theory of the dispersive regime, Physical Review B—Condensed Matter and Materials Physics87, 024510 (2013)

    2013

  31. [31]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Applied physics reviews6 (2019)

    2019

  32. [32]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wall- raff, Circuit quantum electrodynamics, Reviews of Mod- ern Physics93, 025005 (2021)

    2021

  33. [33]

    Brooks, A

    P. Brooks, A. Kitaev, and J. Preskill, Protected gates for superconducting qubits, Physical Review A—Atomic, Molecular, and Optical Physics87, 052306 (2013)

    work page 2013

  34. [34]

    Casparis, M

    L. Casparis, M. R. Connolly, M. Kjaergaard, N. J. Pear- son, A. Kringhøj, T. W. Larsen, F. Kuemmeth, T. Wang, C. Thomas, S. Gronin, G. C. Gardner, M. J. Manfra, C. M. Marcus, and K. D. Petersson, Superconducting gatemon qubit based on a proximitized two-dimensional electron gas, Nature Nanotechnology13, 915 (2018)

    work page 2018

  35. [35]

    Earnest, S

    N. Earnest, S. Chakram, Y. Lu, N. Irons, R. K. Naik, N. Leung, L. Ocola, D. A. Czaplewski, B. Baker, J. Lawrence, J. Koch, and D. I. Schuster, Realization of a Λ system with metastable states of a capacitively shunted fluxonium, Phys. Rev. Lett.120, 150504 (2018)

    2018

  36. [36]

    Brosco, G

    V. Brosco, G. Serpico, V. Vinokur, N. Poccia, and U. Vool, Superconducting qubit based on twisted cuprate van der waals heterostructures, Physical Review Letters 132, 017003 (2024)

    work page 2024

  37. [37]

    Joshi, K

    A. Joshi, K. Noh, and Y. Y. Gao, Quantum information processing with bosonic qubits in circuit qed, Quantum Science and Technology6, 033001 (2021)

    work page 2021

  38. [38]

    J. D. Teoh, P. Winkel, H. K. Babla, B. J. Chapman, J. Claes, S. J. de Graaf, J. W. Garmon, W. D. Kalfus, Y. Lu, A. Maiti,et al., Dual-rail encoding with supercon- ducting cavities, Proceedings of the National Academy of Sciences120, e2221736120 (2023)

    2023

  39. [39]

    M. Hays, J. Kim, and W. D. Oliver, Non-degenerate noise-resilient superconducting qubit, arXiv preprint arXiv:2502.15459 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  40. [40]

    I. V. Pechenezhskiy, R. A. Mencia, L. B. Nguyen, Y.- H. Lin, and V. E. Manucharyan, The superconducting quasicharge qubit, Nature585, 368 (2020)

    work page 2020

  41. [41]

    R. A. Mencia, W.-J. Lin, H. Cho, M. G. Vav- ilov, and V. E. Manucharyan, Integer fluxo- nium qubit, arXiv preprint arXiv:2403.16780 https://doi.org/10.48550/arXiv.2403.16780 (2024)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2403.16780 2024

  42. [42]

    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, Charge-insensitive qubit design de- rived from the cooper pair box, Phys. Rev. A76, 042319 (2007)

    2007

  43. [43]

    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

  44. [44]

    Ciani, B

    A. Ciani, B. M. Varbanov, N. Jolly, C. K. Andersen, and B. M. Terhal, Microwave-activated gates between a flux- onium and a transmon qubit, Physical Review Research 4, 043127 (2022)

    work page 2022

  45. [45]

    Heunisch, L

    L. Heunisch, L. Huang, S. Tasler, J. Schirk, F. Wall- ner, V. Feulner, B. Sarma, K. Liegener, C. M. Schnei- der, S. Filipp,et al., Scalable fluxonium-transmon ar- chitecture for error corrected quantum processors, arXiv preprint arXiv:2508.09267 (2025)

    Pith/arXiv arXiv 2025

  46. [46]

    I. A. Simakov, G. S. Mazhorin, I. N. Moskalenko, S. S. Seidov, and I. S. Besedin, High-fidelity transmon-coupler- activatedcczgate on fluxonium qubits, Phys. Rev. Appl. 21, 044035 (2024)

    work page 2024

  47. [47]

    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 two-qubit fluxonium gates with a transmon coupler, Phys. Rev. X13, 031035 (2023)

    2023

  48. [48]

    Singh, E

    S. Singh, E. Y. Huang, J. Hu, F. Yilmaz, M. F. Zwanen- burg, P. Kumaravadivel, S. Wang, T. V. Stefanski, and C. K. Andersen, Fast microwave-driven two-qubit gates between fluxonium qubits with a transmon coupler, arXiv preprint arXiv:2504.13718 (2025)

    arXiv 2025

  49. [49]

    Sheldon, E

    S. Sheldon, E. Magesan, J. M. Chow, and J. M. Gam- betta, Procedure for systematically tuning up cross-talk in the cross-resonance gate, Phys. Rev. A93, 060302 (2016)

    2016

  50. [50]

    Jurcevic, A

    P. Jurcevic, A. Javadi-Abhari, L. S. Bishop, I. Lauer, D. F. Bogorin, M. Brink, L. Capelluto, O. G¨ unl¨ uk, T. Itoko, N. Kanazawa, A. Kandala, G. A. Keefe, K. Kr- sulich, W. Landers, E. P. Lewandowski, D. T. McClure, G. Nannicini, A. Narasgond, H. M. Nayfeh, E. Pritchett, M. B. Rothwell, S. Srinivasan, N. Sundaresan, C. Wang, K. X. Wei, C. J. Wood, J.-B....

    2021

  51. [51]

    Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, Evidence for the utility of quantum computing before fault tolerance, Nature618, 500 (2023)

    2023

  52. [52]

    Rigetti and M

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

    2010

  53. [53]

    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. Rothwell, M. B. Ketchen, and M. Steffen, Simple all-microwave entangling gate for fixed-frequency super- conducting qubits, Phys. Rev. Lett.107, 080502 (2011)

    work page 2011

  54. [54]

    Magesan and J

    E. Magesan and J. M. Gambetta, Effective hamiltonian models of the cross-resonance gate, Physical Review A 101, 052308 (2020)

    2020

  55. [55]

    De Groot, J

    P. De Groot, J. Lisenfeld, R. Schouten, S. Ashhab, A. Lupa¸ scu, C. Harmans, and J. Mooij, Selective dark- ening of degenerate transitions demonstrated with two 20 superconducting quantum bits, Nature Physics6, 763 (2010)

    work page 2010

  56. [56]

    P. C. de Groot, S. Ashhab, A. Lupa¸ scu, L. DiCarlo, F. Nori, C. J. P. M. Harmans, and J. E. Mooij, Selec- tive darkening of degenerate transitions for implementing quantum controlled-not gates, New Journal of Physics 14, 073038 (2012)

    work page 2012

  57. [57]

    K. N. Nesterov, C. Wang, V. E. Manucharyan, and M. G. Vavilov, cnot gates for fluxonium qubits via selective darkening of transitions, Phys. Rev. Appl.18, 034063 (2022)

    work page 2022

  58. [58]

    Dogan, D

    E. Dogan, D. Rosenstock, L. Le Guevel, H. Xiong, R. A. Mencia, A. Somoroff, K. N. Nesterov, M. G. Vavilov, V. E. Manucharyan, and C. Wang, Two-fluxonium cross- resonance gate, Phys. Rev. Appl.20, 024011 (2023)

    2023

  59. [59]

    W.-J. Lin, H. Cho, Y. Chen, M. G. Vavilov, C. Wang, and V. E. Manucharyan, Verifying the analogy between transversely coupled spin-1/2 systems and inductively- coupled fluxoniums, New Journal of Physics27, 033012 (2025)

    work page 2025

  60. [60]

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

    2025

  61. [61]

    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, Physical Review Applied18, 034031 (2022)

    work page 2022

  62. [62]

    Cohen, A

    J. Cohen, A. Petrescu, R. Shillito, and A. Blais, Reminis- cence of classical chaos in driven transmons, PRX Quan- tum4, 020312 (2023)

    2023

  63. [63]

    Chen, H.-X

    L. Chen, H.-X. Li, Y. Lu, C. W. Warren, C. J. Kriˇ zan, S. Kosen, M. Rommel, S. Ahmed, A. Osman, J. Bizn´ arov´ a,et al., Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier, npj Quantum Information9, 26 (2023)

    work page 2023

  64. [64]

    Swiadek, R

    F. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais,et al., Enhancing dispersive readout of superconducting qubits through dynamic control of the dispersive shift: Experiment and theory, PRX Quantum 5, 040326 (2024)

    work page 2024

  65. [65]

    P. D. Kurilovich, T. Connolly, C. G. Bøttcher, D. K. Weiss, S. Hazra, V. R. Joshi, A. Z. Ding, H. Nho, S. Di- amond, V. D. Kurilovich,et al., High-frequency readout free from transmon multi-excitation resonances, arXiv preprint arXiv:2501.09161 (2025)

    Pith/arXiv arXiv 2025

  66. [66]

    P. A. Spring, L. Milanovic, Y. Sunada, S. Wang, A. F. van Loo, S. Tamate, and Y. Nakamura, Fast multiplexed superconducting-qubit readout with intrinsic purcell fil- tering using a multiconductor transmission line, PRX Quantum6, 020345 (2025)

    2025

  67. [67]

    S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv preprint quant-ph/9811052 (1998)

    Pith/arXiv arXiv 1998

  68. [68]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A86, 032324 (2012)

    2012

  69. [69]

    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. Cle- land, and J. M. Martinis, Superconducting quantum cir- cuits at the surface code threshold for fault toleranc...

    2014

  70. [70]

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

    2019

  71. [71]

    Somoroff, Q

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

    2023

  72. [72]

    E. L. Rosenfeld, C. T. Hann, D. I. Schuster, M. H. Ma- theny, and A. A. Clerk, High-fidelity two-qubit gates be- tween fluxonium qubits with a resonator coupler, PRX Quantum5, 040317 (2024)

    2024

  73. [73]

    Xiong, Q

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

    2022

  74. [74]

    T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, Quantum nondemolition measure- ments for quantum information, Phys. Rev. A73, 012113 (2006)

    work page 2006

  75. [75]

    M. P. Bland, F. Bahrami, J. G. C. Martinez, P. H. Preste- gaard, B. M. Smitham, A. Joshi, E. Hedrick, A. Pakpour- Tabrizi, S. Kumar, A. Jindal, R. D. Chang, A. Yang, G. Cheng, N. Yao, R. J. Cava, N. P. de Leon, and A. A. Houck, 2d transmons with lifetimes and coherence times exceeding 1 millisecond (2025), arXiv:2503.14798 [quant- ph]

    Pith/arXiv arXiv 2025

  76. [76]

    Ziman and V

    M. Ziman and V. Buˇ zek, All (qubit) decoherences: Complete characterization and physical implementation, Physical Review A—Atomic, Molecular, and Optical Physics72, 022110 (2005)

    work page 2005

  77. [77]

    Kofman and A

    A. Kofman and A. Korotkov, Two-qubit decoherence mechanisms revealed via quantum process tomography, Physical Review A—Atomic, Molecular, and Optical Physics80, 042103 (2009)

    work page 2009

  78. [78]

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

    work page 2012

  79. [79]

    J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comp. Phys. Comm.184, 1234 (2013)

    work page 2013

  80. [80]

    Groszkowski and J

    P. Groszkowski and J. Koch, Scqubits: a python package for superconducting qubits, Quantum5, 583 (2021)

    2021

Showing first 80 references.