The Arm Qubit: A Superconducting Qubit Co-Designed for Coherence and Coupling

Alec Yen; Jeremy B. Kline; Kevin P. O'Brien; Stanley Chen

REVIEW 3 major objections 4 minor 70 references

The Arm Qubit: A Superconducting Qubit Co-Designed for Coherence and Coupling

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The paper predicts that the two-mode arm qubit, with decoherence included, would run CZ gates at 8.6e-5 infidelity in 17 ns, read out in 27 ns at 1e-4 assignment error, and execute single-qubit gates below 1e-5 error.

desk verdict The arm qubit is a genuinely new two-mode circuit design with unusually careful simulations, but the headline fidelities are projections that rest on an incomplete environmental model; the architecture deserves refereeing and, if the error budget is made explicit, experimental follow-up. read the letter →

arxiv 2506.05315 v1 pith:XCFHQ2WE submitted 2025-06-05 quant-ph

Jeremy B. Kline , Alec Yen , Stanley Chen , Kevin P. O'Brien This is my paper · ORCID

classification quant-ph

keywords armqubitsuperconductingfluxoniumtransmoncouplercross-KerrcouplingCZgatereadoutcoherence

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes a superconducting qubit made of two strongly coupled modes: a low-frequency double-well 'data' mode (fluxonium-like, with large anharmonicity) that holds the quantum information, and a higher-frequency weakly anharmonic 'arm' mode (transmon-like) that reaches out to other circuit elements. The design keeps the computational wavefunctions almost entirely in the data-mode coordinate, so the arm mode can be coupled nonlinearly with hundreds of megahertz of strength while the qubit states themselves stay linearly isolated. Including decoherence, the simulations predict a microwave-only CZ gate with $8.6\times10^{-5}$ infidelity in 17 ns, a static ZZ interaction below 0.4 kHz, readout with $1\times10^{-4}$ assignment error in 27 ns, and single-qubit gate errors below $1\times10^{-5}$. These numbers would beat current experimental superconducting-qubit errors using only capacitive coupling, which is the kind of scalable wiring a fault-tolerant processor needs.

What carries the argument

The load-bearing object is the two-mode circuit with potential $U=-E_{J12}\cos(\phi_1-\phi_2)+\frac{E_L}{2}(\phi_1-\phi_2+\tilde{\phi})^2 - E_{J2}\cos(\phi_2)$, biased at $\tilde{\phi}=\pi$ with $E_{J12}>E_L$. That combination creates a double well in the $\phi_1-\phi_2$ direction while the $E_{J2}$ term pins the minima to $\phi_2=0$, so the logical states live in $\phi_1$ and the charge operator $\hat{n}_2$ couples to the arm transition almost exclusively. The junction-and-inductor branch between the data and arm nodes acts as a quarton-like element providing a $\phi_1^2\phi_2^2$ term, which produces the large data-arm cross-Kerr shift; the arm then mediates effective cross-Kerr couplings to a transmon coupler (for CZ gates) or to a readout resonator (for amplitude readout). The argument is carried by hierarchical diagonalization of the circuit Hamiltonian followed by Lindblad and stochastic-Schrödinger simulations in a truncated eigenstate basis.

What would settle it

Measure the data-mode $T_1$ of a fabricated arm qubit biased at half a flux quantum, or rerun the gate master-equation simulation with a 240 $\mu$s total $T_1$ for the data modes; if the measured $T_1$ is near 240 $\mu$s rather than the dielectric-limited $\sim 400\,\mu$s, the quoted $8.6\times10^{-5}$ gate and $1\times10^{-4}$ readout errors would have to be revised downward, even if the coupling mechanism still works.

Watch

Extended reading notes

Core claim

The central claim is that separating information storage from coupling inside one circuit removes the usual tradeoff between strong coupling and isolation. In the arm qubit, the data mode is a fluxonium-like double well biased at half a flux quantum, and the arm mode's Josephson term forces the well minima to lie exactly at zero arm-phase ($\phi_2 = 0$); the computational states therefore oscillate almost purely in the data direction. Any element coupled capacitively to the arm mode then sees a large matrix element to the arm transition but a small one to the data transition (a ratio of about 8.5), while the data mode still shifts the arm frequency by a cross-Kerr interaction above 1 GHz. The paper shows in simulation that this combination yields CZ gates with $8.6\times10^{-5}$ infidelity including decoherence in 17 ns, static ZZ of 0.32 kHz, readout assignment error of $1\times10^{-4}$ in 27 ns at quantum efficiency 0.5, Purcell-limited lifetime of 167 ms without a Purcell filter, shot-noise dephasing time of 15.8 ms, and single-qubit gate errors below $1\times10^{-5}$. The gates and readout use only capacitive coupling between arm modes and auxiliary elements.

Load-bearing premise

The headline fidelities assume that dielectric loss with quality factor $Q=3.5\times10^6$ dominates decoherence and that quasiparticles in the junction array add no relaxation; the paper's own pessimistic quasiparticle bound ($x_{\mathrm{qp}}\approx2\times10^{-9}$) would pull the data-mode $T_1$ down to roughly 240 $\mu$s and degrade the quoted gate and readout errors.

Editorial extensions

If this is right

Microwave-only CZ gates between arm qubits reach 8.6e-5 infidelity in 17 ns with static ZZ of 0.32 kHz, so the gate does not rely on dynamically cancelling ZZ or on flux tuning.
Readout reaches 1e-4 assignment error in 27 ns at quantum efficiency 0.5 with QND infidelity about 2.75e-3, and the data mode is Purcell-protected to 167 ms without a Purcell filter.
Single-qubit X/2 gates run in 5 ns with error below 1e-5, enabled by the roughly 3 GHz anharmonicity of the data mode and a qubit frequency around 1.6 GHz that avoids fluxonium's rotating-wave-approximation limit.
Turning the arm-mode junction into a SQUID and tuning it off resonance when idle suppresses shot-noise dephasing to 15.8 ms.
A two-dimensional tiling is feasible with only capacitive coupling: four transmon couplers plus one readout resonator add about 25 fF to the arm mode, about 66 percent of its capacitance budget.

Reading between the lines

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

An implication the paper leaves implicit is that the isolation mechanism is generic: any qubit whose logical wavefunctions sit symmetrically at zero in the coupler coordinate could get the same strong-nonlinear, weak-linear coupling split.
The dominant environmental unknown is array quasiparticle density; a direct measurement of the quasiparticle density in a fluxonium-like junction array would decide whether the headline fidelities are realistic or optimistic.
The amplitude-based readout is naturally compatible with single-photon detection, which in a large processor would remove the need for a quantum-limited amplifier and associated isolators.
If the paper's own pessimistic quasiparticle bound is realized (total data-mode T1 near 240 microseconds), the simulated gate and readout errors would degrade noticeably, but the coupling mechanism and the qualitative speed advantage would likely survive.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read the arm qubit paper. The architecture is the real thing: a fluxonium-like data mode plus a transmon-like arm mode, with the EJ2 term forcing the double-well minima to lie exactly along phi_2=0. That simple condition decouples the computational states from the coupling port while keeping a >1 GHz cross-Kerr between data and arm, so you get strong nonlinear coupling without hybridizing the data mode. I don't see that in the earlier multi-mode work they cite, which mostly uses weakly anharmonic transmon modes. This is a new design idea.

The simulations are a cut above the usual projection paper. They use hierarchical diagonalization, include parasitic capacitances, run a 240-sample Monte Carlo over 5% fabrication variance, and give 90% yield curves for gate error and ZZ. They also disclose the main assumptions, including the quasiparticle neglect in App. C.4. The single-qubit and CZ schemes are plausible, and I believe the design is worth building.

Now the soft spots, in proportion. The headline numbers are projections, and the margin depends on environment parameters that are assumed, not measured. App. C.4's own pessimistic quasiparticle bound gives T1 around 540-560 us, the same order as the dielectric-limited 394-421 us, so neglecting it is not a harmless simplification. Combining the two channels lowers T1 to roughly 240 us. There's no per-channel error budget for the 17 ns CZ, so I can't tell whether 8.6e-5 survives a factor-of-two change in T1; the number is not decomposable from the text. The readout simulation appears to include only the resonator collapse operator, not dielectric or flux T1, so the 27 ns / 1e-4 assignment error may be optimistic for the same reason. None of this is an internal contradiction, and all of it is addressable: give the error budget, include the quasiparticle bound in the headline numbers, run readout with the full decoherence model. The Monte Carlo sweep covers only circuit parameters, so it doesn't probe the environmental uncertainty. And no code or data is shipped, which is a shame given how much detail is in the appendices.

My verdict is conditional, not reject. The architecture is the contribution and it's solid; the quantitative claims should be treated as projections until the error budget is decomposed and, ideally, a device is measured. I'd send this to review, with a request that the authors rerun with the pessimistic quasiparticle density and provide per-channel error bars. For a reader, this is most useful to people working on fluxonium, multi-mode qubits, and fast readout; the design idea is worth their time. I'd cite it.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes the 'arm qubit', a two-mode superconducting circuit with a fluxonium-like data mode and a transmon-like arm mode, designed so that the arm mode mediates strong nonlinear couplings to auxiliary modes while leaving the computational states nearly unhybridized. Numerical simulations of a two-arm-qubit circuit with a transmon coupler predict a microwave-only CZ gate with infidelity 8.6e-5 in 17 ns including decoherence and an always-on ZZ of 0.32 kHz (nominal); single-qubit X/2 gates below 1e-5; and an amplitude readout with assignment error 1e-4 in 27 ns at quantum efficiency 0.5, QND infidelity about 2.75e-3, Purcell-limited lifetime 167 ms, and a shot-noise dephasing time of 15.8 ms. These predictions are obtained by hierarchical diagonalization of the circuit Hamiltonians and Lindblad/stochastic-Schrodinger simulations; coherence times are computed from dielectric loss, flux noise, and charge noise, with quasiparticle dissipation explicitly neglected (Appendix C.4).

Significance. The architecture is genuinely interesting and the simulation study is carefully documented: the hierarchical diagonalization and truncation procedures (Appendix A), the explicit Monte Carlo scan over 5% fabrication variance with re-optimization of the tunable junctions (Section III.C), and the use of standard noise models without fitting to target results are all strengths. The claimed gate and readout fidelities, if correct, would be beyond the current experimental state of the art and would make the arm qubit an attractive building block. However, the headline numbers are projections, not measurements, and their margin is comparable to the uncertainty in the environmental model: the paper's own pessimistic quasiparticle bound and the missing intrinsic-T1 channel in the readout simulation both sit at the same order as the claimed fidelities. The significance is therefore conditional on completing the decoherence model and on demonstrating that the quoted numbers survive a sensitivity scan over environment parameters.

major comments (3)

[§III.B, Table II, Appendix C.4] The gate-fidelity headline (8.6e-5) is computed from the coherence times in Table II, which are obtained with quasiparticle dissipation explicitly excluded (Appendix C.4). Combining the paper's own pessimistic array-quasiparticle bound, T1_qp = 540-560 us (Eq. C13), with the Table II totals of 313/303 us lowers the data-mode T1 to roughly 200 us; even using the dielectric-only values (421/394 us) together with the bound gives about 240 us. The text should report the CZ infidelity under this combined channel and provide a per-channel error budget (dielectric, flux, quasiparticle, transmon dephasing, leakage) so the reader can see how much margin remains in the 8.6e-5 number.
[Appendix B, Eqs. (B1)-(B2)] The readout simulations use only the resonator-mediated collapse operator d; the intrinsic data-mode T1 and Tphi from Table II are not included. Over the claimed 27 ns integration time, the Table II T1 = 313 us alone contributes about 8.6e-5 relaxation probability for a |1> state, which is the same order as the target assignment error of 1e-4; with the quasiparticle-bound T1 (~200 us) the contribution is about 1.4e-4. The Appendix's criterion of discarding rates below 1 MHz eliminates exactly these low-rate channels, but their integrated effect over tens of nanoseconds is not negligible at the 1e-4 level. The stochastic and master-equation readout simulations need to include independent T1 and Tphi collapse operators for the data mode (and arm mode) before the readout fidelity claims can be accepted.
[§III.C, Fig. 3(c)-(d)] The Monte Carlo robustness scan varies only the circuit parameters (junction energies and capacitances) with a 5% standard deviation. The environmental parameters that set the headline fidelities--Q_diel, flux-noise amplitude A_Phi, quasiparticle density x_qp, temperature, and quantum efficiency--are held at their nominal values. Since Fig. 3(b) already shows that changing Q_diel from 1.5e6 to 8e6 changes the CZ error by roughly a factor of three, a sensitivity scan over environment parameters (or at least a table of infidelities versus Q_diel and x_qp) is necessary to support the 'beyond state-of-the-art' claim.

minor comments (4)

[Table II] The 'Tphi Total' entry for data mode 2 is printed as '1.04 us' but the context and the T_E2 entry imply 1.04 ms; please correct the typo.
[Abstract and §III.C] The abstract states 'always-on ZZ interaction less than 0.4 kHz' without qualification, while the Monte Carlo result in Fig. 3(d) gives a 90% yield below 1.8 kHz; the abstract should say 'nominally 0.32 kHz, with 90% yield below 1.8 kHz under 5% fabrication spread'.
[§V, Table IV] The eta=0.5 readout times are obtained by Gaussian SNR extrapolation from the eta=1 stochastic simulations, not by direct simulation; this should be stated in the main text alongside the 1e-4 claim.
[Appendix C.4] The sentence 'We therefore neglect quasiparticle dissipation' is an important assumption and should be echoed in the main text near the coherence-time table and the fidelity claims, since the headline numbers rest on it.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the reported gate and readout fidelities are computed from the circuit Hamiltonian plus standard noise models, with disclosed pulse optimization; the author-overlap citations are explanatory or methodological and not load-bearing.

full rationale

The central claims are produced by a self-contained simulation chain: the circuit Hamiltonian (Eqs. 1, A4, A8) is diagonalized hierarchically, decoherence rates are computed from standard dielectric, flux, and charge noise models (Appendix C), and fidelities are obtained from Lindblad master-equation or stochastic-Schrodinger simulations (Eqs. 3-5, B1-B3). No target result is fed back as an input: the CZ infidelity, single-qubit infidelity, readout assignment error, Purcell lifetime, and shot-noise dephasing time follow from the stated circuit parameters and noise assumptions. The only numerical optimizations are of pulse drive amplitudes and, in the Monte Carlo robustness scan, of junction energies to compensate fabrication spread; this is disclosed pulse/design optimization, not fitting to the quoted fidelities. The author-overlap citations ([13], [36]) are used for an explanatory analogy (quarton-like coupling) and for a simulation procedure that is independently detailed in Appendix B; they do not supply the load-bearing result. The paper's own caveat in Appendix C.4 that quasiparticle dissipation is neglected is a modeling assumption that affects the robustness of the fidelity projections, but it does not make the derivation circular. No step in the claimed derivation reduces, by construction, to its own inputs.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claims rest on five assumed external parameters (dielectric Q, quantum efficiency, flux noise amplitude, bath temperature, and the hand-chosen circuit design point) and on methodological assumptions, most notably that quasiparticle dissipation in the junction array is negligible. No new physical entities are introduced; the arm qubit is a new circuit topology built from standard components. The most exposed assumption is the quasiparticle neglect, since the paper's own pessimistic bound (T1 of 540-560 us) is comparable to the dielectric-limited T1 (394-421 us), which would reduce the combined T1 to about 240 us and raise the simulated gate infidelities.

free parameters (5)

Dielectric quality factor Q_diel = 3.5e6 (sensitivity at 1.5e6 and 8e6)
Assumed for all quoted coherence times and for the headline CZ infidelity of 8.6e-5, single-qubit errors below 1e-5, and readout QND values. The assumption is disclosed in Sec. III.B and Table II, but the headline numbers are tied to this value.
Quantum efficiency eta = 0.5
The headline readout claim (1e-4 assignment error in 27 ns) is extrapolated from ideal-efficiency (eta=1) stochastic simulations via a Gaussian SNR scaling by sqrt(eta) in Sec. V; it is not directly simulated. This is a conservative but unverified projection.
Flux noise amplitude A_Phi = 1 uPhi0/sqrt(Hz)
Standard value assumed in Appendix C.2 for the echo dephasing estimates (1.64 ms and 1.79 ms for the two data modes), which feed the total T_phi used in the gate simulations.
Effective temperature = 45 mK
Assumed thermal occupation of the readout resonator for the shot-noise dephasing estimate of 15.8 ms via Eq. (7) in Sec. V.
Nominal circuit parameters (Tables I and III) = EJ12/2pi=38.5 GHz, EL/2pi=26.2 GHz, EJ2/2pi=19.8 to 33.6 GHz, capacitances 20 to 293 fF
Hand-chosen design point. The headline gate and readout numbers are not averaged over the design space; the Monte Carlo scan in Sec. III.C covers 5% fabrication spread but only for coherent gate error, not for the decoherence-included fidelity.

assumptions (5)

standard math Standard circuit quantization with charge basis and node flux operators, including inductor potentials, is valid for these circuits.
Used throughout Appendix A, e.g., Eq. A4 for the five-mode gate circuit Hamiltonian.
domain assumption The hierarchical diagonalization scheme converges, and the truncations (576 eigenstates, population thresholds of 1e-6 to 1e-7) capture all relevant levels.
Appendix A and Sec. III.B. Convergence is asserted via population thresholds, not demonstrated by a systematic truncation study.
domain assumption The environment is Markovian with zero-temperature baths, and pure dephasing is modeled by 1/T_phi |1><1| collapse operators.
The Lindblad master equation simulations in Sec. III.B and Appendix B assume this standard form.
domain assumption Quasiparticle dissipation in the junction array is negligible for the quoted coherence times.
Appendix C.4 neglects quasiparticles citing fluxonium array measurements (ref 63), yet the paper's own pessimistic bound of 540-560 us is comparable to the dielectric T1 of 394-421 us, so this assumption is material to the headline numbers.
standard math The change-of-variables transformation W (Ding et al., ref 55) correctly isolates the periodic degree of freedom while preserving commutation relations.
Appendix A, Eqs. A1-A3; this is a published method treated as background.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The Arm Qubit: A Superconducting Qubit Co-Designed for Coherence and Coupling." pith.science (2026). https://pith.science/paper/XCFHQ2WE

@misc{pith2026250605315,
  author       = {Pith},
  title        = {Pith review of: The Arm Qubit: A Superconducting Qubit Co-Designed for Coherence and Coupling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XCFHQ2WE}},
  note         = {Machine review of arXiv:2506.05315}
}

abstract

We present a superconducting qubit which consists of two strongly coupled modes: one for data storage and one for coupling, allowing faster, higher-fidelity entangling gates and readout. The use of a dedicated coupling mode allows nonlinear couplings of several hundred MHz between the data mode and other elements, with minimal linear coupling to the data mode. Including decoherence, simulations show that this architecture enables microwave-only CZ gates with an infidelity of $8.6\times10^{-5}$ in 17 ns and always-on ZZ interaction less than 0.4 kHz. Numerical simulations also show readout with state assignment error of $1\times10^{-4}$ in 27 ns (assuming quantum efficiency $\eta=0.5$), Purcell-limited lifetime of 167 ms without a Purcell filter, and a mechanism to suppress shot-noise dephasing ($1/\Gamma_{\phi}=15.8$ ms). Single-qubit gate infidelities are below $1\times10^{-5}$ including decoherence. These beyond experimental state-of-the-art gate and readout fidelities rely only on capacitive coupling between arm qubits, making the arm qubit a promising scalable building block for fault-tolerant quantum computers.

Figures

Figures reproduced from arXiv: 2506.05315 by the authors.

**Figure 2.** FIG. 2. (a) Circuit diagram for two-qubit gates. The arm [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. (a) Circuit for readout of an arm qubit. The arm [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 3.** Figure 3: FIG. 3. (a) Simulated CZ gate coherent error as a function [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 5.** Figure 5: FIG. 5. Readout fidelities and histograms of 13,800 single [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. QND infidelity as a function of gate charge [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

70 extracted references · 34 canonical work pages

[1]

CZ gate circuit To simulate CZ gate fidelity between two arm qubits, we use the circuit from Fig. 2 A. The Hamiltonian for this circuit can be written as H= EL12 2 ( ˆϕ1 − ˆϕ2)2 +E J12 cos( ˆϕ1 − ˆϕ2) −E J2 cos( ˆϕ2)−E J3 cos( ˆϕ3)−E J4 cos( ˆϕ4) EL45 2 ( ˆϕ4 − ˆϕ5)2 +E J45 cos( ˆϕ4 − ˆϕ5) + X ij 4E−1 Cij ˆni ˆnj , (A4) whereE −1 Cij is the charging energ...

work page
[2]

Readout circuit To simulate readout of an arm qubit, we use the circuit of Fig. 4a. The Hamiltonian for this circuit is given by H= EL12 2 ( ˆϕ1 − ˆϕ2)2 +E J12 cos( ˆϕ1 − ˆϕ2) −E J2 cos( ˆϕ2) + ELr 2 ˆϕ2 r + X i,j∈{1,2,r} 4E−1 Cij ˆni ˆnj . (A8) We follow many of the same assumptions as in the gates simulation. When constructing the capacitance matrix, a ...

work page
[3]

Dielectric loss We model dielectric loss as voltage noise where the voltage spectral density for each capacitor is given by [29, 57, 58] SV (ω, C) = ℏ CQ (coth( ℏω 2kBT ) + 1) ,(C1) We then note that the capacitive energy terms in a circuit Hamiltonian can be rewritten as Hcap = X i̸=j 1 2 Cij( ˆVi − ˆVj)2 + X i 1 2 Ci ˆV 2 i ,(C2) whereC ij is the capaci...

work page
[4]

We compute dephasing errors by generating a 1-hour flux 11 noise time series ˜ϕ(t) with power spectral density given by SΦ(ω) =A 2 Φ 2π×1Hz ω ,(C7) withA 2 Φ = (1µΦ0)2/Hz

Flux noise Noise in the flux threading the arm qubit loop can cause both dephasing (T ϕ) and bit flip (T 1) errors. We compute dephasing errors by generating a 1-hour flux 11 noise time series ˜ϕ(t) with power spectral density given by SΦ(ω) =A 2 Φ 2π×1Hz ω ,(C7) withA 2 Φ = (1µΦ0)2/Hz. We then diagonalize the circuit Hamiltonian for a range of ˜ϕ(t) valu...

work page
[5]

This means that the data mode frequencies depend weakly on the offset gate charge of the arm modes

Charge noise The transmon-like arm modes of the arm qubits have a relatively lowE J /EC ≈40. This means that the data mode frequencies depend weakly on the offset gate charge of the arm modes. We estimate the charge noise dephas- ing time of the data modes by including the offset charge in the CZ gate circuit Hamiltonian, such that the capac- itive energy...

work page
[6]

Quasiparticles Quasiparticles tunneling across a Josephson junction can causeT 1 errors. These can be modeled as [61] Γqp = ⟨0|sin ˆϕ 2 |1⟩ 2 8EJ πℏ xqp s 2∆ ℏωq ,(C12) where ˆϕis the phase across the junction,E J is the energy of the junction,x qp is the quasiparticle density, and ∆ is the superconducting gap of the superconductor used. In fluxonium qubi...

work page
[7]

Google Quantum AI and Collaborators, Quantum error correction below the surface code threshold, Nature638, 920 (2025)

2025
[8]

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

Show all 70 references

[9]

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, N. Mahuli, J. Rose, J. C. Owens, H. Levine, E. Rosenfeld, P. Reinhold, L. Mon- celsi, J. A. Alcid, N. Alidoust, P. Arrangoiz-Arriola, J. Barnett, ...

2025
[10]

D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. T. Rosen, J. M. Gertler, T. M. Haz- ard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppress- ing Counter-Rotating Errors for Fast Single-Qubit Gates with Fl...

2024
[11]

Blais, A

A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit Quantum Electrodynamics, Reviews of Modern Physics93, 025005 (2021)

2021
[12]

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
[13]

Y. Sung, L. Ding, J. Braum¨ uller, A. Veps¨ al¨ ainen, B. Kan- nan, M. Kjaergaard, A. Greene, G. O. Samach, C. Mc- Nally, D. Kim, 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 Z ...

2021
[14]

Kandala, K

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

2021
[15]

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. Gus- tavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High-Fidelity, Frequency-Flexibl...

2023 arXiv
[16]

D. Sank, Z. Chen, M. Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Mu- tus, M. Neeley, C. Neill, P. J. J. O’Malley, C. Quin- tana, P. Roushan, A. Vainsencher, T. White, J. Wen- ner, A. N. Korotkov,...

2016
[17]

M. F. Dumas, B. Groleau-Par´ e, A. McDonald, M. H. Mu˜ noz-Arias, C. Lled´ o, B. D’Anjou, and A. Blais, Measurement-Induced Transmon Ionization, Physical Review X14, 041023 (2024)

2024
[18]

A. A. Chapple, O. Benhayoune-Khadraoui, S. Richer, and A. Blais, Balanced cross-Kerr coupling for supercon- ducting qubit readout (2025), arXiv:2501.09010 [quant- ph]

2025
[19]

Y. Ye, J. B. Kline, S. Chen, A. Yen, and K. P. O’Brien, Ultrafast superconducting qubit readout with the quar- ton coupler, Science Advances10, eado9094 (2024)

2024
[20]

Wang, F.-M

C. Wang, F.-M. Liu, H. Chen, Y.-F. Du, C. Ying, J.- W. Wang, Y.-H. Huo, C.-Z. Peng, X. Zhu, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, 99.9%-fidelity in measuring a superconducting qubit (2024), arXiv:2412.13849 [quant- ph]

2024 arXiv
[21]

J. M. Gambetta, A. A. Houck, and A. Blais, Supercon- ducting qubit with purcell protection and tunable cou- pling, Phys. Rev. Lett.106, 030502 (2011)

2011
[22]

Zhang, Y

G. Zhang, Y. Liu, J. J. Raftery, and A. A. Houck, Sup- pression of photon shot noise dephasing in a tunable cou- pling superconducting qubit, npj Quantum Information 3, 1 (2017)

2017
[23]

Hazra, W

S. Hazra, W. Dai, T. Connolly, P. D. Kurilovich, Z. Wang, L. Frunzio, and M. H. Devoret, Benchmark- ing the readout of a superconducting qubit for repeated measurements, Phys. Rev. Lett.134, 100601 (2025)

2025
[24]

Diniz, E

I. Diniz, E. Dumur, O. Buisson, and A. Auff` eves, Ultra- fast quantum nondemolition measurements based on a diamond-shaped artificial atom, Phys. Rev. A87, 033837 (2013)

2013
[25]

T. Roy, S. Kundu, M. Chand, S. Hazra, N. Nehra, R. Cos- mic, A. Ranadive, M. P. Patankar, K. Damle, and R. Vi- jay, Implementation of pairwise longitudinal coupling in a three-qubit superconducting circuit, Phys. Rev. Appl. 7, 054025 (2017)

2017
[26]

Pfeiffer, M

F. Pfeiffer, M. Werninghaus, C. Schweizer, N. Bruck- moser, L. Koch, N. J. Glaser, G. B. P. Huber, D. Bunch, F. X. Haslbeck, M. Knudsen, G. Krylov, K. Liegener, A. Marx, L. Richard, J. H. Romeiro, F. A. Roy, J. Schirk, C. Schneider, M. Singh, L. S¨ odergren, I. Tsitsilin, 13 F...

2024
[27]

Finck, S

A. Finck, S. Carnevale, D. Klaus, C. Scerbo, J. Blair, T. McConkey, C. Kurter, A. Carniol, G. Keefe, M. Kumph, and O. Dial, Suppressed crosstalk be- tween two-junction superconducting qubits with mode- selective exchange coupling, Physical Review Applied16, 10.1103/physrevappl...

2021 doi
[28]

Dassonneville, T

R. Dassonneville, T. Ramos, V. Milchakov, L. Planat, E. Dumur, F. Foroughi, J. Puertas, S. Leger, K. Bharad- waj, J. Delaforce, C. Naud, W. Hasch-Guichard, J. J. Garc ´ ıa-Ripoll, N. Roch, and O. Buisson, Fast high- fidelity quantum nondemolition qubit readout via a nonperturb...

2020
[29]

Dassonneville, T

R. Dassonneville, T. Ramos, V. Milchakov, C. Mori, L. Planat, F. Foroughi, C. Naud, W. Hasch-Guichard, J. Garc ´ ıa-Ripoll, N. Roch, and O. Buisson, Transmon- qubit readout using an in situ bifurcation amplification in the mesoscopic regime, Phys. Rev. Appl.20, 044050 (2023)

2023
[30]

T. Roy, M. Chand, A. Bhattacharjee, S. Hazra, S. Kundu, K. Damle, and R. Vijay, Multimode superconducting cir- cuits for realizing strongly coupled multiqubit processor units, Phys. Rev. A98, 052318 (2018)

2018
[31]

K. V. Salunkhe, S. Kundu, S. Das, J. Deshmukh, M. P. Patankar, and R. Vijay, The quantromon: A qubit- resonator system with orthogonal qubit and readout modes (2025), arXiv:2501.17439 [quant-ph]

2025 arXiv
[32]

Brooks, A

P. Brooks, A. Kitaev, and J. Preskill, Protected gates for superconducting qubits, Phys. Rev. A87, 052306 (2013)

2013
[33]

W. C. Smith, A. Kou, X. Xiao, U. Vool, and M. H. De- voret, Superconducting circuit protected by two-cooper- pair tunneling, npj Quantum Information6, 8 (2020)

2020
[34]

T. W. Larsen, M. E. Gershenson, L. Casparis, A. Kringhøj, N. J. Pearson, R. P. G. McNeil, F. Kuem- meth, P. Krogstrup, K. D. Petersson, and C. M. Marcus, Parity-protected superconductor-semiconductor qubit, Phys. Rev. Lett.125, 056801 (2020)

2020
[35]

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

2025 arXiv
[36]

Kalashnikov, W

K. Kalashnikov, W. T. Hsieh, W. Zhang, W.-S. Lu, P. Kamenov, A. Di Paolo, A. Blais, M. E. Gershenson, and M. Bell, Bifluxon: Fluxon-parity-protected super- conducting qubit, PRX Quantum1, 010307 (2020)

2020
[37]

Schrade, C

C. Schrade, C. M. Marcus, and A. Gyenis, Protected hy- brid superconducting qubit in an array of gate-tunable josephson interferometers, PRX Quantum3, 030303 (2022)

2022
[38]

Levine, A

H. Levine, A. Haim, J. S. C. Hung, N. Alidoust, M. Kalaee, L. DeLorenzo, E. A. Wollack, P. Arrangoiz- Arriola, A. Khalajhedayati, R. Sanil, H. Moradinejad, Y. Vaknin, A. Kubica, D. Hover, S. Aghaeimeibodi, J. A. Alcid, C. Baek, J. Barnett, K. Bawdekar, P. Bienias, H. A. Carson...

2024
[39]

Huang, X

W. Huang, X. Sun, J. Zhang, Z. Guo, P. Huang, Y. Liang, Y. Liu, D. Sun, Z. Wang, Y. Xiong, X. Yang, J. Zhang, L. Zhang, J. Chu, W. Guo, J. Jiang, S. Liu, J. Niu, J. Qiu, Z. Tao, Y. Zhou, X. Linpeng, Y. Zhong, and D. Yu, Logical multi-qubit entanglement with dual-rail super- co...

2025
[40]

K. S. Chou, T. Shemma, H. McCarrick, T.-C. Chien, J. D. Teoh, P. Winkel, A. Anderson, J. Chen, J. C. Cur- tis, S. J. de Graaf, J. W. O. Garmon, B. Gudlewski, W. D. Kalfus, T. Keen, N. Khedkar, C. U. Lei, G. Liu, P. Lu, Y. Lu, A. Maiti, L. Mastalli-Kelly, N. Mehta, S. O. Mundha...

2024
[41]

Mehta, J

N. Mehta, J. D. Teoh, T. Noh, A. Agrawal, A. An- derson, B. Birdsall, A. Brahmbhatt, W. Byrd, M. Ca- cioppo, A. Cabrera, L. Carroll, J. Chen, T.-C. Chien, R. Chamberlain, J. C. Curtis, D. Danso, S. R. Desigan, F. D’Acounto, B. H. Elfeky, S. M. Farzaneh, C. Foley, B. Gudlewski,...

2025 arXiv
[42]

Y. Ye, K. Peng, M. Naghiloo, G. Cunningham, and K. P. O’Brien, Engineering purely nonlinear coupling between superconducting qubits using a quarton, Phys. Rev. Lett. 127, 050502 (2021)

2021
[43]

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
[44]

Lambert, E

N. Lambert, E. Gigu` ere, P. Menczel, B. Li, P. Hopf, G. Su´ arez, M. Gali, J. Lishman, R. Gadhvi, R. Agar- wal, A. Galicia, N. Shammah, P. D. Nation, J. R. Jo- hansson, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, QuTiP 5: The quantum toolbox in Python (2024), arXiv:2412.04...

2024 arXiv
[45]

L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quantum operations, Physics Letters A367, 47 (2007)

2007
[46]

M. A. Nielsen and I. L. Chuang,Quantum Computa- tion and Quantum Information: 10th Anniversary Edi- tion(Cambridge University Press, 2010)

2010
[47]

C. Wang, X. Li, H. Xu, Z. Li, J. Wang, Z. Yang, Z. Mi, X. Liang, T. Su, C. Yang, G. Wang, W. Wang, Y. Li, M. Chen, C. Li, K. Linghu, J. Han, Y. Zhang, Y. Feng, Y. Song, T. Ma, J. Zhang, R. Wang, P. Zhao, W. Liu, G. Xue, Y. Jin, and H. Yu, Towards practical quantum computers: t...

2022
[48]

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 e...

2025 arXiv
[49]

D. R. Jones, C. D. Perttunen, and B. E. Stuckman, Lipschitzian optimization without the lipschitz constant, Journal of Optimization Theory and Applications79, 157–181 (1993)

1993
[50]

Gablonsky and C

J. Gablonsky and C. Kelley, A locally-biased form of the direct algorithm, Journal of Global Optimization21, 27–37 (2001)

2001
[51]

A. A. Clerk and D. W. Utami, Using a qubit to measure photon-number statistics of a driven thermal oscillator, Phys. Rev. A75, 042302 (2007)

2007
[52]

Gambetta, W

J. Gambetta, W. A. Braff, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Protocols for optimal readout of qubits using a continuous quantum nondemolition mea- surement, Phys. Rev. A76, 012325 (2007)

2007
[53]

F. m. c. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais, S. Krinner, and A. Wallraff, Enhanc- ing dispersive readout of superconducting qubits through dynamic control of the dispersive shift: Experiment and t...

2024
[54]

Rigetti, J

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. C´ orcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms, Ph...

2012
[55]

Z. Wang, S. Shankar, Z. Minev, P. Campagne-Ibarcq, A. Narla, and M. Devoret, Cavity attenuators for super- conducting qubits, Phys. Rev. Appl.11, 014031 (2019)

2019
[56]

Opremcak, I

A. Opremcak, I. V. Pechenezhskiy, C. Howington, B. G. Christensen, M. A. Beck, E. Leonard, J. Suttle, C. Wilen, K. N. Nesterov, G. J. Ribeill, T. Thorbeck, F. Schlenker, M. G. Vavilov, B. L. T. Plourde, and R. McDer- mott, Measurement of a superconducting qubit with a microwav...

2018 doi
[57]

Opremcak, C

A. Opremcak, C. H. Liu, C. Wilen, K. Okubo, B. G. Christensen, D. Sank, T. C. White, A. Vainsencher, M. Giustina, A. Megrant, B. Burkett, B. L. T. Plourde, and R. McDermott, High-fidelity measurement of a su- perconducting qubit using an on-chip microwave photon counter, Phys....

2021
[58]

A. J. Kerman, Efficient numerical simulation of complex josephson quantum circuits (2020), arXiv:2010.14929 [quant-ph]

2020 arXiv
[59]

S. P. Chitta, T. Zhao, Z. Huang, I. Mondragon-Shem, and J. Koch, Computer-aided quantization and numeri- cal analysis of superconducting circuits, New Journal of Physics24, 103020 (2022)

2022
[60]

Groszkowski and J

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

2021
[61]

Ding, H.-S

D. Ding, H.-S. Ku, Y. Shi, and H.-H. Zhao, Free-mode re- moval and mode decoupling for simulating general super- conducting quantum circuits, Phys. Rev. B103, 174501 (2021)

2021
[62]

Beaudoin, J

F. Beaudoin, J. M. Gambetta, and A. Blais, Dissipation and ultrastrong coupling in circuit QED, Physical Review A84, 10.1103/physreva.84.043832 (2011)

2011 doi
[63]

R. J. Schoelkopf, A. A. Clerk, S. M. Girvin, K. W. Lehn- ert, and M. H. Devoret, Qubits as spectrometers of quan- tum noise, inQuantum Noise in Mesoscopic Physics, edited by Y. V. Nazarov (Springer Netherlands, Dor- drecht, 2003) pp. 175–203

2003
[64]

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
[65]

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

2019
[66]

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, Physical Review A76, 042319 (2007)

2007
[67]

L. B. Nguyen, G. Koolstra, Y. Kim, A. Morvan, T. Chis- tolini, S. Singh, K. N. Nesterov, C. J¨ unger, L. Chen, Z. Pedramrazi,et al., Blueprint for a high-performance fluxonium quantum processor, PRX Quantum3, 037001 (2022)

2022
[68]

I. M. Pop, K. Geerlings, G. Catelani, R. J. Schoelkopf, L. I. Glazman, and M. H. Devoret, Coherent suppres- sion of electromagnetic dissipation due to superconduct- ing quasiparticles, Nature508, 369–372 (2014)

2014
[69]

Somoroff, Q

A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. Kuzmin, and V. E. Manucharyan, Millisecond Coher- ence in a Superconducting Qubit, Physical Review Let- ters130, 267001 (2023)

2023
[70]

McEwen, K

M. McEwen, K. C. Miao, J. Atalaya, A. Bilmes, A. Crook, J. Bovaird, J. M. Kreikebaum, N. Zo- brist, E. Jeffrey, B. Ying, A. Bengtsson, H.-S. Chang, A. Dunsworth, J. Kelly, Y. Zhang, E. Forati, R. Acharya, J. Iveland, W. Liu, S. Kim, B. Burkett, A. Megrant, Y. Chen, C. Neill, D...

2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

CZ gate circuit To simulate CZ gate fidelity between two arm qubits, we use the circuit from Fig. 2 A. The Hamiltonian for this circuit can be written as H= EL12 2 ( ˆϕ1 − ˆϕ2)2 +E J12 cos( ˆϕ1 − ˆϕ2) −E J2 cos( ˆϕ2)−E J3 cos( ˆϕ3)−E J4 cos( ˆϕ4) EL45 2 ( ˆϕ4 − ˆϕ5)2 +E J45 cos( ˆϕ4 − ˆϕ5) + X ij 4E−1 Cij ˆni ˆnj , (A4) whereE −1 Cij is the charging energ...

work page

[2] [2]

Readout circuit To simulate readout of an arm qubit, we use the circuit of Fig. 4a. The Hamiltonian for this circuit is given by H= EL12 2 ( ˆϕ1 − ˆϕ2)2 +E J12 cos( ˆϕ1 − ˆϕ2) −E J2 cos( ˆϕ2) + ELr 2 ˆϕ2 r + X i,j∈{1,2,r} 4E−1 Cij ˆni ˆnj . (A8) We follow many of the same assumptions as in the gates simulation. When constructing the capacitance matrix, a ...

work page

[3] [3]

Dielectric loss We model dielectric loss as voltage noise where the voltage spectral density for each capacitor is given by [29, 57, 58] SV (ω, C) = ℏ CQ (coth( ℏω 2kBT ) + 1) ,(C1) We then note that the capacitive energy terms in a circuit Hamiltonian can be rewritten as Hcap = X i̸=j 1 2 Cij( ˆVi − ˆVj)2 + X i 1 2 Ci ˆV 2 i ,(C2) whereC ij is the capaci...

work page

[4] [4]

We compute dephasing errors by generating a 1-hour flux 11 noise time series ˜ϕ(t) with power spectral density given by SΦ(ω) =A 2 Φ 2π×1Hz ω ,(C7) withA 2 Φ = (1µΦ0)2/Hz

Flux noise Noise in the flux threading the arm qubit loop can cause both dephasing (T ϕ) and bit flip (T 1) errors. We compute dephasing errors by generating a 1-hour flux 11 noise time series ˜ϕ(t) with power spectral density given by SΦ(ω) =A 2 Φ 2π×1Hz ω ,(C7) withA 2 Φ = (1µΦ0)2/Hz. We then diagonalize the circuit Hamiltonian for a range of ˜ϕ(t) valu...

work page

[5] [5]

This means that the data mode frequencies depend weakly on the offset gate charge of the arm modes

Charge noise The transmon-like arm modes of the arm qubits have a relatively lowE J /EC ≈40. This means that the data mode frequencies depend weakly on the offset gate charge of the arm modes. We estimate the charge noise dephas- ing time of the data modes by including the offset charge in the CZ gate circuit Hamiltonian, such that the capac- itive energy...

work page

[6] [6]

Quasiparticles Quasiparticles tunneling across a Josephson junction can causeT 1 errors. These can be modeled as [61] Γqp = ⟨0|sin ˆϕ 2 |1⟩ 2 8EJ πℏ xqp s 2∆ ℏωq ,(C12) where ˆϕis the phase across the junction,E J is the energy of the junction,x qp is the quasiparticle density, and ∆ is the superconducting gap of the superconductor used. In fluxonium qubi...

work page

[7] [7]

Google Quantum AI and Collaborators, Quantum error correction below the surface code threshold, Nature638, 920 (2025)

2025

[8] [8]

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