Pith. sign in

REVIEW 4 major objections 4 minor 2 cited by

The paper demonstrates that a junction plus flux-tunable SQUID in series behaves as one effective Josephson element with a second harmonic up to ~10% of the fundamental and a flux point where the dispersive shift cancels.

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

2026-08-03 17:40 UTC pith:FPNA2HEF

load-bearing objection A solid, carefully done demonstration of flux-tunable higher Josephson harmonics in an all-SIS circuit; the headline 10.7% second harmonic is a model inference, not a direct measurement, but the out-of-sample checks and anharmonicity data make the case credible. the 4 major comments →

arxiv 2512.08470 v3 pith:FPNA2HEF submitted 2025-12-09 quant-ph cond-mat.mes-hall

Higher Josephson harmonics in a tunable double-junction transmon qubit

Ksenia Shagalov , David Feldstein-Bofill , Leo Uhre Jakobsen , Zhenhai Sun , Casper Wied , Amalie T. J. Paulsen , Johann Bock Severin , Malthe A. Marciniak
show 6 more authors
Clinton A. Potts Anders Kringh{\o}j Jacob Hastrup Karsten Flensberg Svend Kr{\o}jer Morten Kjaergaard
This is my paper
classification quant-ph cond-mat.mes-hall
keywords Josephson harmonicstransmon qubitflux-tunable SQUIDdouble-junction circuitBorn-Oppenheimer approximationdispersive shiftprotected qubitsJosephson potential engineering
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to establish that an all-superconducting circuit can reshape its Josephson potential in situ, with no semiconductor weak links. The device is a transmon made from a single tunnel junction in series with a flux-tunable SQUID; two sinusoidal junctions in series combine into an effective potential whose second harmonic grows with the junction-asymmetry parameter, which magnetic flux controls. Spectroscopy of the first four qubit transitions, plus a Born-Oppenheimer correction from an internal island mode, yields a second harmonic about 10% of the fundamental — far above typical single-junction values — and explains the qubit's non-monotonic, flux-dependent anharmonicity. The internal mode also couples to the readout resonator with opposite sign to the qubit, producing a flux point where the net dispersive shift vanishes. If correct, the result gives a purely SIS route to protected qubits such as the cos(2φ) qubit.

Core claim

A single tunnel junction in series with a flux-tunable SQUID acts as one effective Josephson element whose harmonic content is flux-tunable: the two sinusoidal junctions combine into U_red(φ_q) = -E_JΣ sqrt(1 - λ sin²(φ_q/2)), which at the measured λ≈0.85 has a second harmonic about 10% of the fundamental. Adding a Born-Oppenheimer correction from the internal island mode reproduces the measured anharmonicity (hα ≈ -E_C/3 at Φ_e=0, non-monotonic in flux) and yields U_k = [1, 0.107, 0.023, 0.006]. The internal mode also produces a dispersive shift opposite to the qubit's, so at Φ_e≈0.44Φ0 the net resonator shift cancels. The authors conclude this is an all-superconducting route to protected-q

What carries the argument

The load-bearing object is the effective single-mode potential U_red(φ_q) = -E_JΣ sqrt(1 - λ sin²(φ_q/2)), with λ = 4E_J1 E_J2/(E_J1+E_J2)^2 the junction-asymmetry parameter tuned by external flux. Its non-sinusoidal shape creates the higher harmonics; its quartic expansion gives hα ≈ -E_C^q(1 - 3λ/4). Because the reduced model alone does not match the measured spectra, the paper adds a Born-Oppenheimer correction U_BO(φ_q) = E_JΣ sqrt(2E_C^int/E_JΣ) sqrt(1 - λ sin²(φ_q/2)) for the fast internal mode, and extracts harmonic coefficients by Fourier projection. The full two-mode Hamiltonian 4E_C1 n1^2 + 4E_C2 n2^2 + g12 n1 n2 - E_J1 cosφ1 - E_J2 cosφ2 is what actually fits the transition freque

Load-bearing premise

The results stand or fall on the assumption that both junctions are perfectly sinusoidal and that the first-order Born-Oppenheimer correction from the unpublished companion theory is correct and complete; if the junctions carry intrinsic higher harmonics of a few percent, or if U_BO is wrong, the extracted U2/U1=0.107 and the harmonic flux dependence would shift.

What would settle it

Directly measure the effective current-phase relation of the series pair (phase-resolved) at the same flux points; if U2/U1 comes out at the reference transmon's ≈0.015 instead of ≈0.107, the geometric-harmonic claim is falsified. A second route is to re-fit the spectra letting each junction carry its own intrinsic U2 and check whether those intrinsic terms are forced to zero at all fluxes.

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

If this is right

  • The design offers an all-superconducting, flux-tunable source of a ~10% second harmonic, so cos(2φ)-type protected qubits no longer require hybrid semiconductor junctions.
  • At Φ_e≈0.44Φ0 the qubit and internal-mode dispersive shifts cancel, leaving the readout resonator unmoved despite continued coupling — a new flux knob for readout engineering.
  • The non-monotonic anharmonicity, reaching hα≈-E_C/3 at zero flux, changes how flux-tunable transmon frequencies and anharmonicities are predicted.
  • Any two-junction transmon model must include series-geometry harmonics; the ~10% U2 is far above the few-percent intrinsic values of single SIS junctions.
  • Near Φ_e≈0.31Φ0 and 0.47Φ0 the internal mode crosses higher qubit states, so single-mode approximations fail there and a two-mode treatment is required.

Where Pith is reading between the lines

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

  • One extension is to put three or more junctions in series; tuning their asymmetries could synthesize dominant third or fourth harmonics, opening different protected-qubit potential shapes.
  • Since the key correction U_BO comes from an unpublished companion paper, an exact non-perturbative two-mode calculation near the avoided crossings would independently check whether U2/U1≈0.107 survives without the BO approximation.
  • A simple experimental test of the geometric origin is to fabricate series pairs with different E_J1/E_J2 ratios and verify that U2/U1 follows the predicted λ-dependence before invoking internal-mode corrections.
  • The zero-net-dispersive-shift point could serve as an in-situ calibration of the internal-mode frequency, or as a 'cloaking' condition where the resonator becomes insensitive to the qubit state.

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

4 major / 4 minor

Summary. The paper reports a superconducting circuit element: a single Josephson junction in series with a flux-tunable SQUID, shunted by a large capacitor (a tunable double-junction transmon). The authors measure the first four qubit transition frequencies as a function of flux and fit them to a two-mode Hamiltonian with purely sinusoidal junction potentials. Using a Born-Oppenheimer reduction to an effective single-mode potential, they extract the harmonic content of the qubit phase potential, finding at zero flux U = [1, 0.107, 0.023, 0.006], i.e., a second harmonic of about 10% of the fundamental. They also observe a non-monotonic flux dependence of the anharmonicity, consistent with the reduced model, and a flux point where the qubit and internal-mode dispersive shifts to the readout resonator cancel. The paper claims this all-SIS platform enables in situ engineering of Josephson potential harmonics, relevant for protected qubits.

Significance. If the central quantitative claim is robust, this is a valuable experimental demonstration: it shows that a purely superconducting SIS–SIS circuit can generate a large and tunable second harmonic in the effective qubit potential, without hybrid semiconductor junctions. The work has several concrete strengths: the two-mode fit to f01/f02 predicts f03/f04 out of sample with about 6 MHz average deviation (Fig. 6b); the anharmonicity at Φ_e=0 is close to −E_C/3, a nontrivial signature of the double-junction geometry; the non-monotonic flux dependence distinguishes this device from a conventional flux-tunable transmon; and a fixed-frequency reference transmon provides a comparison of intrinsic harmonic content. However, the headline harmonic coefficients U_k are not directly measured but are computed from a Born-Oppenheimer potential whose derivation is referenced to an unpublished companion paper and whose input parameters come from a fit that assumes each junction is exactly sinusoidal. The quantitative claim therefore depends on assumptions that are not fully tested or quantified.

major comments (4)
  1. [Fig. 3b, Eq. (11), Section V] The extracted harmonic content U_k is not a direct measurement: it is computed from Eq. (11) using the BO potential U_red + U_BO, with parameters obtained from a fit to the two-mode model of Eq. (5)–(6), which assumes each junction has a purely sinusoidal potential. Any intrinsic higher harmonics in the physical SIS junctions—which Refs. [3–6] and the reference transmon (U_2/U_1 = 0.015) show can be a few percent—would be absorbed into the extracted U_k. The reference transmon is a different junction and does not bound the harmonic content of the SQUID junctions or the large-area single junction in this device. Please perform a sensitivity analysis: for example, refit the spectra with each junction potential including an intrinsic U_2 in the range 0–0.02 and show how the extracted U_2/U_1 at Φ_e=0 changes. Without this, the statement that 0.107 is significantly larger than intrinsic SIS
  2. [Eq. (9), Section IV, Ref. [34]] The Born-Oppenheimer correction U_BO in Eq. (9) contributes directly to the extracted harmonics via Eq. (11), but its derivation is not fully provided: the text refers to the unpublished companion Ref. [34], and Section IV only sketches a minimization around ϕ_int=0. For the asymmetric device (λ=0.85), the potential minimum in the internal coordinate is not obviously at ϕ_int=0, and the role of the capacitance asymmetry (C_J1 ≠ C_J2) is not addressed. Because this formula is load-bearing for the central quantitative claim, the full derivation must be included in the supplement (or Ref. [34] made available), and the approximations should be validated, e.g., against a numerical solution of the two-mode Hamiltonian.
  3. [Fig. 3b and fitting procedure] No uncertainty is propagated to the harmonic coefficients U_k. The two-mode fit has residuals of order 6 MHz (Fig. 6b), while the BO model deviates by up to 200 MHz near Φ_e=0.5Φ_0, and the extraction is performed at Φ_e=0 where the BO model is most accurate but not perfect. As presented, the value U_2/U_1 = 0.107 is a point estimate without error bars, so the reader cannot assess whether it is statistically distinguishable from, say, 0.05 or from the reference-junction value 0.015. Please provide confidence intervals, e.g., from a bootstrap of the transition-frequency data or from the covariance of the fitted parameters.
  4. [Abstract and Conclusions] The paper states that the extracted second harmonic is 'substantially higher than previously observed in single SIS junctions.' This comparison conflates the effective harmonic content of the single-mode potential—which is generated geometrically by the series combination of two sinusoidal junctions—with intrinsic higher harmonics of a single SIS junction. The manuscript should explicitly clarify that the reported U_k describe the effective potential in the qubit phase coordinate, not microscopic Josephson harmonics in the junction current–phase relation. This framing affects how the result is interpreted in the context of Ref. [3–6] and should be stated prominently.
minor comments (4)
  1. [Fig. 6b and Section II] The text says 'the average difference in frequency being ~6 MHz' but does not specify whether this is for the two-mode model across all flux points or for a subset. Please clarify.
  2. [Section III, Eq. (19)] The definitions of E_C1, E_C2, and g_12 in Eqs. (21)–(24) are dense; a sentence connecting them to the capacitance matrix in Eq. (18) would help readability.
  3. [Section V, Fig. 8] The reference transmon fit uses a phenomenological model H_T = 4E_C n^2 − Σ U_k cos(kφ). Please specify whether the same E_C was used for the four transitions and what constraints were applied to the U_k.
  4. [Title] Consider adding 'effective' to 'Higher Josephson harmonics' or rephrasing to 'higher harmonics in the effective Josephson potential' to avoid the implication of intrinsic junction harmonics.

Circularity Check

0 steps flagged

No circular reduction: harmonic content is a model-derived output constrained by f01/f02 and checked by out-of-sample f03/f04 predictions.

full rationale

The claimed harmonic coefficients U_k=[1,0.107,0.023,0.006] are not fit parameters. The two-mode model (Eq. 5) with sinusoidal junctions is fitted to f01 and f02/2, and the resulting parameters then predict f03/f04 out of sample (Fig. 2a, dotted lines), which is a genuine non-circular check. The harmonic content is obtained by Fourier-transforming the model potential U_red+U_BO (Eqs. 9-11), i.e. as a deterministic output of a constrained model, not as an input fed back into the fit. The reduced-model relation between lambda and anharmonicity (Eq. 8) is used for interpretation, but U_k never appears in the fit cost function, so no fitted parameter is renamed as a prediction. The BO correction is attributed to the authors' unpublished companion [34], but Section IV re-derives it from a stated Born-Oppenheimer minimize-and-expand procedure; thus the central argument does not reduce to an unverified self-citation. The reference transmon gives an empirical baseline for intrinsic junction harmonics, and its limited ability to bound the specific SQUID junctions is a modeling/uncertainty caveat rather than a circular step. No load-bearing step was found in which an output equals an input by construction.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 1 invented entities

The modeling pipeline is standard circuit QED (Lagrangian quantization, Schrieffer-Wolff) plus three domain assumptions that carry the central result: junctions are pure sinusoids, the internal mode is treatable at first order in E_C^int/E_JΣ via the BO formula of the unpublished companion Ref [34], and the Fourier coefficients of the effective potential equal the observable harmonic content. All fitted parameters enter through the two-mode model; the extracted harmonics are deterministic functions of those fits.

free parameters (7)
  • E_J1 (single-junction Josephson energy) = 23.4 GHz (CD2); 25.7 GHz (CD1)
    Fit to flux-dependent f01/f02 spectra in the two-mode model; sets the potential scale.
  • E_JA, E_JB (SQUID junction Josephson energies) = 30.0 / 34.5 GHz (CD2)
    Fit to the flux dependence of the SQUID energy; their ratio determines λ and hence the harmonic content.
  • C (qubit island capacitance) = 63.3 fF
    Fitted in CD1 from f01/f02 (and f_res), reused in CD2.
  • C_J1, C_JA, C_JB (junction capacitances) = 27.8 / 34.5 / 25.6 fF
    Fitted in CD1; set E_C^int, which enters the BO correction and the dispersive-shift analysis.
  • C_g, C_r (coupling and resonator capacitances) = 7.3 fF / 1.2 pF
    Enter the dispersive-shift formulas (Eqs. 21-26); taken from calibration/design and the fit.
  • λ (junction asymmetry parameter) = 0.85 at Φ_e=0
    Not measured directly; computed from fitted E_Js via Eq. (3). The extracted U_2/U_1 = 0.107 is a monotone transform of λ through the sqrt potential (Eq. 4, Fig. 1e).
  • U_k harmonic coefficients = [1, 0.107, 0.023, 0.006] at Φ_e=0
    Outputs of Eq. (11) applied to the fitted-plus-BO potentials. Headline numbers quoted without error bars; not independent observables.
axioms (6)
  • domain assumption Each SIS junction potential is purely sinusoidal, U = -E_J cos φ (Eq. 6); intrinsic higher harmonics are negligible for these junctions.
    Load-bearing: all extracted non-sinusoidal content is thereby attributed to the series geometry and internal mode. The reference transmon (U2/U1 ≈ 0.015, Sec. V) partially supports this for the same fabrication.
  • domain assumption The SQUID is a single flux-dependent junction, E_J2(Φ_e), periodic in flux; λ(Φ_e) follows Eq. (3).
    Standard lumped-element SQUID model used to fit the flux dependence of the spectra.
  • domain assumption Born-Oppenheimer separation: internal mode fast, qubit slow; first-order correction in E_C^int/E_JΣ ≈ 1/300 given by Eq. (9) (Ref [34]).
    The U_BO correction is central to the harmonic extraction (Eqs. 10-11) but its derivation is deferred to an unpublished companion paper by the same group.
  • domain assumption Fourier coefficients of the effective 1D potential (Eq. 11) equal the harmonic content quoted as the result.
    Defines what 'second harmonic U_2/U_1' means in the single-mode picture; the BO validity limits where this is reliable.
  • standard math Standard circuit-QED quantization and Schrieffer-Wolff dispersive-shift formulas (Eqs. 12-26).
    Textbook apparatus; not disputed.
  • standard math Transmon approximation E_JΣ/E_C ≫ 1 for the analytic anharmonicity (Eq. 8).
    Used only for comparison; the numerical two-mode model covers the full regime.
invented entities (1)
  • Internal mode (middle-island charge degree of freedom) independent evidence
    purpose: Renormalizes the qubit spectrum (BO correction, Eq. 9) and produces the opposite-sign dispersive shift that cancels χ_q at Φ_e ≈ 0.44Φ_0.
    The island is a physical part of the circuit, not a postulated entity. The paper provides falsifiable handles: the predicted f_int crossing f_03 near Φ_e ≈ 0.31Φ_0 (avoided crossing in Fig. 6a), the measured sign change of the total dispersive shift (Fig. 4), and the resonator-coupling fit.

pith-pipeline@v1.3.0-alltime-deepseek · 14199 in / 27375 out tokens · 242824 ms · 2026-08-03T17:40:44.794613+00:00 · methodology

0 comments
read the original abstract

Tunable Josephson harmonics open new avenues for qubit design. We demonstrate a superconducting circuit element consisting of a tunnel junction in series with a SQUID loop, yielding a Josephson potential whose harmonic content is strongly tunable by magnetic flux. Through spectroscopy of the first four qubit transitions, together with an effective single-mode model renormalized by the internal mode, we resolve a second harmonic with an amplitude up to $\sim10\%$ of the fundamental. We identify a flux sweet spot where the dispersive shift vanishes, achieved by balancing the dispersive couplings to the internal and qubit modes. This highly tunable element provides a route toward protected qubits and customizable nonlinear microwave devices.

Figures

Figures reproduced from arXiv: 2512.08470 by Amalie T. J. Paulsen, Anders Kringh{\o}j, Casper Wied, Clinton A. Potts, David Feldstein-Bofill, Jacob Hastrup, Johann Bock Severin, Karsten Flensberg, Ksenia Shagalov, Leo Uhre Jakobsen, Malthe A. Marciniak, Morten Kjaergaard, Svend Kr{\o}jer, Zhenhai Sun.

Figure 1
Figure 1. Figure 1: FIG. 1. Qubit circuit and device design. (a) Circuit [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Flux-dependent two-tone spectroscopy of the tun [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Measured anharmonicity as a function of flux and [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Flux dependence of the total dispersive shift in the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: presents the data analysis that was done in order to extract the transition frequencies from the raw data. We started from performing a two-tone power spec- [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Measurement of the four transitions as a function [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Simulation of the dispersive shift, [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Two-tone spectroscopy of a traditional single [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Coherence limitations of a Fourier-engineered $\cos(2\varphi)$ transmon qubit

    quant-ph 2026-05 unverdicted novelty 6.0

    A Fourier-engineered cos(2φ) qubit achieves spectral agreement with theory but its energy relaxation is limited by 1/f flux noise from residual first-harmonic fluctuations, unlike similar fluxonium qubits.

  2. Fraxonium: Fractional fluxon states for qudit encoding

    quant-ph 2026-05 unverdicted novelty 5.0

    Superconducting circuit hosts fractional fluxon states (fraxons) in a tailored Josephson potential to realize protected qudits with a STIRAP gate protocol.

Reference graph

Works this paper leans on

47 extracted references · 7 canonical work pages · cited by 2 Pith papers

  1. [1]

    Blais, A

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

    2021

  2. [2]

    Josephson, Possible new effects in superconductive tunnelling, Physics Letters1, 251 (1962)

    B. Josephson, Possible new effects in superconductive tunnelling, Physics Letters1, 251 (1962)

    1962

  3. [3]

    Willsch, D

    D. Willsch, D. Rieger, P. Winkel, M. Willsch, C. Dickel, J. Krause, Y. Ando, R. Lescanne, Z. Leghtas, N. T. Bronn, P. Deb, O. Lanes, Z. K. Minev, B. Dennig, S. Geisert, S. G¨ unzler, S. Ihssen, P. Paluch, T. Reisinger, R. Hanna, J. H. Bae, P. Sch¨ uffelgen, D. Gr¨ utzmacher, L. Buimaga-Iarinca, C. Morari, W. Wernsdorfer, D. P. DiVincenzo, K. Michielsen, G...

    2024

  4. [4]

    J. Kim, M. Hays, I. T. Rosen, J. An, H. Zhang, A. Goswami, K. Azar, J. M. Gertler, B. M. Niedzielski, M. E. Schwartz, T. P. Orlando, J. A. Grover, K. Ser- niak, and W. D. Oliver, Emergent harmonics in joseph- son tunnel junctions due to series inductance (2025), arXiv:2507.08171 [quant-ph]

    Pith/arXiv arXiv 2025

  5. [5]

    Z. Wang, R. W. Parker, E. Champion, and M. S. Blok, High-ej/ec transmon qudits with up to 12 levels, Physical Review Applied23, 10.1103/physrevapplied.23.034046 (2025). 6

    doi:10.1103/physrevapplied.23.034046 2025

  6. [6]

    F´ echant, M

    M. F´ echant, M. F. Dumas, D. B´ enˆ atre, N. Gosling, P. Lenhard, M. Spiecker, S. Geisert, S. Ihssen, W. Werns- dorfer, B. D’Anjou, A. Blais, and I. M. Pop, Offset charge dependence of measurement-induced transitions in trans- mons, Physical Review Letters135, 10.1103/yljv-b4kj (2025)

    work page doi:10.1103/yljv-b4kj 2025

  7. [7]

    A. A. Golubov, M. Y. Kupriyanov, and E. Il’ichev, The current-phase relation in josephson junctions, Rev. Mod. Phys.76, 411 (2004)

    2004

  8. [8]

    Larsen, M

    T. Larsen, M. Gershenson, L. Casparis, A. Kringhøj, N. Pearson, R. McNeil, F. Kuemmeth, P. Krogstrup, K. Petersson, and C. Marcus, Parity-protected superconductor-semiconductor qubit, Physical Re- view Letters125, 10.1103/physrevlett.125.056801 (2020)

    work page doi:10.1103/physrevlett.125.056801 2020

  9. [9]

    Gyenis, A

    A. Gyenis, A. Di Paolo, J. Koch, A. Blais, A. A. Houck, and D. I. Schuster, Moving beyond the transmon: Noise- protected superconducting quantum circuits, PRX Quan- tum2, 030101 (2021)

    2021

  10. [10]

    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

  11. [11]

    Banszerus, C

    L. Banszerus, C. Andersson, W. Marshall, T. Linde- mann, M. Manfra, C. Marcus, and S. Vaitiek˙ enas, Hybrid josephson rhombus: A superconducting element with tailored current-phase relation, Physical Review X15, 10.1103/physrevx.15.011021 (2025)

    work page doi:10.1103/physrevx.15.011021 2025

  12. [12]

    R. S. Souto, M. Leijnse, and C. Schrade, Josephson diode effect in supercurrent interferometers, Phys. Rev. Lett. 129, 267702 (2022)

    2022

  13. [13]

    Ciaccia, R

    C. Ciaccia, R. Haller, A. C. C. Drachmann, T. Linde- mann, M. J. Manfra, C. Schrade, and C. Sch¨ onenberger, Gate-tunable josephson diode in proximitized inas su- percurrent interferometers, Phys. Rev. Res.5, 033131 (2023)

    2023

  14. [14]

    Reinhardt, T

    S. Reinhardt, T. Ascherl, A. Costa, J. Berger, S. Gronin, G. C. Gardner, T. Lindemann, M. J. Manfra, J. Fabian, D. Kochan, C. Strunk, and N. Paradiso, Link between supercurrent diode and anomalous josephson effect re- vealed by gate-controlled interferometry, Nature Com- munications15, 10.1038/s41467-024-48741-z (2024)

    work page doi:10.1038/s41467-024-48741-z 2024

  15. [15]

    C. Ishii, Josephson currents through junctions with normal metal barriers, Progress of Theoretical Physics 44, 1525 (1970), https://academic.oup.com/ptp/article- pdf/44/6/1525/5378760/44-6-1525.pdf

    1970

  16. [16]

    Y.-J. Doh, J. A. van Dam, A. L. Roest, E. P. A. M. Bakkers, L. P. Kouwenhoven, and S. De Franceschi, Tun- able supercurrent through semiconductor nanowires, Sci- ence309, 272–275 (2005)

    2005

  17. [17]

    M. F. Goffman, C. Urbina, H. Pothier, J. Nyg ˚ ard, C. M. Marcus, and P. Krogstrup, Conduction channels of an inas-al nanowire josephson weak link, New Journal of Physics19, 092002 (2017)

    2017

  18. [18]

    Maiani, K

    A. Maiani, K. Flensberg, M. Leijnse, C. Schrade, S. Vaitiek˙ enas, and R. Seoane Souto, Nonsinu- soidal current-phase relations in semiconductor– superconductor– ferromagnetic insulator devices, Phys. Rev. B107, 245415 (2023)

    2023

  19. [19]

    E. M. Spanton, M. Deng, S. Vaitiek˙ enas, P. Krogstrup, J. Nyg ˚ ard, C. M. Marcus, and K. A. Moler, Cur- rent–phase relations of few-mode inas nanowire josephson junctions, Nature Physics13, 1177–1181 (2017)

    2017

  20. [20]

    T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jes- persen, P. Krogstrup, J. Nyg ˚ ard, and C. M. Marcus, Semiconductor-nanowire-based superconducting qubit, Phys. Rev. Lett.115, 127001 (2015)

    2015

  21. [21]

    de Lange, B

    G. de Lange, B. van Heck, A. Bruno, D. van Wo- erkom, A. Geresdi, S. Plissard, E. Bakkers, A. Akhmerov, and L. DiCarlo, Realization of microwave quantum circuits using hybrid superconducting-semiconducting nanowire josephson elements, Physical Review Letters 115, 10.1103/physrevlett.115.127002 (2015)

    doi:10.1103/physrevlett.115.127002 2015

  22. [22]

    Zhang, Z

    B. Zhang, Z. Li, V. Aguilar, P. Zhang, M. Pendharkar, C. P. Dempsey, J. S. Lee, S. D. Harrington, S. Tan, J. S. Meyer, M. Houzet, C. J. Palmstrøm, and S. M. Frolov, Evidence ofϕ 0-josephson junction from skewed diffrac- tion patterns in sn-insb nanowires, SciPost Physics18, 10.21468/scipostphys.18.1.013 (2025)

    work page doi:10.21468/scipostphys.18.1.013 2025

  23. [23]

    Feldstein-Bofill, Z

    D. Feldstein-Bofill, Z. Sun, C. Wied, S. Singh, B. D. Isakov, S. Krøjer, J. Hastrup, A. Gyenis, and M. Kjaer- gaard, Gatemon qubit revisited for improved reliability and stability, Phys. Rev. Appl.24, 044099 (2025)

    2025

  24. [24]

    J. M. Ch´ avez-Garcia, F. Solgun, J. B. Hertzberg, O. Jinka, M. Brink, and B. Abdo, Weakly flux-tunable superconducting qubit, Physical Review Applied18, 10.1103/physrevapplied.18.034057 (2022)

    work page doi:10.1103/physrevapplied.18.034057 2022

  25. [25]

    E. Y. Egorova, A. S. Kazmina, and I. N. Moskalenko, A weakly-tunable transmon qubit with an optimized shape of the shunted capacitance, Pisma v Zhurnal Tekhnich- eskoi Fiziki50, 10 (2024)

    2024

  26. [26]

    E. Y. Egorova, A. S. Kazmina, I. A. Simakov, I. N. Moskalenko, N. N. Abramov, D. A. Kalacheva, V. B. Lubsanov, A. N. Bolgar, N. Maleeva, and I. S. Besedin, Three-mode tunable coupler for superconducting two- qubit gates (2025), arXiv:2405.10886 [quant-ph]

    Pith/arXiv arXiv 2025

  27. [27]

    J. Hu, A. L. R. Manesco, A. Melo, T. V. Stefanski, C. K. Andersen, and V. Fatemi, Mixed spin-boson coupling for qubit readout with suppressed residual shot-noise de- phasing (2025), arXiv:2503.13411 [quant-ph]

    Pith/arXiv arXiv 2025

  28. [28]

    Sethi, O

    P. Sethi, O. Prakash, J.-P. Kaikkonen, M. Kervinen, E. T. Mannila, M. Ribeiro, D. Datta, C. W. F¨ orbom, J. Senior, R. P. Loreto, J. H¨ atinen, K. Viisanen, J. I. V¨ ayrynen, A. Ronzani, A. Kemppinen, V. Vesterinen, M. Prunnila, and J. Govenius, Native-oxide-passivated trilayer junctions for superconducting qubits (2025), arXiv:2504.03481 [quant-ph]

    arXiv 2025

  29. [29]

    A. M. Bozkurt, J. Brookman, V. Fatemi, and A. R. Akhmerov, Double-fourier engineering of josephson energy-phase relationships applied to diodes, SciPost Physics15, 10.21468/scipostphys.15.5.204 (2023)

    work page doi:10.21468/scipostphys.15.5.204 2023

  30. [30]

    Banszerus, W

    L. Banszerus, W. Marshall, C. W. Andersson, T. Linde- mann, M. J. Manfra, C. M. Marcus, and S. Vaitiek˙ enas, Voltage-controlled synthesis of higher harmonics in hy- brid josephson junction circuits (2024), arXiv:2402.11603 [cond-mat.mes-hall]

    Pith/arXiv arXiv 2024

  31. [31]

    R. C. Jaklevic, J. Lambe, A. H. Silver, and J. E. Mer- cereau, Quantum interference effects in josephson tunnel- ing, Phys. Rev. Lett.12, 159 (1964)

    1964

  32. [32]

    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, 10.1063/1.5089550 (2019)

    doi:10.1063/1.5089550 2019

  33. [33]

    Supplementary material

  34. [34]

    Jakobsen, K

    L. Jakobsen, K. Shagalov, D. Feldstein-Bofill, M. Kjaer- gaard, K. Flensberg, and S. Krøjer, (in preparation) (2025)

    2025

  35. [35]

    C. W. J. Beenakker, Universal limit of critical-current 7 fluctuations in mesoscopic josephson junctions, Phys. Rev. Lett.67, 3836 (1991)

    1991

  36. [36]

    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

  37. [37]

    Kringhøj, L

    A. Kringhøj, L. Casparis, M. Hell, T. W. Larsen, F. Kuemmeth, M. Leijnse, K. Flensberg, P. Krogstrup, J. Nyg ˚ ard, K. D. Petersson, and C. M. Marcus, Anhar- monicity of a superconducting qubit with a few-mode josephson junction, Physical Review B97, 10.1103/phys- revb.97.060508 (2018)

    doi:10.1103/phys- 2018

  38. [38]

    V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single cooper-pair cir- cuit free of charge offsets, Science326, 113 (2009), https://www.science.org/doi/pdf/10.1126/science.1175552

    doi:10.1126/science.1175552 2009

  39. [39]

    Di Paolo, T

    A. Di Paolo, T. E. Baker, A. Foley, D. S´ en´ echal, and A. Blais, Efficient modeling of superconducting quantum circuits with tensor networks, npj Quantum Information 7, 11 (2021)

    2021

  40. [40]

    Ciani, D

    A. Ciani, D. P. DiVincenzo, and B. M. Terhal,Lecture Notes on Quantum Electrical Circuits(TU Delft OPEN Publishing, 2024)

    2024

  41. [41]

    Rymarz and D

    M. Rymarz and D. P. DiVincenzo, Consistent quantiza- tion of nearly singular superconducting circuits, Phys. Rev. X13, 021017 (2023)

    2023

  42. [42]

    Lled´ o, R

    C. Lled´ o, R. Dassonneville, A. Moulinas, J. Cohen, R. Shillito, A. Bienfait, B. Huard, and A. Blais, Cloak- ing a qubit in a cavity, Nature Communications14, 10.1038/s41467-023-42060-5 (2023)

    doi:10.1038/s41467-023-42060-5 2023

  43. [43]

    M. H. Mu˜ noz Arias, C. Lled´ o, and A. Blais, Qubit read- out enabled by qubit cloaking, Phys. Rev. Appl.20, 054013 (2023)

    2023

  44. [44]

    Swiadek, R

    F. 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 theory, PRX Quantum5, 10.1103/prxquantum.5.040326 (2024)

    doi:10.1103/prxquantum.5.040326 2024

  45. [45]

    T. V. Stefanski and C. K. Andersen, Flux-pulse-assisted readout of a fluxonium qubit, Phys. Rev. Appl.22, 014079 (2024)

    2024

  46. [46]

    T. V. Stefanski, F. Yilmaz, E. Y. Huang, M. F. S. Zwa- nenburg, S. Singh, S. Wang, L. J. Splitthoff, and C. K. Andersen, Improved fluxonium readout through dynamic flux pulsing (2024), arXiv:2411.13437 [quant-ph]. I. F ABRICA TION AND MEASUREMENT SETUP The qubit island was patterned from a 200 nm thick Al film evaporated on a high-resistivity silicon subs...

    Pith/arXiv arXiv 2024

  47. [47]

    4) Josephson energy of the left junction in the SQUID loop

    Capacitance of the single junction. 4) Josephson energy of the left junction in the SQUID loop. 5) Capacitance of the left junction in the SQUID loop. 6) Josephson energy of the right junction in the SQUID loop. 7) Capacitance of the right junction in the SQUID loop. 8) Bare resonator frequency. 9) Qubit-resonator coupling capacitance. 9) Resonator self-c...