Pith. sign in

REVIEW 3 major objections 4 minor 71 references

Quantifying Non-Abelian Stability in Majorana Qubits through Rabi Beating Signatures

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 beating frequency between even- and odd-parity Rabi oscillations in a quantum dot coupled to a Majorana qubit scales linearly with the deviation parameters $E_1$ and $t_2$, independent of the base Rabi frequency, yielding a direct…

desk verdict A plausible Rabi-beating protocol for Majorana qubit stability, but the abstract overstates the parameter independence and the Kitaev-chain benchmark stays qualitative. read the letter →

arxiv 2502.09062 v2 pith:NZSIWPMH submitted 2025-02-13 cond-mat.mes-hall

Yu Zhang , Jiayi Chen , Jie Liu , X.C. Xie This is my paper · ORCID
classification cond-mat.mes-hall PACS 74.45.+c74.20.Mn74.78.-w
keywords MajoranaqubitstabilityRabioscillationsbeatingsignaturequantumdotAndreevboundstatesminimalKitaevchaintopologicalsuperconductorchargesensing
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 simple readout for how close a Majorana qubit is to ideal: couple a quantum dot to the qubit, quickly switch the coupling on, and watch the dot's charge occupation oscillate. In an ideal qubit the even- and odd-parity Rabi oscillations share one frequency, but any deviation—the internal Majorana–Majorana coupling $E_1$ or the parasitic dot–Majorana coupling $t_2$—splits the two frequencies and creates a beating pattern. The paper's central claim is that the beating frequency scales linearly with $E_1$ and $t_2$ and is independent of the base Rabi frequency, so reading the beat period gives a direct, quantitative number for the qubit's stability. It further shows the beat survives weak dissipation and that an effective two-parameter model reproduces the Rabi dynamics of a minimal Kitaev chain.

What carries the argument

The load-bearing object is the decomposition of the coupled quantum-dot–Majorana-qubit Hamiltonian into even- and odd-parity two-level blocks, $H = H_+ \oplus H_-$, with $H_\pm = \begin{pmatrix} E_d \pm E_1 & t_1 \pm t_2 \\ t_1 \pm t_2 & -E_d \mp E_1 \end{pmatrix}$. Each block gives a Rabi frequency $\Omega_\pm$, and the beat in the dot charge is the difference $|\Omega_+ - \Omega_-|$; the first-order expansion $|\Omega_+ - \Omega_-| \approx 2(E_d E_1 + t_1 t_2)/\Omega_0$ is the identity that converts a measured beat period into the deviation parameters. A Lindblad-form quantum master equation is used to show that weak dissipation damps the overall oscillation without shifting the beat frequency.

What would settle it

A sweep of $t_2$ at fixed $E_1=0$ in which the measured beat frequency does not grow linearly with $t_2$ (for example, saturating or turning quadratic) would disprove the linear-scaling claim; alternatively, fitting Rabi traces of a minimal Kitaev chain to the effective model and finding that the extracted $E_1, t_2$ disagree with the chain's microscopic couplings would show that the benchmark is not quantitative.

Watch

Extended reading notes

Core claim

For the model-independent Hamiltonian $H_E = -E_d d^\dagger d + t_1(d^\dagger - d)\gamma_1 + iE_1\gamma_1\gamma_2 + it_2(d + d^\dagger)\gamma_2$, the quantum-dot population in each fermion-parity sector oscillates at its own Rabi frequency $\Omega_\pm = \sqrt{(E_d \pm E_1)^2 + (t_1 \pm t_2)^2}$. When the initial Majorana-qubit state is a superposition of both parities, the measured dot population is the sum of the two oscillations, and the envelope beats at frequency $|\Omega_+ - \Omega_-|$, which to first order in the deviations equals $2(E_d E_1 + t_1 t_2)/\Omega_0$ with $\Omega_0 = \sqrt{E_d^2 + t_1^2}$. Because this beat frequency is linear in $E_1$ and $t_2$ and, in the operating regime considered, insensitive to the base Rabi frequency, the authors argue that a single Rabi trace, read with existing single-shot charge sensing, provides a direct quantitative measure of Majorana-qubit stability, including for small deviations that conductance measurements cannot resolve.

Load-bearing premise

The whole protocol assumes that every realistic imperfection in a Majorana qubit can be captured by two constant numbers, $E_1$ and $t_2$, in the effective Hamiltonian, and that this effective model remains quantitatively accurate for concrete systems such as a minimal Kitaev chain.

Editorial extensions

If this is right

  • A single charge-sensing Rabi trace yields estimates of $E_1$ and $t_2$ directly from the beat period, without needing to resolve tiny energy splittings in conductance spectra.
  • Because the beat frequency is insensitive to the base Rabi frequency and varies little with $E_d$, the quantum-dot energy does not need fine-tuning for the stability readout, which relaxes the experimental requirements.
  • Weak dissipation damps the Rabi envelope but leaves the beat frequency intact, so the stability measure remains usable in the presence of quasiparticle poisoning and dephasing.
  • In the minimal Kitaev chain, the beat frequency tracks the deviation $t-\Delta$ from the sweet spot, so the same protocol doubles as a sweet-spot diagnostic.
  • The protocol is platform-agnostic: it works for nanowire topological-superconductor devices, vortex Majoranas probed by an STM-tip molecule, and other architectures that realize the same effective Hamiltonian.

Reading between the lines

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

  • If the linear scaling survives experimental test, the Rabi-beat readout could be used as a factory calibration step before braiding: devices whose beat period corresponds to $E_1$ or $t_2$ above a threshold would be rejected without lengthy braiding checks.
  • The asymmetry under dissipation—noise on $\gamma_2$ being dark in an ideal qubit but active when $t_2 \neq 0$—suggests the same experiment could map which Majorana terminal is more exposed to local noise, turning a stability measurement into a spatial diagnostic.
  • A quantitative map from minimal-Kitaev-chain parameters to the effective $E_1, t_2$ would let the protocol predict beat frequencies from microscopic device settings; the paper demonstrates qualitative agreement only, so deriving that map is a natural next step.
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.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes a protocol for quantifying the stability of a Majorana qubit (MQ) by coupling it to a quantum dot (QD) and measuring Rabi oscillations in the QD occupation. Within a four-state model, the dynamics split by fermion parity into two two-level systems; when the MQ is imperfect (nonzero internal Majorana coupling E1 and extra QD-Majorana coupling t2), the two parity sectors acquire slightly different Rabi frequencies, producing beats. A Lindblad master equation is used to argue that weak dissipation does not shift the beat frequency, and a two-dot minimal Kitaev chain is simulated to show that beats appear when the hopping and pairing parameters differ. The paper claims that the beating frequency scales linearly with E1 and t2, is independent of the base Rabi frequency, and can serve as a quantitative measure of MQ stability.

Significance. If fully established, the protocol would offer a simple, experimentally accessible route to characterizing Majorana-qubit deviations using single-shot charge readout. The exact two-level reduction in Eq. (4) is transparent and the numerical simulations are straightforward to reproduce. The robustness of the beat frequency against weak dissipation is a useful and non-obvious observation, and the minimal Kitaev chain simulations show that beating is not an artifact of the effective model. However, the quantitative promises in the abstract currently exceed what is demonstrated: the independence-of-base-frequency claim is an overstatement, and the benchmark against the minimal Kitaev chain is only qualitative.

major comments (3)
  1. [Abstract and Eq. (4) in 'Rabi beats in MQ'] The central claim that the beating frequency 'remains independent of the base Rabi frequency' is not supported by Eq. (4). Since Omega_+^2 - Omega_-^2 = 4(Ed E1 + t1 t2), the small-deviation beat frequency is |Omega_+ - Omega_-| = 2(Ed E1 + t1 t2)/Omega_0 with Omega_0 = sqrt(Ed^2 + t1^2). This depends explicitly on Omega_0: changing Ed or t1 while keeping E1 and t2 fixed changes the beat frequency. The advertised independence holds only in a restricted parameter regime, for example Ed much smaller than t1, or under a simultaneous rescaling of Ed and t1, not as stated. The abstract and the section 'Rabi beats in MQ' should be revised to state the actual condition for weak dependence, and Fig. 2(d) should be tied quantitatively to that condition.
  2. ['Rabi Oscillation in minimal Kitaev chain'] The benchmark that is supposed to establish quantitative accuracy is only qualitative. The authors show that exact-chain Rabi oscillations develop beats when the hopping t differs from the pairing Delta and that the beat frequency grows with the deviation delta = t - Delta (Fig. 4(b)), but no mapping or numerical extraction of the effective parameters E1 and t2 from the chain Hamiltonian is provided. The sentence 'All the picture can be captured by the effective model' is an assertion, not a quantitative comparison. Without a relation between the microscopic deviation delta and the effective parameters (E1, t2), a measured beat frequency cannot be converted into a quantitative stability parameter, which is the paper's central promise. I request an analytical mapping or a numerical fit of the exact chain dynamics to Eq. (4) that extracts E1 and t2 and quantifies the agreement.
  3. ['Rabi beats in MQ'] The protocol's visibility rests on the initial state being a superposition alpha|0> + beta f-dagger|0> of both parities, with alpha = beta singled out as optimal. The manuscript does not discuss how this qubit state is prepared or verified in the proposed QD-MQ setups, nor whether the beat signature survives an ensemble average over unknown alpha and beta or over a thermal mixture. Since the beat pattern is the measured observable, a discussion of initialization and expected visibility is needed to support the claimed experimental accessibility.
minor comments (4)
  1. [Fig. 2 caption / text] The body text for Fig. 2(b) states that t2 = 0.01 meV and 0.005 meV are compared, while the caption lists t2 = 0.01 meV and 0.02 meV; please correct the inconsistency.
  2. [Throughout] There are several typos and grammatical slips, including 'diabetic' for 'diabatic', 'suddendly', 'quantitively', and 'sweet pot'; a careful proofreading pass is needed.
  3. [Eq. (2)] The Lindblad equation uses 'h' where h-bar is meant, or the text should state that natural units with h-bar = 1 are used.
  4. [Fig. 4(b) and surrounding text] The text says 'the Rabi frequency is proportional to the deviation of t - Delta'; the quantity shown to scale with the deviation is the beating frequency, not the individual Rabi frequency, and the wording should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the beating-frequency dependence on E1 and t2 is derived directly from the model Hamiltonian, and the Kitaev-chain comparison is a qualitative benchmark rather than a fitted prediction.

full rationale

The paper's central claim is a derived consequence of its own stated Hamiltonian, not a fitted parameter renamed as a prediction. From Eq. (1), the parity subspaces give H± in Eq. (3), and the Rabi formula Eq. (4) yields Ω± = sqrt((Ed±E1)^2 + (t1±t2)^2). The beating frequency |Ω+−Ω−| is therefore proportional, to first order, to 2(EdE1 + t1t2)/Ω0, so the observed linear scaling with E1 and t2 is a direct mathematical consequence of the model, not an independent empirical input. The protocol then inverts this relation to infer E1 and t2 from a measured beat frequency, which is a standard model-based measurement rather than circular reasoning. The minimal Kitaev chain simulation in Fig. 4 is an independent microscopic check showing beats when t≠Δ and a beat frequency that grows with t−Δ; although the paper does not derive the quantitative mapping between (t−Δ) and (E1,t2), that missing mapping is a support gap, not a circular reduction. The self-citations [61,62] for the ABS model are accompanied by external references [30,31] and are not the sole load-bearing evidence. The abstract's statement that the beat frequency is 'independent of the base Rabi frequency' is not strictly true from Eq. (4) (the first-order expression depends on Ω0), but this is an overstatement, not circularity. Overall, the derivation chain is self-contained and no step reduces to its own input by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles or forces; it relies on established Majorana physics. The key assumptions are the effective model and its claimed quantitative accuracy. No parameters are fitted to external data; E1 and t2 are the target quantities to be measured, but in the simulations they are chosen by hand.

free parameters (3)
  • E1 = 0.01-0.02 meV in simulations
    Internal coupling between the two Majoranas; it is a chosen model parameter that the beating frequency depends on linearly. It is not fitted to data, but it is varied by hand to demonstrate the effect.
  • t2 = 0.005-0.02 meV in simulations
    Parity-breaking coupling between the quantum dot and the second Majorana; it is the other parameter that the beating frequency depends on. Chosen in simulations, not measured.
  • alpha/beta ratio = set to 1 in Fig. 2a for maximal visibility
    The initial superposition weights of the Majorana qubit state. The beat visibility depends on this ratio, though the beat frequency does not. The paper assumes an arbitrary superposition but does not discuss how to prepare or verify it.
assumptions (5)
  • domain assumption The model Hamiltonian Eq. (1) with couplings t1, t2 and internal coupling E1 describes a quantum dot coupled to a Majorana qubit in all relevant experimental platforms.
    Stated in Section 'Model-independent Hamiltonian...' as a universal framework. This is the starting point of all derivations.
  • standard math The dynamics of the quantum dot occupation follow the Lindblad master equation Eq. (2) with Lindblad operators being the Majorana operators gamma1 and gamma2.
    The Lindblad equation is a standard tool for open quantum systems. The specific choice of gamma operators as jump operators is a modeling assumption.
  • domain assumption The initial state of the Majorana qubit is a superposition of even and odd parity states, alpha|0> + beta f†|0>.
    Necessary for beats to appear. The paper states 'MQ would be in an arbitrary qubit state' but does not justify why this is realistic or how to control it.
  • standard math The minimal Kitaev chain at the sweet spot t = Delta hosts two Majorana zero modes.
    Standard result in the field, cited with refs [53-60]. Used for the benchmark simulation.
  • ad hoc to paper The effective model remains 'quantitatively accurate' when benchmarked against the minimal Kitaev chain.
    Claimed at the end of the Kitaev chain section, but no quantitative mapping between chain parameters and E1, t2 is provided. This is an unproven assertion that is central to the protocol's practical validity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantifying Non-Abelian Stability in Majorana Qubits through Rabi Beating Signatures." pith.science (2026). https://pith.science/paper/NZSIWPMH

@misc{pith2026250209062,
  author       = {Pith},
  title        = {Pith review of: Quantifying Non-Abelian Stability in Majorana Qubits through Rabi Beating Signatures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NZSIWPMH}},
  note         = {Machine review of arXiv:2502.09062}
}
read the original abstract

Evaluating the stability of Majorana qubits (MQs) is a central challenge for topological quantum computation. Here we propose a simple and experimentally accessible protocol to quantify MQ stability by coupling a quantum dot (QD) to an MQ, which induces Rabi oscillations in the QD charge occupation that can be directly detected using recently developed single-shot readout techniques. In realistic systems, deviations from ideal MQ behavior lead to a characteristic beating pattern in the Rabi dynamics. We show that the beating frequency scales linearly with these deviations while remaining independent of the base Rabi frequency, thereby providing a direct and quantitative measure of MQ stability. Importantly, the beating signature is robust against weak dissipation, and we further demonstrate that the effective model remains quantitatively accurate when benchmarked against a realistic minimal Kitaev chain. Our results establish a practical and scalable route for quantitatively characterizing Majorana qubit stability in current experimental platforms.

Figures

Figures reproduced from arXiv: 2502.09062 by the authors.

Figure 1
Figure 1. FIG. 1: (a) Schematic diagram of the setup. Top panel sug [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Dissipation in MQ. Influence of dissipation term [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4: Rabi oscillation in minimal kitaev chain. Here [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 64 canonical work pages

  1. [1]

    As shown in Fig

    How- ever, nonzero E1 and t2 introduce a small deviation in the Rabi frequency. As shown in Fig. 1(d), the frequen- cies in the two parity subspaces exhibit slight deviations under these conditions. 0 100 200 300 400 0 0.5 1P1 1=0 1=0.01 0 100 200 300 400 0 0.5 1P1 2=0 2=0.01 0 100 200 300 400 (1/mev) 0 0.5 1P1 2=0.01 1=0.01 0 100 200 300 400 (1/mev) 0 0....

    work page

  2. [2]

    Kitaev, Phys

    A. Kitaev, Phys. Usp. 44, 131 (2000)

    work page 2000

  3. [3]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008)

    work page 2008

  4. [4]

    D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001)

    2001

  5. [5]

    Alicea, Y

    J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M. P. A. Fisher, Nat. Phys. 7, 1915 (2011)

    work page 2011

  6. [6]

    Fu, and C

    L. Fu, and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008)

    work page 2008

  7. [7]

    J. D. Sau, R. M. Lutchyn, S. Tewari, S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010)

    2010

  8. [8]

    Fujimoto, Phys

    S. Fujimoto, Phys. Rev. B. 77, 220501(R) (2008)

    work page 2008

Show all 71 references
  1. [9]

    M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. B 82,134521 (2010)

    2010

  2. [10]

    Alicea, Phys

    J. Alicea, Phys. Rev. B 81, 125318 (2010)

    2010

  3. [11]

    Lutchyn, J.D

    R.M. Lutchyn, J.D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010)

    2010

  4. [12]

    Mourik, K

    V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, L. P. Kouwenhoven, Science 336, 1003 (2012)

    2012

  5. [13]

    M. T. Deng, C.L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, Nano Lett. 12, 6414 (2012)

    2012

  6. [14]

    A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, H.Shtrikman, Nat. Phys. 8, 887 (2012)

    2012

  7. [15]

    Bommer, Michiel W.A

    ¨Onder G¨ ul, Hao Zhang, Jouri D.S. Bommer, Michiel W.A. de Moor, Diana Car, S´ ebastien R. Plissard, Erik P.A.M. Bakkers, Attila Geresdi, Kenji Watanabe, Takashi Taniguchi, Leo P. Kouwenhoven, Nature Nan- otechnology 13, 192 (2018)

    2018

  8. [16]

    S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygard, P. Krogstrup and C. M. Marcus, Nature 531, 206 (2016)

    2016

  9. [17]

    M. T. Deng, S. Vaitiekenas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nyg ˚ ard, P. Krogstrup, C. M. Marcus, Science 354, 1557 (2016)

    2016

  10. [18]

    Nadj-perge, llya K

    S. Nadj-perge, llya K. Drozdov, Jian Li, Hua Chen, Sangjun Jeon, J. Seo, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani, Science 346, 6209 (2014)

    2014

  11. [19]

    B. E. Feldman, M. T. Randeria, Jian Li, Sangjun Jeon, Yonglong Xie, Zhijun Wang, Ilya K. Drozdov, B. Andrei Bernevig, Ali Yazdani, Nat. Phys. 13, 286 (2017)

    2017

  12. [20]

    Whiticar, F

    Antonio Fornieri, Alexander M. Whiticar, F. Setiawan, El ´ ıas Portol´ es, Asbjørn C. C. Drachmann, Anna Kesel- man, Sergei Gronin, Candice Thomas, Tian Wang, Ray Kallaher, Geoffrey C. Gardner, Erez Berg, Michael J. Manfra, Ady Stern, Charles M. Marcus, and Fabrizio Nichele, N...

    2019

  13. [21]

    H. Ren, F. Pientka, S. Hart, A. Pierce, M. Kosowsky, L. Lunczer, R. Schlereth, B. Scharf, E. M. Hankiewicz, L. W. Molenkamp, B. I. Halperin, and A. Yacoby, Nature 569, 93 (2019)

    2019

  14. [22]

    Liu, Ke He, Runan Shang, Jianhua Zhao, and Hao Zhang, Phys

    Zhaoyu Wang, Huading Song, Dong Pan, Zitong Zhang, Wentao Miao, Ruidong Li, Zhan Cao, Gu Zhang, Lei Liu, Lianjun Wen, Ran Zhuo, Dong E. Liu, Ke He, Runan Shang, Jianhua Zhao, and Hao Zhang, Phys. Rev. Lett. 129, 167702(2022)

    2022

  15. [23]

    Leo Kouwenhoven, Mod. Phys. Lett. B bf 39 2540002 (2025)

    2025

  16. [24]

    Potter, K

    Jie Liu, Andrew C. Potter, K. T. Law, Patrick A. Lee, Phys. Rev. Lett. 109, 267002 (2012)

    2012

  17. [25]

    Kells, D

    G. Kells, D. Meidan, and P. W. Brouwer, Phys. Rev. B 86, 100503(R) (2012)

    2012

  18. [26]

    Prada, P

    E. Prada, P. San-Jose, and R. Aguado, Phys. Rev. B 86, 180503(R) (2012)

    2012

  19. [27]

    Prada, R

    E. Prada, R. Aguado, and P. San-Jose, Phys. Rev. B 96, 085418 (2017)

    2017

  20. [28]

    Fleckenstein, F

    C. Fleckenstein, F. Dominguez, N. Traverso Ziani, and B. Trauzettel, Phys. Rev. B 97, 155425 (2018)

    2018

  21. [29]

    Moore, T

    C. Moore, T. D. Stanescu, and S. Tewari, Phys. Rev. B 97, 165302 (2018)

    2018

  22. [30]

    Sau, and S

    Chun-Xiao Liu, Jay D. Sau, and S. Das Sarma, Phys. Rev. B 97, 214502 (2018)

    2018

  23. [31]

    Penaranda, R

    F. Penaranda, R. Aguado, P. San-Jose, and E. Prada, Phys. Rev. B 98, 235406 (2018)

    2018

  24. [32]

    A. Vuik, B. Nijholt, A. R. Akhmerov and M. Wimmer, SciPost Phys. 7, 061 (2019)

    2019

  25. [33]

    T. D. Stanescu, and S. Tewari, Phys. Rev. B 100, 155429 (2019)

    2019

  26. [34]

    Sau, Tudor D

    Chun-Xiao Liu, Jay D. Sau, Tudor D. Stanescu, and S. Das Sarma Phys. Rev. B 96, 075161 (2017)

    2017

  27. [35]

    Setiawan, Chun-Xiao Liu, Jay D

    F. Setiawan, Chun-Xiao Liu, Jay D. Sau, and S. Das Sarma Phys. Rev. B 96, 184520 (2017)

    2017

  28. [36]

    Das Sarma Phys

    Ching-Kai Chiu and S. Das Sarma Phys. Rev. B 99, 035312 (2019)

    2019

  29. [37]

    Stanescu, and Sumanta Tewari Phys

    Christopher Moore, Chuanchang Zeng, Tudor D. Stanescu, and Sumanta Tewari Phys. Rev. B 98, 155314 (2018)

    2018

  30. [38]

    Liu Phys

    Zhan Cao, Gu Zhang, Hao Zhang, Wan-Xiu He, Chuan- chang Zeng, Ke He, and Dong E. Liu Phys. Rev. B 106, 075416 (2022)

    2022

  31. [39]

    Haining Pan and Sankar Das Sarma Phys. Rev. B 104, 054510 (2021)

    2021

  32. [40]

    Das Sarma Phys

    Haining Pan and S. Das Sarma Phys. Rev. Research 2, 013377 (2020)

    2020

  33. [41]

    R. V. Mishmash, D. Aasen, A. P. Higginbotham, and J. Alicea, Phys. Rev. B 93, 245404 (2016)

    2016

  34. [42]

    Jie Liu, Juntao Song, Qing-Feng Sun, and X. C. Xie, Phys. Rev. B 96, 195307 (2017). 6

    2017

  35. [43]

    T. O. Rosdahl, A. Vuik, M. Kjaergaard, and A. R. Akhmerov, Phys. Rev. B 97, 045421 (2018)

    2018

  36. [44]

    Aguado, Phys

    Jorge Cayao, Elsa Prada, Pablo San-Jose, and R. Aguado, Phys. Rev. B 91, 024514 (2015)

    2015

  37. [45]

    Danon, A

    J. Danon, A. B. Hellenes, E. B. Hansen, L. Casparis, A. P. Hig-ginbotham, and K. Flensberg, arXiv: 1905.05438 (2019)

    2019 arXiv

  38. [46]

    G. C. Menard, G. L. R. Anselmetti, E. A. Martinez, D. Puglia,F. K. Malinowski, J. S. Lee, S. Choi, M. Pend- harkar, C. J. Palm-strom, K. Flensberg, C. M. Marcus, L. Casparis, and A. P. Hig-ginbotham, arXiv: 1905.05505 (2019)

    2019 arXiv

  39. [47]

    Zhang, D

    H. Zhang, D. E. Liu, M. Wimmer, and L. P. Kouwen- hoven, arXiv: 1905.07882 (2019)

    2019 arXiv

  40. [48]

    B 100 241408(R) (2019)

    Konstantin Yavilberg, Eran Ginossar, Eytan Grosfeld, Phys.Rev. B 100 241408(R) (2019)

    2019

  41. [49]

    Andrzej Ptok, Aksel Kobialka, and Tadeusz Domanski, Phys. Rev. B 96, 195430 (2017)

    2017

  42. [50]

    Awoga, Jorge Cayao, and Annica M

    Oladunjoye A. Awoga, Jorge Cayao, and Annica M. Black-Schaffer, Phys. Rev. Lett. 123, 117001 (2019)

    2019

  43. [51]

    C. Reeg, O. Dmytruk, D. Chevallier, D. Loss and J. Kli- novaja, Phys. Rev. B 98, 245407 (2018)

    2018

  44. [52]

    Pikulin, Bernard van Heck, Torsten Karzig, Esteban A

    Dmitry I. Pikulin, Bernard van Heck, Torsten Karzig, Esteban A. Martinez, Bas Nijholt, Tom Laeven, Georg W. Winkler, John D. Watson, Sebastian Heedt, Mine Temurhan, Vicky Svidenko, Roman M. Lutchyn, Mason Thomas, Gijs de Lange, Lucas Casparis, Chetan Nayak, arXiv:2103.12217(2021)

    2021 arXiv

  45. [53]

    (Microsoft Quantum) , Phys

    Morteza Aghaee et al. (Microsoft Quantum) , Phys. Rev. B 107, 245423 (2023)

    2023

  46. [54]

    Jay D. Sau, S. Das Sarma, Nature Communications 3, 964 (2012)

    2012

  47. [55]

    Martin Leijnse, Karsten Flensberg, Phys. Rev. B 86, 134528 (2012)

    2012

  48. [56]

    Chun-Xiao Liu, Guanzhong Wang, Tom Dvir, Michael Wimmer, Phys. Rev. Lett. 129, 267701 (2022)

    2022

  49. [57]

    Athanasios Tsintzis, Ruben Seoane Souto, Karsten Flensberg, Jeroen Danon, Martin Leijnse, PRX Quan- tum 5, 010323 (2024)

    2024

  50. [58]

    Mazur, Alberto Bordin, Sebastiaan L

    Tom Dvir, Guanzhong Wang, Nick van Loo, Chun-Xiao Liu, Grzegorz P. Mazur, Alberto Bordin, Sebastiaan L. D. ten Haaf, Ji-Yin Wang, David van Driel, Francesco Zatelli, Xiang Li, Filip K. Malinowski, Sasa Gazibegovic, Ghada Badawy, Erik P. A. M. Bakkers, Michael Wimmer, Leo P. Ko...

    2023

  51. [59]

    Mazur, Nick van Loo, Jan C

    Francesco Zatelli, David van Driel, Di Xu, Guanzhong Wang, Chun-Xiao Liu, Alberto Bordin, Bart Roovers, Grzegorz P. Mazur, Nick van Loo, Jan C. Wolff, A. Mert Bozkurt, Ghada Badawy, Sasa Gazibegovic, Erik P. A. M. Bakkers, Michael Wimmer, Leo P. Kouwenhoven, Tom Dvir , Nature ...

    2024

  52. [60]

    Bordin, Guanzhong Wang, Chun-Xiao Liu, S

    A. Bordin, Guanzhong Wang, Chun-Xiao Liu, S. L. ten Haaf, N. van Loo, G. P. Mazur, Di Xu, D. van Driel, Francesco Zatelli, S. Gazibegovic, G. Badawy, E. Bakkers, M. Wimmer, L. Kouwenhoven, T. Dvir, Physi- cal Review X 13 ,031031(2023)

    2023

  53. [61]

    Bordin, Chun-Xiao Liu, Tom Dvir, Francesco Zatelli, Sebastiaan L

    A. Bordin, Chun-Xiao Liu, Tom Dvir, Francesco Zatelli, Sebastiaan L. D. ten Haaf, David van Driel, Guanzhong Wang, Nick van Loo, Thomas van Caekenberghe, Jan Cornelis Wolff, Yining Zhang, Ghada Badawy, Sasa Gaz- ibegovic, Erik P.A.M. Bakkers, Michael Wimmer, Leo P. Kouwenhoven...

    2024 arXiv

  54. [62]

    Yu Zhang, Y. Wu, J. Liu, and X.C. Xie, arXiv:2410.17014 (2024)

    2024 arXiv

  55. [63]

    W. Chen, J. Wang, Y. Wu, J. Qi, J. Liu, and X.C. Xie, Phys. Rev. B 105, 054507 (2022)

    2022

  56. [64]

    Jay D Sau and Sankar Das Sarma, arXiv:2406.18080 (2024)

    2024 arXiv

  57. [65]

    Haining Pan, Sankar Das Sarma, and Chun-Xiao Liu, arXiv:2407.16750 (2024)

    2024 arXiv

  58. [66]

    M. Gong, Y. Wu, Hua Jiang, J. Liu, and X.C. Xie, Phys. Rev. B 105, 014507 (2022)

    2022

  59. [67]

    Tianzhen Zhang †, Yining Hu, Wei Su, Chen Chen, Xu Wang, Dong Li, Zouyouwei Lu, Wentao Yang, Qingle Zhang, Xiaoli Dong, Rui Wang, Xiaoqun Wang, Donglai Feng, Tong Zhang, Phys. Rev. Lett. 130, 206001 (2023)

    2023

  60. [68]

    Stephan Plugge, Asbjorn Rasmussen, Reinhold Egger, Karsten Flensberg, New J. Phys. 19, 012001(2017)

    2017

  61. [69]

    Steiner, Felix von Oppen, Phys

    Jacob F. Steiner, Felix von Oppen, Phys. Rev. Research 2, 033255 (2020)

    2020

  62. [70]

    Mazur, Sasa Gazibegovic, Ghada Badawy, Erik P

    David van Driel, Bart Roovers, Francesco Zatelli, Al- berto Bordin, Guanzhong Wang, Nick van Loo, Jan Cor- nelis Wolff, Grzegorz P. Mazur, Sasa Gazibegovic, Ghada Badawy, Erik P. A. M. Bakkers, Leo P. Kouwenhoven, Tom Dvir, PRX Quantum 5, 020301

  63. [71]

    Microsoft Azure Quantum, arXiv:2401.09549 (2024)

    2024 arXiv

Pith tools

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