Pith. sign in

REVIEW 3 major objections 3 minor 3 cited by

Distinct Lifetimes for $X$ and $Z$ Loop Measurements in a Majorana Tetron Device

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read A tetron qubit device supports two distinct parity-measurement loops with lifetimes of 14.5 µs and 12.4 ms.

desk verdict Two-loop parity readout in a tetron works, and the timescale asymmetry is real; the Majorana-specific interpretation of the fast X-loop switches is the soft underbelly, and the authors mostly admit it. read the letter →

arxiv 2507.08795 v2 pith:5DPZLCDF submitted 2025-07-11 cond-mat.mes-hall quant-ph

Morteza Aghaee , Zulfi Alam , Rikke Andersen , Mariusz Andrzejczuk , Andrey Antipov , Mikhail Astafev , Lukas Avilovas , Ahmad Azizimanesh
show 158 more authors
Eric Banek Bela Bauer Jonathan Becker Umesh Kumar Bhaskar Andrea G. Boa Srini Boddapati Nichlaus Bohac Jouri D.S. Bommer Jan Borovsky Léo Bourdet Samuel Boutin Lucas Casparis Srivatsa Chakravarthi Hamidreza Chalabi Benjamin J. Chapman Nikolaos Chatzaras Tzu-Chiao Chien Jason Cho Patrick Codd William Cole Paul W. Cooper Fabiano Corsetti Ajuan Cui Tareq El Dandachi Celine Dinesen Andreas Ekefjärd Saeed Fallahi Luca Galletti Geoffrey C. Gardner Gonzalo Leon Gonzalez Deshan Govender Flavio Griggio Ruben Grigoryan Sebastian Grijalva Sergei Gronin Jan Gukelberger Marzie Hamdast A. Ben Hamida Esben Bork Hansen Caroline Tynell Hansen Sebastian Heedt Samantha Ho Laurens Holgaard Kevin van Hoogdalem John Hornibrook Henrik Ingerslev Lovro Ivancevic Sherwan Jamo Max Jantos Thomas Jensen Jaspreet Singh Jhoja Jeffrey C Jones Vidul Joshi Konstantin V. Kalashnikov Ray Kallaher Rachpon Kalra Farhad Karimi Torsten Karzig Seth Kimes Evelyn King Maren Elisabeth Kloster Christina Knapp Jonne V. Koski Pasi Kostamo Tom Laeven Jeffrey Lai Gijs de Lange Thorvald W. Larsen Kyunghoon Lee Kongyi Li Guangze Li Shuang Liang Tyler Lindemann Matthew Looij Marijn Lucas Roman Lutchyn Morten Hannibal Madsen Nasiari Madulid Michael J. Manfra Laveena Manjunath Signe Markussen Esteban Martinez Marco Mattila J. R. Mattinson R. P. G. McNeil Alba Pérez Millan Ryan V. Mishmash Sarang Mittal Christian M{o}llgaard M. W. A. de Moor Eduardo Puchol Morejon Trevor Morgan George Moussa B.P. Nabar Anirudh Narla Chetan Nayak Jens Hedegaard Nielsen William Hvidtfelt Padk{ae}r Nielsen Frédéric Nolet Michael J. Nystrom Eoin O'Farrell Thomas A. Ohki Keita Otani Camille Papon Karl D Petersson Luca Petit Dima Pikulin Mohana Rajpalke Alejandro Alcaraz Ramirez David Razmadze Yuan Ren Ivan Sadovskyy Lauri Sainiemi Juan Carlos Estrada Saldaña Irene Sanlorenzo Tatiane Pereira dos Santos Simon Schaal John Schack Emma R. Schmidgall Christina Sfetsou Cristina Sfiligoj Sarat Sinha Patrick Sohr Thomas L. S{o}rensen Kasper Spiegelhauer Tomaš Stankević Lieuwe J. Stek Patrick Str{o}m-Hansen Henri J. Suominen Judith Suter Samuel M. L. Teicher Raj Tholapi Mason Thomas D.W. Tom Emily Toomey Joshua Tracy Michelle Turley Matthew D. Turner Shivendra Upadhyay Ivan Urban Dmitrii V. Viazmitinov Anna Wulff Viazmitinova Beatriz Viegas Dominik J. Vogel John Watson Alex Webster Joseph Weston Timothy Williamson Georg W. Winkler David J. van Woerkom Brian Paquelet Wuetz Chung-Kai Yang Shang-Jyun (Richard) Yu Emrah Yucelen Jesús Herranz Zamorano Roland Zeisel Guoji Zheng A.M. Zimmerman
This is my paper · ORCID
classification cond-mat.mes-hallquant-ph
keywords Majoranazeromodestetronqubitfermionparityreadoutquantumcapacitancerandomtelegraphsignalquasiparticlepoisoningmeasurement-basedcomputationInAs-Alhybridnanowires
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

This paper reports the first demonstration of two distinct projective measurements of fermion parity in a single tetron device, a proposed building block for topological quantum computers. The authors measure the quantum capacitance of quantum dots that are part of two different interference loops, implementing Pauli-X and Pauli-Z measurements of the tetron. Repeated single-shot measurements show parity switches on two widely separated timescales: τX = 14.5 ± 0.3 µs for the X loop and τZ = 12.4 ± 0.4 ms for the Z loop. They attribute the fast X-loop switches to intra-wire fermion transitions between Majorana zero modes and the slow Z-loop switches to external quasiparticle poisoning. If this interpretation holds, it validates a central component of the measurement-based topological quantum computing roadmap.

What carries the argument

The central object is the tetron: two parallel hybrid nanowires connected by a trivial superconducting backbone, supporting four Majorana zero modes when tuned into the topological phase. Two interferometer loops are formed by coupling the superconductor to quantum dots: the X loop (dots 1 and 3 bridging the two wires) and the Z loop (dots 3, L, and 4 along the bottom wire). Measurement is by dispersive gate sensing of the quantum capacitance of a readout dot, which is parity-dependent and h/2e-periodic in applied flux. The theoretical engine is a minimal effective Hamiltonian H = i Σ E_ij γ_i γ_j plus dot terms, with charge noise on the dot detuning as the dominant noise source; a Schrieffer-Wolff reduction leads to an explicit rate formula 1/τ_X = S_N(±ΔE) $E_M^{2}$ / (2 $t^{2}$) in the balanced limit, showing that the X-loop rate scales with the square of the average Majorana splitting E_M = (E12 + E34)/2.

What would settle it

Observe a device that passes the same topological-gap protocol at the same field, then measure long X-loop time records at the flux of maximal h/2e-periodic bimodality: if no fast (≈10 µs) random telegraph signal appears even when wire-plunger voltages are varied, or if the Z-loop dwell time stays unchanged while the device is deliberately exposed to a controllable quasiparticle source, the claimed timescale separation and its physical attributions would be contradicted.

Watch

Extended reading notes

Core claim

The central claim is that the tetron hardware realizes the two non-commuting Pauli measurements needed for measurement-only topological qubit operation, and that the two measurements fail by different physical mechanisms. The X loop, which threads the left halves of the two nanowires and the superconducting backbone, shows a random telegraph signal with a 14.5 µs switching time, attributed to residual splitting between Majorana modes within a wire; the Z loop, which runs along the bottom nanowire, shows a 12.4 ms switching time, attributed to externally generated quasiparticles tunnelling into the device. The corresponding operational assignment errors are 16% for X and 0.5% for Z. The authors back this with a minimal four-Majorana Hamiltonian in which charge noise induces transitions between parity eigenstates, giving a Fermi-golden-rule rate proportional to the square of the average intra-wire Majorana splitting.

Load-bearing premise

The interpretation assumes the two nanowires are actually in the topological phase with four Majorana zero modes and a fully depleted superconducting backbone; if the low-energy modes are trivial Andreev or quasi-Majorana states, the attribution of the two lifetimes to intra-wire switching and quasiparticle poisoning would collapse, even though the two-loop readout itself would still work.

Editorial extensions

If this is right

  • The two measured lifetimes are evidence that X and Z parity measurements in a tetron are distinct, and the separation by roughly three orders of magnitude provides a clear signature for distinguishing intra-wire switching from external quasiparticle poisoning in future devices.
  • With the quoted assignment errors of 0.5% for Z and 16% for X, these are the first device-level numbers for the operational error metric that the topological-qubit roadmap uses to project fault-tolerant thresholds.
  • The model predicts that the X-loop switching rate grows as the square of the residual Majorana splitting, so improving device quality to increase the ratio of wire length to coherence length L/ξ should exponentially suppress τX.
  • The next anticipated step, rapid sequences of X and Z measurements, would demonstrate that the two measurements do not commute, establishing the single-qubit operations needed for error correction.

Reading between the lines

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

  • If the Z-loop lifetime is truly set by quasiparticle poisoning, the same two-loop readout could serve as a quantitative poisoning sensor: measured changes in τZ would track the density of external quasiparticles independently of the Majorana interpretation.
  • The X-loop rate's quadratic dependence on residual splitting could be turned into a diagnostic: mapping τX over wire-plunger voltage space may reveal mesoscopic fluctuations in Majorana overlap, potentially distinguishing localized Majorana modes from quasi-Majorana or Andreev states that would show a different tuning sensitivity.
  • A testable extension is to repeat the measurement with a controllable quasiparticle source, such as a nearby heated island or gate-controlled trap, and check whether τZ varies while τX stays constant, which would confirm the two distinct failure mechanisms.
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 / 3 minor

Summary. The manuscript reports on a tetron device in which two interferometric readout circuits, called X and Z loops, are used to measure fermion parity. Repeated single-shot measurements yield two widely separated random-telegraph-switching timescales, τX = 14.5±0.3 μs and τZ = 12.4±0.4 ms, which the authors attribute to intra-wire Majorana parity switches and external quasiparticle poisoning, respectively. They also report operational assignment errors of 16% for X and 0.5% for Z, with a two-parameter-free error model that agrees with data. The theoretical model (Appendix A–B) connects τX to finite intra-wire MZM splittings EM and charge noise, while Appendix C discusses alternative Andreev and quasi-Majorana scenarios. The paper includes detailed device fabrication, tuning, readout, and error-analysis documentation, and provides data and code on Zenodo and GitHub.

Significance. If the interpretation holds, this is a significant experimental step: it is the first demonstration of two distinct types of fermion-parity measurements in a tetron device, a core building block for measurement-based topological quantum computation. The two-loop observation is directly measured and robust, and the three-order-of-magnitude separation between τX and τZ is a new and interesting result. The paper's strengths include transparent uncertainty reporting, a carefully described error model (Eq. D2) that reproduces measured assignment errors without additional fitting, and the explicit discussion of non-topological alternatives and admitted limitations. The central caveat is that the identification of the fast X-loop dynamics as intra-wire Majorana parity switching is model-dependent and not uniquely excluded by the present data.

major comments (3)
  1. [Appendix B.b and Eq. (3)] The estimate of EM ≃ 0.1–0.3 μeV is obtained by inserting the sub-optimal τX into the same rate formula (Eq. 3) that the model is supposed to predict. Consequently, the subsequent statement that the model is consistent with the measured τX is not an independent test; it is a parameter extraction. The authors should either obtain EM from an independent observable (e.g., the flux-dependence of ΔCQ near avoided crossings, as described in Appendix A) or explicitly label the comparison as a self-consistent fit rather than a validation. This is load-bearing because the abstract's attribution of τX to intra-wire parity switches rests on this rate formula.
  2. [Section c, footnote 56] The quoted τZ = 12.4±0.4 ms is extracted from dwell-time distributions after applying a kurtosis threshold to select time records, and the records are only 100 ms long. As the footnote concedes, this procedure can bias the distribution toward short dwell times and may underestimate τZ. Because τZ is one of the two central quantitative results, the authors should quantify the bias (e.g., through Monte Carlo simulation of the selection procedure) or present an unbiased estimator. Without this, the reported τZ value may not be a reliable characterization of the Z-loop lifetime.
  3. [Section c, Section d, and Appendix C] The identification of the fast X-loop RTS as an intra-wire Majorana parity switch is not uniquely supported by the data. A two-level charge fluctuator in dot 1 or readout-backaction-induced transitions would produce the same bimodal CQ signal with h/2e-periodic visibility and an exponentially decaying autocorrelation. Appendix C carefully treats Andreev and quasi-Majorana wire scenarios, but it does not address local charge traps in the dot/junction or drive-induced switching. The authors should either provide a discriminating measurement (e.g., τX as a function of readout power or dot-sensor coupling) or explicitly state in the abstract and conclusions that the attribution is a model-dependent interpretation rather than an established fact. This is the least secure premise of the central claim.
minor comments (3)
  1. [Section c, Fig. 2(i)] The wire-plunger scan in Fig. 2(i) shows a drift of the optimal tuning by about 100 μV between measurements taken several days apart; the text should state whether the quoted τX values were all measured at the same effective tuning or whether the drift was compensated in the analysis.
  2. [Appendix F.b] The description of diversity combining is clear, but the derivation of the √2 SNR improvement assumes equal uncorrelated noise at signal and idler; the text should note how this assumption was verified for the actual readout chain, for instance by measuring noise correlations.
  3. [Appendix G.c] In the sentence "The finer resolution dataset was obtained following the drive amplitude optimization..." the phrase "uses a larger drive amplitude compared to the coarser scans" could be misleading; please specify the actual drive amplitudes used for the data in Fig. 2(b) versus the zoomed scans.

Circularity Check

1 steps flagged · score 4.0 of 10

The two-lifetime observation is direct and not circular; the circular reduction is limited to the model-consistency claim, where EM is inferred from the same tau_X via Eq. (3) using a self-cited noise strength.

  1. fitted input called prediction [Appendix B.b; main-text Section d (Minimal model)]
    "To estimate the typical values of residual coupling EM, it is useful to extract the timescale tau_X away from the optimal tuning points. ... We observe that typical timescales away from optimal tuning are in the range of 2-5 us. Using the value of sub-optimal tau_X^-1 ~ gamma_eff E_M^2/(2t)^2 with t ~ 2 ueV and gamma_eff ~ 0.1-1 GHz [51], we estimate E_M ~ 0.1-0.3 ueV. ... Away from optimal tuning we observe tau_X ~ 2-5 us which is consistent with E_M ~ 0.1-0.3 ueV using the model presented here."

    E_M is not independently measured: it is the value that makes the model's own rate formula, Eq. (3), reproduce the observed tau_X, with the noise scale gamma_eff taken from prior same-group simulation work (Ref. [51]) rather than measured in this device. The main text's statement that the observed tau_X (2-5 us) is 'consistent with' E_M (0.1-0.3 ueV) is therefore true by construction: the two quantities are tied by the same equation used to define E_M. This does not affect the raw two-timescale observation, but it means the model-based attribution of the fast RTS to intra-wire MZM splitting is not independently confirmed by this consistency check; a flux-sensitive dot charge fluctuator or readout backaction producing the same h/2e-periodic RTS would pass the same check.

full rationale

The paper's central empirical result - two widely separated lifetimes tau_X = 14.5 +/- 0.3 us and tau_Z = 12.4 +/- 0.4 ms for the X and Z loop readouts - is a direct time-domain measurement of the quantum capacitance fluctuations, with tau_X extracted from an autocorrelation fit and tau_Z from a dwell-time histogram; no model parameters enter those extractions. The h/2e flux periodicity and bimodality are likewise direct data features. The error-model comparison in Appendix D uses the independently measured lifetimes and SNR as inputs and reproduces the measured assignment errors without further fitting, so that comparison is not circular. The one genuine reduction is in Appendix B.b: the estimate E_M ~ 0.1-0.3 ueV is obtained by inverting the model's rate formula for the same sub-optimal tau_X data, using gamma_eff imported from the authors' own prior simulation paper (Ref. [51]). The paper's claim that the data are 'consistent with' this E_M is therefore a restatement of the inversion rather than an independent test of the mechanism. The paper also explicitly concedes that fine-tuned non-topological models can reproduce the observations, which is an underdetermination caveat rather than a circular step. Overall, the central two-lifetime observation is self-contained and independently valuable; only the supporting model-consistency claim is partially post hoc, giving a moderate circularity score.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central experimental observation, two distinct parity-switch timescales, does not depend on the theoretical model. However, the physical attribution of tau_X and tau_Z to specific mechanisms, and the quoted consistency with a Majorana model, rest on the axioms above and on two fitted quantities (gamma_eff from prior work, EM from the data itself). The alternative-scenario analysis in Appendix C tightens but does not eliminate non-topological explanations.

free parameters (2)
  • gamma_eff (effective charge noise strength) = 0.1-1 GHz (imported from Ref. [51], not measured in this device)
    Appears in the spectral function S_N(omega) = gamma_eff / [1 + exp(-omega/kBT)] used in Eq. (A3) and in the rate formula Eq. (3). Together with the fitted EM it sets the predicted tau_X scale; the quoted range is a prior estimate, so the model is not parameter-free for this device.
  • EM = (E12 + E34) / 2 (average intra-wire MZM splitting) = 0.1-0.3 micro-eV
    Estimated in Appendix B from the sub-optimal tau_X values (2-5 microseconds) using the model's own rate expression, Eq. (3). The model is then used to argue consistency with tau_X = 14.5 microseconds, so the 'prediction' is partially a fit to the data it explains.
assumptions (5)
  • domain assumption The two nanowires are in the topological phase and host four Majorana zero modes.
    This is the foundation of the tetron interpretation. It is argued from TGP pass (Fig. A10) and zero-bias peaks, but is not directly proven; the paper concedes non-topological low-energy modes could be fine-tuned to mimic the data (Section e).
  • domain assumption The superconducting backbone is fully depleted, so it does not couple the two wires.
    Used to neglect E13, E14, E23, E24 in Eq. (A2) and to justify the two-loop model. Supported by depletion simulations (Fig. A8) and h/2e flux periodicity, but not directly verified in the operating device.
  • domain assumption Charge noise on the dots follows S_N(omega) = gamma_eff / [1 + exp(-omega/kBT)].
    Adopted from Ref. [51] and used to compute noise-induced transition rates (Eq. (A7)); the effective strength gamma_eff is not extracted from this device.
  • domain assumption The rf dispersive readout is a projective, quantum-non-demolition measurement of the low-energy eigenstates.
    Stated in Appendix A with citations to Refs. 9, 42, 51, 73; needed to map the two-level random telegraph signal to fermion parity switches.
  • ad hoc to paper Approximately equal intra-wire splittings, E12 = E34 (i.e., y = 0), in the main rate expression.
    Eq. (3) and Eq. (A8) are derived in the limit EM >> |y| with |delta-phi| small; away from that regime the rate formulas change. The paper motivates this by the observed diagonal features in Fig. 2(i) but it is a modeling choice.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Distinct Lifetimes for $X$ and $Z$ Loop Measurements in a Majorana Tetron Device." pith.science (2026). https://pith.science/paper/5DPZLCDF

@misc{pith2026250708795,
  author       = {Pith},
  title        = {Pith review of: Distinct Lifetimes for $X$ and $Z$ Loop Measurements in a Majorana Tetron Device},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DPZLCDF}},
  note         = {Machine review of arXiv:2507.08795}
}
abstract

We present a hardware realization and measurements of a tetron qubit device in a superconductor-semiconductor heterostructure. The device architecture contains two parallel superconducting nanowires, which support four Majorana zero modes (MZMs) when tuned into the topological phase, and a trivial superconducting backbone. Two distinct readout interferometers are formed by connecting the superconducting structure to a series of quantum dots. We perform single-shot interferometric measurements of the fermion parity for the two loops, designed to implement Pauli-$X$ and $Z$ measurements of the tetron. Performing repeated single-shot measurements yields two widely separated time scales $\tau_X = 14.5\pm 0.3 \, \mathrm{\mu s}$ and $\tau_Z = 12.4\pm 0.4\, \mathrm{ms}$ for parity switches observed in the $X$ and $Z$ measurement loops, which we attribute to intra-wire parity switches and external quasiparticle poisoning, respectively. We estimate assignment errors of $\mathrm{err}^X_a=16\%$ and $\mathrm{err}^Z_a=0.5\%$ for $X$ and $Z$ measurement-based operations, respectively.

Figures

Figures reproduced from arXiv: 2507.08795 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of a tetron, highlighting the hybrid [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Schematic of the interference loop involved in the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The interference loop involved in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The conditional probabilities for the outcome of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Magnetic-Field and Temperature Limits of a Kinetic-Inductance Traveling-Wave Parametric Amplifier

    quant-ph 2025-09 conditional novelty 6.5 of 10

    A NbTiN/Nb kinetic-inductance TWPA keeps >3 dB SNR improvement up to 0.35 T in-plane and 50 mT out-of-plane, and keeps gain to 3 K, far beyond Josephson-junction TWPA field tolerance.

  2. Hybrid superinductance with Al/InAs

    cond-mat.mes-hall 2026-01 conditional novelty 6.0 of 10

    Al/InAs Josephson-junction chains exhibit superinductance with linear dispersion to 12 GHz, while internal loss increases roughly as 1/frequency.

  3. Parity readout in Majorana box qubits from the dispersive to the resonant regime

    cond-mat.str-el 2026-03 accept novelty 5.0 of 10

    A general χ_z(ω) covers resonant-to-dispersive Majorana parity readout, and the semiclassical factorization is accurate dispersively but errs by a few percent near resonance.

Reference graph

Works this paper leans on

92 extracted references · 46 canonical work pages · cited by 3 Pith papers

  1. [1]

    Device tune up using TGP on both wire segments, which entails stable ZBPs at all 4 ends of the device and a bulk transport gap in both wires

  2. [2]

    RTS of τX = 2–15 µs time scale for X measurement, depending on flux

  3. [3]

    RTS visibility (∆CQ) consistent with h/2e period for X measurement

  4. [4]

    RTS of τZ ∼ 12 ms time scale for Z measurement

  5. [5]

    RTS visibility (∆CQ) consistent with h/2e period for Z measurement

  6. [6]

    backbone

    Slower time scale ∼ 10 ms RTS in X measurement with smaller amplitude ∆ C∆M . Due to the presence of stable ZBPs at all four ends of the device, we limit the discussion to scenarios where low-energy modes can be accessed from both sides of both nanowires. For a given wire, we consider three scenarios, see Fig. A5: (a) the topological scenario, (b) a spin-...

  7. [7]

    H. J. Suominen, M. Kjaergaard, A. R. Hamilton, J. Sha- bani, C. J. Palmstrøm, C. M. Marcus, and F. Nichele, Zero-energy modes from coalescing Andreev states in a two-dimensional semiconductor-superconductor hybrid platform, Phys. Rev. Lett. 119, 176805 (2017)

    2017

  8. [8]

    Quantum dot

    is also present on the device, but is omitted from the schematic for clarity. Parameters for the circuit compo- nents and the readout modes are given in Table I. Loop Quantum dot L [nH] C [fF] Cc [fF] f0 [MHz] Qc Qi Z QDL 247 197 910 722 36 160 X QD1 173 224 840 808 25 145 TABLE I. Circuit parameters for the readout circuit depicted in Fig. A9 at 2 .3 T. ...

Show all 92 references
  1. [9]

    At each point in VWP1 and VWP2, image convolution analysis is used to properly calibrate the dot detunings, enabling automated exploration of the parameter space. d. RF drive amplitude. Once a signal is identified, we perform the X loop parity readout for several readout tone ...

  2. [10]

    A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003), quant-ph/9707021

    2003 arXiv

  3. [11]

    M. H. Freedman, P /N P, and the quantum field computer, Proc. Natl. Acad. Sci. USA 95, 98 (1998)

    1998

  4. [12]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quan- tum computation, Rev. Mod. Phys. 80, 1083 (2008), arXiv:0707.1889

    2008 arXiv

  5. [13]

    A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.-Usp. 44, 31 (2001), arXiv:cond-mat/0010440

    2001 arXiv

  6. [14]

    R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Ma- jorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett. 105, 077001 (2010), arXiv:1002.4033

    2010 arXiv

  7. [15]

    Y. Oreg, G. Refael, and F. von Oppen, Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett. 105, 177002 (2010), arXiv:1003.1145

    2010 arXiv

  8. [16]

    Hassler, A

    F. Hassler, A. R. Akhmerov, C.-Y. Hou, and C. W. J. Beenakker, Anyonic interferometry without anyons: how a flux qubit can read out a topological qubit, New J. Phys. 12, 125002 (2010), arXiv:1005.3423

    2010 arXiv

  9. [17]

    Plugge, A

    S. Plugge, A. Rasmussen, R. Egger, and K. Flensberg, Majorana box qubits, New J. Phys. 19, 012001 (2017)

    2017

  10. [18]

    Karzig, C

    T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes, Phys. Rev...

    2017

  11. [19]

    M. E. Beverland, P. Murali, M. Troyer, K. M. Svore, T. Hoefler, V. Kliuchnikov, G. H. Low, M. Soeken, A. Sun- daram, and A. Vaschillo, Assessing requirements to scale to practical quantum advantage (2022), arXiv:2211.07629

    2022 arXiv

  12. [20]

    Aasen et al

    D. Aasen et al. (Microsoft Quantum), Roadmap to fault tolerant quantum computation using topological qubit arrays (2025), arXiv:2502.12252

    2025 arXiv

  13. [21]

    Fu and C

    L. Fu and C. L. Kane, Josephson current and noise at a superconductor/quantum-spin-Hall- insulator/superconductor junction, Phys. Rev. B 79, 161408(R) (2009)

    2009

  14. [22]

    A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Electrically detected interferometry of Majorana fermions in a topological insulator, Phys. Rev. Lett. 102, 216404 (2009), arXiv:0903.2196

    2009 arXiv

  15. [23]

    Fu and C

    L. Fu and C. L. Kane, Probing neutral Majorana fermion edge modes with charge transport, Phys. Rev. Lett. 102, 216403 (2009)

    2009

  16. [24]

    Fu, Electron teleportation via Majorana bound states in a mesoscopic superconductor, Phys

    L. Fu, Electron teleportation via Majorana bound states in a mesoscopic superconductor, Phys. Rev. Lett. 104, 056402 (2010), arXiv:0909.5172

    2010 arXiv

  17. [25]

    Pientka, A

    F. Pientka, A. Romito, M. Duckheim, Y. Oreg, and F. von Oppen, Signatures of topological phase transi- tions in mesoscopic superconducting rings, New J. Phys. 15, 025001 (2013)

    2013

  18. [26]

    J. D. Sau, D. J. Clarke, and S. Tewari, Controlling non-Abelian statistics of Majorana fermions in semi- conductor nanowires, Phys. Rev. B 84, 094505 (2011), arXiv:1012.0561

    2011 arXiv

  19. [27]

    Fidkowski, R

    L. Fidkowski, R. M. Lutchyn, C. Nayak, and M. P. A. Fisher, Majorana zero modes in one-dimensional quantum wires without long-ranged superconducting order, Phys. Rev. B 84, 195436 (2011), arXiv:1106.2598

    2011 arXiv

  20. [28]

    Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep

    J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75, 076501 (2012), arXiv:1202.1293

    2012 arXiv

  21. [29]

    S. D. Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Inf. 1, 15001 (2015)

    2015

  22. [30]

    van Heck, F

    B. van Heck, F. Hassler, A. R. Akhmerov, and C. W. J. Beenakker, Coulomb stability of the 4 π-periodic Joseph- son effect of Majorana fermions, Phys. Rev. B 84, 180502 22 (2011)

    2011

  23. [31]

    van Heck, A

    B. van Heck, A. R. Akhmerov, F. Hassler, M. Burrello, and C. W. J. Beenakker, Coulomb-assisted braiding of Majorana fermions in a Josephson junction array, New J. Phys. 14, 035019 (2012), arXiv:1111.6001

    2012 arXiv

  24. [32]

    Hyart, B

    T. Hyart, B. van Heck, I. C. Fulga, M. Burrello, A. R. Akhmerov, and C. W. J. Beenakker, Flux-controlled quan- tum computation with Majorana fermions, Phys. Rev. B 88, 035121 (2013), arXiv:1303.4379

    2013 arXiv

  25. [33]

    Houzet, J

    M. Houzet, J. S. Meyer, D. M. Badiane, and L. I. Glazman, Dynamics of Majorana states in a topological Josephson junction, Phys. Rev. Lett. 111, 046401 (2013)

    2013

  26. [34]

    Vijay and L

    S. Vijay and L. Fu, Physical implementation of a Majorana fermion surface code for fault-tolerant quantum computa- tion, Phys. Scr. T168, 014002 (2016), arXiv:1509.08134

    2016 arXiv

  27. [35]

    Cheng and R

    M. Cheng and R. Lutchyn, Fractional Josephson effect in number-conserving systems, Phys. Rev. B 92, 134516 (2015)

    2015

  28. [36]

    J. D. Sau, B. Swingle, and S. Tewari, Proposal to probe quantum nonlocality of Majorana fermions in tunneling experiments, Phys. Rev. B 92, 020511 (2015)

    2015

  29. [37]

    Yavilberg, E

    K. Yavilberg, E. Ginossar, and E. Grosfeld, Fermion parity measurement and control in Majorana circuit quantum electrodynamics, Phys. Rev. B 92, 075143 (2015)

    2015

  30. [38]

    Aasen, M

    D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg, and J. Alicea, Milestones toward Majorana-based quantum computing, Phys. Rev. X 6, 031016 (2016), arXiv:1511.05153

    2016 arXiv

  31. [39]

    M. Hell, K. Flensberg, and M. Leijnse, Distinguishing Majorana bound states from localized Andreev bound states by interferometry, Phys. Rev. B 97, 161401 (2018)

    2018

  32. [40]

    C.-K. Chiu, J. D. Sau, and S. Das Sarma, Conductance interference in a superconducting Coulomb blockaded Majorana ring, Phys. Rev. B 97, 035310 (2018)

    2018

  33. [41]

    Drukier, H.-G

    C. Drukier, H.-G. Zirnstein, B. Rosenow, A. Stern, and Y. Oreg, Evolution of the transmission phase through a Coulomb-blockaded Majorana wire, Phys. Rev. B 98, 161401 (2018)

    2018

  34. [42]

    Vijay, T

    S. Vijay, T. H. Hsieh, and L. Fu, Majorana fermion surface code for universal quantum computation, Phys. Rev. X 5, 041038 (2015), arXiv:1504.01724

    2015 arXiv

  35. [43]

    Plugge, L

    S. Plugge, L. A. Landau, E. Sela, A. Altland, K. Flensberg, and R. Egger, Roadmap to Majorana surface codes, Phys. Rev. B 94, 174514 (2016)

    2016

  36. [44]

    Vijay and L

    S. Vijay and L. Fu, Teleportation-based quantum infor- mation processing with Majorana zero modes, Phys. Rev. B 94, 235446 (2016), arXiv:1609.00950

    2016 arXiv

  37. [45]

    Knapp, T

    C. Knapp, T. Karzig, R. M. Lutchyn, and C. Nayak, Dephasing of Majorana-based qubits, Phys. Rev. B 97, 125404 (2018)

    2018

  38. [46]

    Knapp, M

    C. Knapp, M. Beverland, D. I. Pikulin, and T. Karzig, Modeling noise and error correction for Majorana-based quantum computing, Quantum 2, 88 (2018)

    2018

  39. [47]

    C.-X. Liu, W. S. Cole, and J. D. Sau, Proposal for mea- suring the parity anomaly in a topological superconductor ring, Phys. Rev. Lett. 122, 117001 (2019)

    2019

  40. [48]

    M. I. K. Munk, J. Schulenborg, R. Egger, and K. Flens- berg, Parity-to-charge conversion in Majorana qubit read- out, Phys. Rev. Res. 2, 033254 (2020), arXiv:2004.02123

    2020 arXiv

  41. [49]

    J. F. Steiner and F. von Oppen, Readout of Ma- jorana qubits, Phys. Rev. Res. 2, 033255 (2020), arXiv:2004.02124

    2020 arXiv

  42. [50]

    Khindanov, D

    A. Khindanov, D. Pikulin, and T. Karzig, Visibility of noisy quantum dot-based measurements of Majorana qubits, SciPost Phys. 10, 127 (2021), arXiv:2007.11024

    2021 arXiv

  43. [51]

    Aghaee et al

    M. Aghaee et al. (Microsoft Quantum), Interferometric single-shot parity measurement in InAs-Al hybrid devices, Nature 638, 651 (2025), arXiv:2401.09549

    2025 arXiv

  44. [52]

    using dots 1, 3, L and 4

    In principle, one can also define loops corresponding to a Y measurement, e.g. using dots 1, 3, L and 4. However, this would require suppressing the coupling between dot 3 and its adjacent zero mode. We will not use such loops in this paper

  45. [53]

    van Loo, F

    N. van Loo, F. Zatelli, G. O. Steffensen, B. Roovers, G. Wang, T. V. Caekenberghe, A. Bordin, D. van Driel, Y. Zhang, W. D. Huisman, G. Badawy, E. P. A. M. Bakkers, G. P. Mazur, R. Aguado, and L. P. Kouwen- hoven, Single-shot parity readout of a minimal kitaev chain (2025), ar...

    2025 arXiv

  46. [54]

    J. I. Colless, A. C. Mahoney, J. M. Hornibrook, A. C. Doherty, H. Lu, A. C. Gossard, and D. J. Reilly, Disper- sive readout of a few-electron double quantum dot with fast rf gate sensors, Phys. Rev. Lett. 110, 046805 (2013), arXiv:1210.4645

    2013 arXiv

  47. [55]

    Bonderson, M

    P. Bonderson, M. Freedman, and C. Nayak, Measurement- only topological quantum computation, Phys. Rev. Lett. 101, 010501 (2008), arXiv:0802.0279

    2008 arXiv

  48. [56]

    Bonderson, M

    P. Bonderson, M. Freedman, and C. Nayak, Measurement- only topological quantum computation via anyonic inter- ferometry, Ann. Phys. 324, 787 (2009), arXiv:0808.1933

    2009 arXiv

  49. [57]

    We observe mobilities typically in excess of 60 000cm2/Vs and, in some growths, exceeding 100 000 cm2/Vs

  50. [58]

    D. I. Pikulin, B. van Heck, T. Karzig, E. A. Martinez, B. Nijholt, T. Laeven, G. W. Winkler, J. D. Watson, S. Heedt, M. Temurhan, V. Svidenko, R. M. Lutchyn, M. Thomas, G. de Lange, L. Casparis, and C. Nayak, Protocol to identify a topological superconducting phase in a three-...

    2021 arXiv

  51. [59]

    Aghaee et al

    M. Aghaee et al. (Microsoft Quantum), InAs-Al hybrid devices passing the topological gap protocol, Phys. Rev. B 107, 245423 (2023), arXiv:2207.02472

    2023 arXiv

  52. [60]

    Boutin, T

    S. Boutin, T. Karzig, T. E. Dandachi, R. V. Mishmash, J. Gukelberger, R. M. Lutchyn, and B. Bauer, Predic- tive simulations of the dynamical response of mesoscopic devices (2025), arXiv:2502.12960

    2025 arXiv

  53. [61]

    P. W. Brouwer, M. Duckheim, A. Romito, and F. von Oppen, Probability distribution of Majorana end-state energies in disordered wires, Phys. Rev. Lett. 107, 196804 (2011)

    2011

  54. [62]

    The data shown in Fig

    The data acquisition of the raw data corresponds to a close-to-boxcar integration of 1 µs per data point with some additional filtering as discussed in Appendix F.c. The data shown in Fig. 2 is coarsened (except for the autocorrelation analysis) to an effective integration tim...

  55. [63]

    42, we sweep the x-axis of our vector magnet

    As was done in Ref. 42, we sweep the x-axis of our vector magnet. Due to mechanical offsets, this results in a negli- gible misalignment (< 0.25 deg) between Bx and B⊥, esti- mated from the angular dependence of local and non-local differential conductance. Throughout the manu...

  56. [64]

    Nayak, Towards topological quantum computing using InAs-Al hybrid devices, APS Global Physics Summit 2025, Session MAR-F14

    C. Nayak, Towards topological quantum computing using InAs-Al hybrid devices, APS Global Physics Summit 2025, Session MAR-F14

    2025

  57. [65]

    Instances of the distribution with long dwell time realizations may show a significant asymmetry between the two states of the RTS due to a small number of switches

    Note that the kurtosis-based selection of time records together with the finite 100 ms length of time records may bias towards shorter dwell times. Instances of the distribution with long dwell time realizations may show a significant asymmetry between the two states of the RT...

  58. [66]

    Specifically, we extract an SNR of 1.9 in 2 µs from the Gaussian fits in Fig. 2(e). We rescale this by √ 2 to extrap- olate to 1 µs. Note that the SNR from the autocorrelation function ∆ CQ/2σCQ = 1 .66 is slightly different, likely due to the GMM fits being sensitive to addit...

  59. [67]

    Cheng, R

    M. Cheng, R. M. Lutchyn, V. Galitski, and S. Das Sarma, Splitting of Majorana-fermion modes due to intervortex tunneling in a px + ipy superconductor, Phys. Rev. Lett. 103, 107001 (2009)

    2009

  60. [68]

    Das Sarma, J

    S. Das Sarma, J. Sau, and T. Stanescu, A Majorana smoking gun for the superconductor-semiconductor hybrid topological system (2012), arXiv:1211.0539

    2012 arXiv

  61. [69]

    Motrunich, K

    O. Motrunich, K. Damle, and D. A. Huse, Griffiths effects and quantum critical points in dirty superconductors with- out spin-rotation invariance: One-dimensional examples, Phys. Rev. B 63, 224204 (2001)

    2001

  62. [70]

    C.-X. Liu, J. D. Sau, T. D. Stanescu, and S. Das Sarma, Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks, Phys. Rev. B 96, 075161 (2017)

    2017

  63. [71]

    4(d)] to shorter integration times we expect errZ a ≈ 0.2% at optimal integration times of ∼ 20 µs

    Extrapolating our error model [orange line in Fig. 4(d)] to shorter integration times we expect errZ a ≈ 0.2% at optimal integration times of ∼ 20 µs

  64. [72]

    Adagideli, M

    I. Adagideli, M. Wimmer, and A. Teker, Effects of elec- tron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices, Phys. Rev. B 89, 144506 (2014)

    2014

  65. [73]

    Janvier, L

    C. Janvier, L. Tosi, L. Bretheau, C ¸. ¨O. Girit, M. Stern, P. Bertet, P. Joyes, D. Vion, D. Esteve, M. F. Goffman, H. Pothier, and C. Urbina, Coherent manipulation of An- dreev states in superconducting atomic contacts, Science 349, 1199 (2015)

    2015

  66. [74]

    M. Hays, G. de Lange, K. Serniak, D. J. van Wo- erkom, D. Bouman, P. Krogstrup, J. Nygˆ ard, A. Geresdi, and M. H. Devoret, Direct microwave measurement of Andreev-bound-state dynamics in a semiconductor- nanowire Josephson junction, Phys. Rev. Lett. 121, 047001 (2018)

    2018

  67. [75]

    M. Hays, V. Fatemi, D. Bouman, J. Cerrillo, S. Diamond, K. Serniak, T. Connolly, P. Krogstrup, J. Nyg ˚ ard, A. L. Yeyati, A. Geresdi, and M. H. Devoret, Coherent ma- nipulation of an Andreev spin qubit, Science 373, 430 (2021)

    2021

  68. [76]

    tetron device

    In a large voltage range above the depletion voltage of the wires, comprising the lowest subband, the backbone is depleted. the linear device. This results in smaller capacitive losses in readout lines and more optimal RF performance. The improvements in the tetron design come...

  69. [77]

    J. J. Wesdorp, L. Gr¨ unhaupt, A. Vaartjes, M. Pita-Vidal, A. Bargerbos, L. J. Splitthoff, P. Krogstrup, B. van Heck, and G. de Lange, Dynamical polarization of the fermion parity in a nanowire Josephson junction, Phys. Rev. Lett. 131, 117001 (2023), arXiv:2112.01936

    2023 arXiv

  70. [78]

    B. H. Elfeky, J. J. Cuozzo, N. Lotfizadeh, W. F. Schiela, S. M. Farzaneh, W. M. Strickland, D. Langone, E. Rossi, and J. Shabani, Evolution of 4 π-periodic supercurrent in the presence of an in-plane magnetic field, ACS Nano 17, 4650–4658 (2023)

    2023

  71. [79]

    Kells, D

    G. Kells, D. Meidan, and P. W. Brouwer, Near-zero-energy end states in topologically trivial spin-orbit coupled super- conducting nanowires with a smooth confinement, Phys. Rev. B 86, 100503 (2012)

    2012

  72. [80]

    A. Vuik, B. Nijholt, A. R. Akhmerov, and M. Wimmer, Reproducing topological properties with quasi-Majorana states, SciPost Phys. 7, 061 (2019)

    2019

  73. [81]

    Valentini, F

    M. Valentini, F. Pe˜ naranda, A. Hofmann, M. Brauns, R. Hauschild, P. Krogstrup, P. San-Jose, E. Prada, R. Aguado, and G. Katsaros, Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable An- dreev states, Science 373, 82–88 (2021)

    2021

  74. [82]

    J. D. Sau and S. Das Sarma, Capacitance-based fermion parity readout and predicted rabi oscillations in a Majo- rana nanowire, Phys. Rev. B 111, 224509 (2025)

    2025

  75. [83]

    Prada, P

    E. Prada, P. San-Jose, and R. Aguado, Transport spectroscopy of N S nanowire junctions with Ma- jorana fermions, Phys. Rev. B 86, 180503 (2012), arXiv:1203.4488

    2012 arXiv

  76. [84]

    A. E. Antipov, A. Bargerbos, G. W. Winkler, B. Bauer, E. Rossi, and R. M. Lutchyn, Effects of gate-induced electric fields on semiconductor Majorana nanowires, Phys. Rev. X 8, 031041 (2018)

    2018

  77. [85]

    G. W. Winkler, A. E. Antipov, B. van Heck, A. A. Soluyanov, L. I. Glazman, M. Wimmer, and R. M. Lutchyn, Unified numerical approach to topological semiconductor-superconductor heterostructures, Phys. Rev. B 99, 245408 (2019)

    2019

  78. [86]

    Macklin, K

    C. Macklin, K. O’Brien, D. Hover, M. Schwartz, V. Bolkhovsky, X. Zhang, W. Oliver, and I. Siddiqi, A near–quantum-limited Josephson traveling-wave paramet- ric amplifier, Science 350, 307 (2015)

    2015

  79. [87]

    D. G. Brennan, Linear diversity combining techniques, Proceedings of the IEEE 91, 331 (2003)

    2003

  80. [88]

    J. Y. Qiu, A. Grimsmo, K. Peng, B. Kannan, B. Lienhard, Y. Sung, P. Krantz, V. Bolkhovsky, G. Calusine, D. Kim, A. Melville, B. M. Niedzielski, J. Yoder, M. E. Schwartz, T. P. Orlando, I. Siddiqi, S. Gustavsson, K. P. O’Brien, and W. D. Oliver, Broadband squeezed microwaves an...

    2023

  81. [89]

    O’Brien, C

    K. O’Brien, C. Macklin, I. Siddiqi, and X. Zhang, Res- onant phase matching of josephson junction traveling wave parametric amplifiers, Phys. Rev. Lett. 113, 157001 (2014)

    2014

  82. [90]

    Flensberg, Capacitance and conductance of mesoscopic systems connected by quantum point contacts, Phys

    K. Flensberg, Capacitance and conductance of mesoscopic systems connected by quantum point contacts, Phys. Rev. B 48, 11156 (1993)

    1993

  83. [91]

    J. V. Koski, A. J. Landig, A. P´ alyi, P. Scarlino, C. Reichl, W. Wegscheider, G. Burkard, A. Wallraff, K. Ensslin, and T. Ihn, Floquet spectroscopy of a strongly driven quantum dot charge qubit with a microwave resonator, Phys. Rev. Lett. 121, 043603 (2018)

    2018

  84. [92]

    J. H. Nielsen, M. Astafev, W. H. Nielsen, D. Vogel, lakho- tiaharshit, A. Johnson, A. Hardal, Akshita, sohail cha- toor, P. Eendebak, F. Bonabi, S. Pauka, T. Morgan, 24 Liang, G. Ungaretti, Adriaan, Samantha, B. Nijholt, qSae- var, P. Eendebak, S. Droege, J. Darulova, R. van G...

    2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.