Protocol for Purifying Noisy Preparation and Measurements of Qubits

Benjamin Lienhard; Jaemin Kim; Jiyoung Yun; Joonwoo Bae; Seungchan Seo

REVIEW 4 major objections 4 minor 19 references

Protocol for Purifying Noisy Preparation and Measurements of Qubits

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Repeated noisy SPAMs can be post-selected into near-perfect qubit preparation and measurement, suppressing realistic 5% errors to 10^-3 with two ancillas and 10^-6 with four.

desk verdict Interesting SPAM-purification claim with concrete numbers, but the supplied full text is unreadable and its header cites a different arXiv paper, so I couldn't verify anything beyond the abstract. read the letter →

arxiv 2508.16136 v2 pith:NKPWKV5B submitted 2025-08-22 quant-ph

Jaemin Kim , Seungchan Seo , Jiyoung Yun , Benjamin Lienhard , Joonwoo Bae This is my paper · ORCID

classification quant-ph

keywords SPAMpurificationquantumstatepreparationmeasurementnoisepost-selectionancilla-assistederrormitigationsuperconductingqubitsentanglementdistribution

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 claims that state preparation and measurement (SPAM) noise, a major error source in quantum information processing, can be purified away by repeating noisy SPAM operations and post-selecting on the outcomes. In a realistic scenario with 0.05 error in both preparation and measurement, it reports suppression to about 10^-3 with two ancilla qubits and 10^-6 with four. The idea is to distill error-free SPAM from noisy SPAM rather than to correct each error as it happens, so the protocol needs no pre-existing clean SPAM source. If the claim holds, SPAM errors become a negligible budget item for variational quantum algorithms, quantum error correction, and entanglement distribution through quantum repeaters. The paper also argues the protocol is feasible with superconducting qubits.

What carries the argument

The mechanism is a distillation circuit built from repeated noisy SPAM rounds plus ancilla qubits: the noisy SPAM is run multiple times, the ancillas are coupled to those runs, and a round is kept only when the ancilla outcomes indicate an error-free run. The load-bearing step is post-selection, which converts a stochastic per-round preparation or measurement error into a much lower probability that an error survives all checks. The number of ancillas sets the order of purification: two ancillas give the stated 10^-3 suppression from 0.05 noise, and four give 10^-6.

What would settle it

Run the protocol on a superconducting qubit whose preparation and measurement errors are independently measured near 5%, then measure the SPAM error of the post-selected output with two and four ancillas. If the residual error does not drop to about 10^-3 and 10^-6, or if the post-selection success probability is too low to be usable, the central claim is falsified. A second check: inject a known coherent preparation error; if the protocol cannot suppress it, that confirms the protocol's stochastic-noise scope.

Watch

Extended reading notes

Core claim

The paper's central claim is that noisy state preparation and measurement can be purified to an arbitrary level by running many noisy SPAMs and using ancilla qubits to flag or reject the noisy runs. With preparation and measurement error rates around 5%, two ancillas are said to reduce the residual error to roughly 10^-3 and four ancillas to roughly 10^-6; adding more ancillas pushes it lower. The protocol is presented as a way to distill error-free SPAM out of noisy SPAM, which would let experiments keep the convenience of imperfect preparation and measurement while effectively eliminating their contribution to the error budget.

Load-bearing premise

The load-bearing premise is that SPAM noise is stochastic and structured enough that repeated noisy rounds plus ancilla post-selection can separate clean runs from errored runs, and that the entangling gates used in the checks are much less noisy than the 5% preparation and measurement error being removed.

Editorial extensions

If this is right

Variational quantum algorithms can stop treating SPAM as a dominant error source, since imperfect initialization and readout can be purified into negligible overhead.
Quantum error correction can assume near-ideal state injection and measurement, simplifying the error budget for fault-tolerant operation.
Entanglement distribution through quantum repeaters becomes viable with imperfect local SPAM, because purified SPAM can be produced on demand via post-selection.
Error suppression scales with ancilla count, offering a tunable trade between extra qubits and the achievable SPAM error rate.
Because the protocol needs no clean SPAM source, it can be implemented with the existing noisy operations plus relatively clean entangling gates for the ancillas.

Reading between the lines

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

I infer that the main hidden cost is post-selection overhead: suppressing error from 5% to 10^-6 must reject most rounds, so the protocol is most useful when SPAM errors are the dominant bottleneck and total shot count is not the limiting resource.
A natural extension would be to apply the same repeated-copy post-selection idea to detector calibration or measurement tomography, where one noisy device is compared with itself.
The protocol's scope likely assumes stochastic SPAM noise with a known structure; if preparation errors are dominated by coherent rotations, additional randomization or twirling would probably be needed for the post-selection checks to isolate errors.
On platforms where two-qubit gate error is comparable to the 5% SPAM error, the ancilla checks themselves would inject errors, so the claimed suppression hinges on the gates being substantially cleaner than the SPAM being removed.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: the abstract promises a concrete SPAM-purification protocol with specific numbers—0.05 to 10^-3 with two ancillas, 10^-6 with four—and that is exactly the kind of result people in near-term quantum computing would care about. The problem is I cannot check any of it. The supplied full text is unreadable character garbage, and the one clean line in it is an arXiv header for a different paper (2508.16135, cs.LG), not this one. So this review is abstract-only.

What the paper does well: it identifies a real pain point, gives a concrete protocol mechanism (repeat noisy SPAM, post-select to distill cleaner SPAM), and states quantitative targets rather than vague hopes. The applications listed (variational algorithms, QEC, repeaters) are sensible. No circularity or fitting visible in the abstract; these look like derived claims under an unstated noise model.

The soft spots are proportionate to what I can see. First, the abstract gives no noise model. Any post-selection scheme has a threshold: if the entangling gates used to correlate copies have error q comparable to the 0.05 SPAM error, the best you can post-select to is O(q). To reach 10^-6 you need gate errors far below 10^-6 unless the protocol includes additional encoding. The abstract does not state this budget, and it is load-bearing. Second, no success probability is given. If the acceptance rate is exponential in the number of ancillas, the protocol becomes impractical at four ancillas; if it is polynomial, that is worth saying. Third, the claim of suppressing to "arbitrarily low level" is too strong as stated; with finite ancillas and non-zero gate noise there is a floor. Presumably the full text says this, but the abstract alone invites a skeptical reader.

None of these are necessarily fatal. The ideas are not new at the principle level—multi-copy purification is a known family—but applying it to SPAM with explicit ancilla counts is a useful contribution if the derivation holds. I have not been able to verify the derivation, the circuit, the references, or the comparison with prior work because the body text is not usable.

Bottom line: if the actual arXiv version is intact, this is a candidate for peer review. As presented, I cannot recommend citing it or trusting the numbers. The editor should first confirm the submission is not corrupted. Then a referee can check the gate-error budget, the success probability, and the comparison with randomized benchmarking or other SPAM-mitigation work.

Referee Report

4 major / 4 minor

Summary. The paper claims a protocol for purifying noisy qubit state preparation and measurement (SPAM) by repeating noisy SPAM operations and post-selecting on auxiliary qubits. The abstract gives concrete quantitative claims: with per-round preparation and measurement error around 0.05, the protocol suppresses the error to about 10^-3 with two ancillas and 10^-6 with four ancillas, and the method is claimed to be feasible with superconducting qubits and applicable to variational quantum algorithms, quantum error correction, and quantum repeaters. The supplied full text, however, is largely unreadable character-encoding corruption and contains an embedded header 'arXiv:2508.16135v1 [cs.LG] 22 Aug 2025', which does not match the declared arXiv identifier 2508.16136 or its quant-ph category. As a result, no circuit, equation, derivation, or numerical analysis can be inspected, and the central quantitative claims are unsupported in the submitted text.

Significance. If the claimed protocol is correct and its assumptions are made explicit, the result would be significant: SPAM errors are a recognized bottleneck in near-term quantum computing and communication. The idea of distilling near-ideal SPAM from repeated noisy SPAM is concrete, falsifiable, and potentially impactful. The abstract provides specific target numbers (0.05 -> 10^-3 with two ancillas, 10^-6 with four), which are the kind of quantitative predictions that can be checked. However, because the submission as provided contains no readable derivation, noise model, or gate-error budget, I cannot currently verify those predictions. The claimed benefits are therefore conditional on details that are absent.

major comments (4)

[Full text (header)] The supplied full text is not readable: it is a character-encoding corruption, and the embedded header reads 'arXiv:2508.16135v1 [cs.LG] 22 Aug 2025', which does not match this paper's arXiv identifier (2508.16136) or quant-ph category. No equation, circuit, or proof can be inspected. Because the abstract's quantitative claims (0.05 to 10^-3 with two ancillas and 10^-6 with four ancillas) depend on an explicit protocol and derivation, the central claim is unsupported in the submitted text. The authors must supply a legible and correctly matched full text before a technical review is possible.
[Abstract] The abstract does not state the noise model. The claimed suppression requires assumptions: the SPAM noise is stochastic and in a known basis (e.g., bit-flip or depolarizing with known rate), copies are independent, and post-selection is exact. If preparation or measurement errors are coherent rotations or have unknown basis, repeated-copy post-selection need not purify them. The authors should specify the noise model and provide a derivation of the output error probability p_out(n,p) as a function of the SPAM error rate p and the number of ancillas n, including a check that p_out(2,0.05) is approximately 10^-3.
[Abstract / assumed gate budget] The protocol requires entangling gates and ancilla readout. If each verification CNOT has error q, accepted events can be corrupted at rate O(q); for the four-ancilla claim of 10^-6, q must be far below 10^-6 unless additional encoding is used. The text does not state any gate-error budget or ancilla-readout error requirement. The authors should include gate noise q in the error analysis and give the threshold condition q < f(p,n) required to reach the claimed suppression levels.
[Full text / success probability] No success probability or repetition overhead is given. Distilling by post-selection typically has acceptance probability p_success(n,p) that decreases with the number of ancillas, and the practical overhead is 1/p_success. Without this quantity, the claim that the protocol is 'feasible with superconducting qubits' cannot be evaluated. Please provide the acceptance probability and compare the effective per-logical-operation cost with direct noisy SPAM.

minor comments (4)

[Abstract] The phrase 'suppress error rates up to 10^-3' should read 'suppress error rates to 10^-3' or 'down to 10^-3'.
[Title / abstract] SPAM should be expanded at first use, and 'purify noisy SPAM' should specify that both the preparation channel and the measurement channel are being distilled.
[Full text] The embedded arXiv header mismatch should be corrected; the supplied body appears to belong to a different document.
[Introduction / related work] Please add references to existing SPAM characterization and mitigation techniques (e.g., randomized benchmarking, readout calibration, measurement error mitigation) to contextualize the novelty.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity detectable: the supplied full text is corrupted and header-mismatched, so no derivation chain can be inspected.

full rationale

The abstract reports a protocol that is claimed to purify noisy state preparation and measurement, with numerical suppression factors (10^-3 with two ancillas, 10^-6 with four). These are presented as derived results, not as definitions: the 'purified error rate' is not defined in the supplied text as the protocol output by construction, and no fitted parameter is renamed as a prediction. The full text provided is unreadable due to character-encoding corruption, and its embedded arXiv header—'arXiv:2508.16135v1 [cs.LG] 22 Aug 2025'—does not match the target paper's identifier and category (2508.16136, quant-ph). Consequently, no equation, circuit, or proof can be inspected, and no quotable reduction of the central claim to its inputs can be exhibited. The absence of a stated gate-error budget or noise model is a correctness/verifiability concern, not evidence of circularity. Under the hard rule that circularity must be demonstrated by quoting the paper and showing a specific reduction, the correct finding is no significant circularity.

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

At the abstract level the protocol introduces no fitted parameters: the 0.05 / 10^-3 / 10^-6 numbers are example operating points, not fits. The load-bearing assumptions are the noise model (stochastic, known-rate SPAM errors) and the availability of entangling gates much cleaner than the SPAM being purified; both are standard for post-selection purification but are not stated in the abstract. Because the full text is unreadable, additional axioms or per-round parameters inside the protocol may exist and could not be audited.

assumptions (3)

domain assumption Noisy state preparation and measurement errors are stochastic, known-rate errors (the abstract's example is 0.05 in both).
Purification by repeated copies only suppresses noise that is random and characterizable in a known basis; coherent errors would not be removed by post-selection. The abstract does not state this condition.
domain assumption Entangling gates on the system and ancilla qubits are accurate enough that their errors do not dominate the SPAM errors being purified.
Every repetition round couples the copy and ancillas with gates; if those gates carry error comparable to the 0.05 SPAM error, the claimed floors of 10^-3 and 10^-6 are unattainable. Unstated in the abstract.
standard math Standard quantum mechanics background: fresh ancillas in known states, projective measurements, and Born-rule statistics for post-selection.
Invoked implicitly by 'repeating noisy SPAMs' and distillation by post-selection; no alternative physics is proposed.

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Cite this review

Pith. "Pith review of Protocol for Purifying Noisy Preparation and Measurements of Qubits." pith.science (2026). https://pith.science/paper/NKPWKV5B

@misc{pith2026250816136,
  author       = {Pith},
  title        = {Pith review of: Protocol for Purifying Noisy Preparation and Measurements of Qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NKPWKV5B}},
  note         = {Machine review of arXiv:2508.16136}
}

abstract

Noise affecting qubit preparation and measurements accounts for a significant fraction of errors in quantum information processing. This is especially critical in tasks like variational quantum algorithms, quantum error correction, and entanglement distribution through repeaters. In this work, we present a protocol to purify noisy SPAM, effectively suppressing these errors to an arbitrarily low level. For instance, in a realistic scenario where qubits contain error rates around $0.05$ in both preparation and measurement, the protocol can suppress error rates up to $10^{-3}$ with two ancillas and $10^{-6}$ with four ancillas. We show how to distill error-free SPAM by repeating noisy SPAMs. The protocol is also feasible with superconducting qubits. We envisage that our results can be used to realize quantum information tasks in computing and communication with negligible SPAM errors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

19 extracted references · 2 canonical work pages

[1]

Bharti , author A

author author K. Bharti , author A. Cervera-Lierta , author T. H. \ Kyaw , author T. Haug , author S. Alperin-Lea , author A. Anand , author M. Degroote , author H. Heimonen , author J. S. \ Kottmann , author T. Menke , author W.-K. \ Mok , author S. Sim , author L.-C. \ Kwek ,\ and\ author A. Aspuru-Guzik ,\ https://doi.org/10.1103/RevModPhys.94.015004 j...

doi:10.1103/revmodphys.94.015004 2022
[2]

Tilly , author H

author author J. Tilly , author H. Chen , author S. Cao , author D. Picozzi , author K. Setia , author Y. Li , author E. Grant , author L. Wossnig , author I. Rungger , author G. H. \ Booth ,\ and\ author J. Tennyson ,\ https://doi.org/https://doi.org/10.1016/j.physrep.2022.08.003 journal journal Physics Reports \ volume 986 ,\ pages 1 ( year 2022 ) ,\ no...

doi:10.1016/j.physrep.2022.08.003 2022
[3]

author author D. Gottesman ,\ https://arxiv.org/abs/quant-ph/9705052 title Stabilizer codes and quantum error correction ( year 1997 ),\ https://arxiv.org/abs/quant-ph/9705052 arXiv:quant-ph/9705052 [quant-ph] NoStop

arXiv 1997
[4]

author author M. A. \ Nielsen \ and\ author I. L. \ Chuang ,\ https://doi.org/10.1017/CBO9780511976667 title Quantum Computation and Quantum Information: 10th Anniversary Edition \ ( publisher Cambridge University Press ,\ year 2010 ) NoStop

doi:10.1017/cbo9780511976667 2010
[5]

Endo , author S

author author S. Endo , author S. C. \ Benjamin ,\ and\ author Y. Li ,\ https://doi.org/10.1103/PhysRevX.8.031027 journal journal Phys. Rev. X \ volume 8 ,\ pages 031027 ( year 2018 ) NoStop

doi:10.1103/physrevx.8.031027 2018
[6]

Cai , author R

author author Z. Cai , author R. Babbush , author S. C. \ Benjamin , author S. Endo , author W. J. \ Huggins , author Y. Li , author J. R. \ McClean ,\ and\ author T. E. \ O'Brien ,\ https://doi.org/10.1103/RevModPhys.95.045005 journal journal Rev. Mod. Phys. \ volume 95 ,\ pages 045005 ( year 2023 ) NoStop

doi:10.1103/revmodphys.95.045005 2023
[7]

Takagi , author H

author author R. Takagi , author H. Tajima ,\ and\ author M. Gu ,\ https://doi.org/10.1103/PhysRevLett.131.210602 journal journal Phys. Rev. Lett. \ volume 131 ,\ pages 210602 ( year 2023 ) NoStop

doi:10.1103/physrevlett.131.210602 2023
[8]

author author G. Q. \ AI \ and\ author Collaborators ,\ https://doi.org/10.1038/s41586-024-08449-y journal journal Nature \ volume 638 ,\ pages 920 ( year 2025 ) NoStop

doi:10.1038/s41586-024-08449-y 2025

Show all 19 references

[9]

Bravyi , author A

author author S. Bravyi , author A. W. \ Cross , author J. M. \ Gambetta , author D. Maslov , author P. Rall ,\ and\ author T. J. \ Yoder ,\ https://doi.org/10.1038/s41586-024-07107-7 journal journal Nature \ volume 627 ,\ pages 778 ( year 2024 ) NoStop

2024 doi
[10]

Kjaergaard , author M

author author M. Kjaergaard , author M. E. \ Schwartz , author J. Braumüller , author P. Krantz , author J. I.-J. \ Wang , author S. Gustavsson ,\ and\ author W. D. \ Oliver ,\ https://doi.org/https://doi.org/10.1146/annurev-conmatphys-031119-050605 journal journal Annual Revi...

2020 doi
[11]

Lienhard , author A

author author B. Lienhard , author A. Veps\"al\"ainen , author L. C. \ Govia , author C. R. \ Hoffer , author J. Y. \ Qiu , author D. Rist\`e , author M. Ware , author D. Kim , author R. Winik , author A. Melville , author B. Niedzielski , author J. Yoder , author G. J. \ Ribe...

2022 doi
[12]

Yan , author P

author author F. Yan , author P. Krantz , author Y. Sung , author M. Kjaergaard , author D. L. \ Campbell , author T. P. \ Orlando , author S. Gustavsson ,\ and\ author W. D. \ Oliver ,\ https://doi.org/10.1103/PhysRevApplied.10.054062 journal journal Phys. Rev. Appl. \ volume...

2018 doi
[13]

Stehlik , author D

author author J. Stehlik , author D. M. \ Zajac , author D. L. \ Underwood , author T. Phung , author J. Blair , author S. Carnevale , author D. Klaus , author G. A. \ Keefe , author A. Carniol , author M. Kumph , author M. Steffen ,\ and\ author O. E. \ Dial ,\ https://doi.or...

2021 doi
[14]

author author A. G. \ Fowler , author M. Mariantoni , author J. M. \ Martinis ,\ and\ author A. N. \ Cleland ,\ https://doi.org/10.1103/PhysRevA.86.032324 journal journal Phys. Rev. A \ volume 86 ,\ pages 032324 ( year 2012 ) NoStop

2012 doi
[15]

Gisin \ and\ author S

author author N. Gisin \ and\ author S. Wolf ,\ https://doi.org/10.1103/PhysRevLett.83.4200 journal journal Phys. Rev. Lett. \ volume 83 ,\ pages 4200 ( year 1999 ) NoStop

1999 doi
[16]

Horodecki , author P

author author R. Horodecki , author P. Horodecki , author M. Horodecki ,\ and\ author K. Horodecki ,\ https://doi.org/10.1103/RevModPhys.81.865 journal journal Rev. Mod. Phys. \ volume 81 ,\ pages 865 ( year 2009 ) NoStop

2009 doi
[17]

Kim , author J

author author J. Kim , author J. Yun ,\ and\ author J. Bae ,\ @noop journal journal arXiv:2404.10538 \ ( year 2024 ) NoStop

2024 arXiv
[18]

D\"ur , author H.-J

author author W. D\"ur , author H.-J. \ Briegel , author J. I. \ Cirac ,\ and\ author P. Zoller ,\ https://doi.org/10.1103/PhysRevA.59.169 journal journal Phys. Rev. A \ volume 59 ,\ pages 169 ( year 1999 ) NoStop

1999 doi
[19]

author author C. H. \ Bennett , author G. Brassard , author S. Popescu , author B. Schumacher , author J. A. \ Smolin ,\ and\ author W. K. \ Wootters ,\ https://doi.org/10.1103/PhysRevLett.76.722 journal journal Phys. Rev. Lett. \ volume 76 ,\ pages 722 ( year 1996 ) NoStop

1996 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Bharti , author A

author author K. Bharti , author A. Cervera-Lierta , author T. H. \ Kyaw , author T. Haug , author S. Alperin-Lea , author A. Anand , author M. Degroote , author H. Heimonen , author J. S. \ Kottmann , author T. Menke , author W.-K. \ Mok , author S. Sim , author L.-C. \ Kwek ,\ and\ author A. Aspuru-Guzik ,\ https://doi.org/10.1103/RevModPhys.94.015004 j...

doi:10.1103/revmodphys.94.015004 2022

[2] [2]

Tilly , author H

author author J. Tilly , author H. Chen , author S. Cao , author D. Picozzi , author K. Setia , author Y. Li , author E. Grant , author L. Wossnig , author I. Rungger , author G. H. \ Booth ,\ and\ author J. Tennyson ,\ https://doi.org/https://doi.org/10.1016/j.physrep.2022.08.003 journal journal Physics Reports \ volume 986 ,\ pages 1 ( year 2022 ) ,\ no...

doi:10.1016/j.physrep.2022.08.003 2022

[3] [3]

author author D. Gottesman ,\ https://arxiv.org/abs/quant-ph/9705052 title Stabilizer codes and quantum error correction ( year 1997 ),\ https://arxiv.org/abs/quant-ph/9705052 arXiv:quant-ph/9705052 [quant-ph] NoStop

arXiv 1997

[4] [4]

author author M. A. \ Nielsen \ and\ author I. L. \ Chuang ,\ https://doi.org/10.1017/CBO9780511976667 title Quantum Computation and Quantum Information: 10th Anniversary Edition \ ( publisher Cambridge University Press ,\ year 2010 ) NoStop

doi:10.1017/cbo9780511976667 2010

[5] [5]

Endo , author S

author author S. Endo , author S. C. \ Benjamin ,\ and\ author Y. Li ,\ https://doi.org/10.1103/PhysRevX.8.031027 journal journal Phys. Rev. X \ volume 8 ,\ pages 031027 ( year 2018 ) NoStop

doi:10.1103/physrevx.8.031027 2018

[6] [6]

Cai , author R

author author Z. Cai , author R. Babbush , author S. C. \ Benjamin , author S. Endo , author W. J. \ Huggins , author Y. Li , author J. R. \ McClean ,\ and\ author T. E. \ O'Brien ,\ https://doi.org/10.1103/RevModPhys.95.045005 journal journal Rev. Mod. Phys. \ volume 95 ,\ pages 045005 ( year 2023 ) NoStop

doi:10.1103/revmodphys.95.045005 2023

[7] [7]

Takagi , author H

author author R. Takagi , author H. Tajima ,\ and\ author M. Gu ,\ https://doi.org/10.1103/PhysRevLett.131.210602 journal journal Phys. Rev. Lett. \ volume 131 ,\ pages 210602 ( year 2023 ) NoStop

doi:10.1103/physrevlett.131.210602 2023

[8] [8]

author author G. Q. \ AI \ and\ author Collaborators ,\ https://doi.org/10.1038/s41586-024-08449-y journal journal Nature \ volume 638 ,\ pages 920 ( year 2025 ) NoStop

doi:10.1038/s41586-024-08449-y 2025