Quantum memristors for neuromorphic quantum machine learning

Lucas Lamata

REVIEW 3 major objections 4 minor 32 references

Quantum memristors for neuromorphic quantum machine learning

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that quantum memristors—units combining unitary evolution, weak measurement, and feedforward—could be the modular building blocks for scalable neuromorphic quantum machine learning on near-term devices.

desk verdict A clear, honestly hedged perspective, but with zero new technical content and a load-bearing scalability claim that is only an analogy with quantum error correction. read the letter →

arxiv 2412.18979 v1 pith:JHTBEB3Y submitted 2024-12-25 quant-ph cs.NE

Lucas Lamata This is my paper · ORCID

classification quant-phcs.NE

keywords quantummemristorneuromorphiccomputingmachinelearningmeasurementandfeedforwardquantum-classicalprotocolsnear-termdevicesneuralnetworks

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

Quantum machine learning needs more than reversible unitary evolution to learn; it needs a nonlinearity, and that can come from measurement and feedforward. This paper argues that a quantum memristor bundles those ingredients into a single hardware unit: a two-level quantum system whose weak measurement and feedforward give nonlinear behavior while keeping unitary evolution. Because several such units can be coupled, the paper proposes, networks of quantum memristors could form neuromorphic quantum architectures that scale more easily than purely unitary quantum circuits. The paper identifies near-term platforms such as photonics, superconducting circuits, trapped ions, and polaritons, and suggests reusing measurement-and-feedforward techniques from quantum error correction to build scalable networks. The central claim is that this modular route could make neuromorphic quantum machine learning practical in the mid-term.

What carries the argument

The central object is the quantum memristor: a two-dimensional quantum system in one unit with a weak measurement and feedforward. It carries the argument by supplying the nonlinearity that pure unitary evolution lacks—the measurement outcome changes the subsequent dynamics—while preserving unitary evolution in each step. The paper also leans on the extension to networks of entangled quantum memristors and on the analogy between quantum memristor measurement-feedforward and the measurement-and-feedforward protocols used in quantum error correction.

What would settle it

Build a network of quantum memristors on a photonic or superconducting platform and train it on a simple supervised learning task, while training a control network that uses only unitary evolution and a final measurement. If the control network matches or beats the memristor network's performance, the claim that measurement-induced nonlinearity is necessary for quantum learning collapses. A second direct check is to run error-correction-style measurement and feedforward at increasing network sizes and test whether the resource overhead scales the way the paper assumes; if the overhead grows too fast, the scalability claim fails.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is a design principle: the quantum memristor is the smallest hardware block that contains both reversible quantum evolution and the irreversibility of measurement, with feedforward to connect them, and so it is a natural constituent for quantum learning. In the classical limit this block reproduces memristive hysteresis, while quantum-mechanically it retains coherence. The author's claim is that this combination, repeated in a network, is a plausible route to neuromorphic quantum machine learning—not that a specific advantage has been demonstrated, but that the ingredients are all present in one modular unit, and that error-correction-style measurement and feedforward can be adapted to scale it.

Load-bearing premise

The load-bearing premise is that the nonlinearity created by measuring and feeding forward inside a single quantum memristor is enough to drive a useful learning process, and that the measurement-and-feedforward techniques used in quantum error correction can be scaled up directly to a large network of quantum memristors with no fundamental obstacle appearing.

Editorial extensions

If this is right

Networks of quantum memristors could be assembled into neuromorphic quantum architectures without requiring a fully fault-tolerant quantum computer.
The same measurement-and-feedforward engineering developed for quantum error correction could be reused to build scalable quantum memristor networks.
Quantum memristor units could be combined with digital-analog quantum simulation to give both modularity and scalable control.
If the central claim holds, quantum machine learning tasks that map naturally to neuromorphic processing could be run on near-term devices with better resource or energy scaling than unitary-only circuits.

Reading between the lines

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

The paper implies that the quantum memristor could serve as a unified primitive for both noise mitigation and learning, since the measurement-feedforward structure is exactly what error correction uses; this is a consequence the author leaves implicit.
One testable extension the paper does not carry out is a concrete simulation of a small quantum memristor network on a benchmark learning task, comparing its performance to a unitary-only circuit of the same size; if the unitary-only version performs equally, the central premise fails.
A broader inference is that the memristive nonlinearity might also be used for quantum state preparation or quantum control tasks beyond machine learning, since the same measurement-induced nonlinearity is a resource in those settings too.

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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

Short version: this is a perspective, not a research paper. It contains no equations, data, benchmarks, or new architectures. What it does well: it is a concise, readable argument that quantum memristors are a natural fit for neuromorphic QML because they combine unitary evolution and measurement in one unit. The author is honestly hedged throughout, even admitting that it is hard to predict whether this will outperform classical neural networks. The single-photon memristor experiment is cited correctly as the main experimental evidence.

The soft spot sits in the 'Possible implementations' section. The paper claims that QEC-style measurement-and-feedforward protocols 'may be directly employed' to build a scalable network of quantum memristors. That is the load-bearing step, and it is unsupported. QEC is engineered to suppress measurement backaction and preserve logical information; a learning network has to do the opposite, converting measurement outcomes into irreversible, information-discarding dynamics. The analogy is suggestive at best and possibly backwards. No learning rule, no convergence argument, no simulation, and no coupled-network experiment is supplied. The paper's own hedging does not substitute for evidence. For a perspective, flagging this as an open question would be fine; instead, it is presented as a path forward.

Everything else is a reasonable restatement of existing work. The self-citation is heavy, but that is acceptable in a perspective by someone who co-authored several of the founding proposals. The novelty is zero, which is fine for a perspective, but the preprint is not labeled as one. As a research submission, it would be a desk reject: there is nothing technically checkable. If the author wants to publish it, it should go to a venue with a perspective category, and the QEC-to-network jump should be explicitly labeled as an untested conjecture.

Who gets value from this? A newcomer wanting a quick overview of quantum memristors and why they might matter for QML. It is not something I would cite for a specific technical claim, and I would not bring it to a reading group as a paper to dissect, though it could seed a discussion about hardware directions. Recommendation: desk reject as a research paper; consider only as an invited perspective after the scalability claim is softened.

Referee Report

3 major / 4 minor

Summary. The manuscript is a perspective article arguing that quantum memristors—devices that integrate unitary evolution, weak measurement, and feedforward into a single hardware unit—are promising building blocks for neuromorphic quantum machine learning. The author reviews the concept, notes that classical-quantum protocols are necessary for learning because of irreversibility, and proposes that networks of quantum memristors could provide a scalable architecture. The paper highlights possible implementations in photonics, superconducting circuits, trapped ions, and Rydberg atoms, and suggests that measurement-and-feedforward techniques from quantum error correction could be directly repurposed for deploying scalable quantum memristor networks. The conclusions reinforce the promise of this paradigm while acknowledging the difficulty of predicting its performance relative to classical machine learning.

Significance. If the program is realized, a modular hardware unit combining coherent evolution with measurement-induced nonlinearity would be a valuable addition to the quantum machine learning toolbox, particularly for near-term devices. The paper is honest about uncertainty, explicitly acknowledging that it is hard to predict whether networks of quantum memristors will outperform classical neural networks. Strengths include a clear positioning of quantum memristors within the broader landscape of quantum-classical protocols and appropriate citation of the existing experimental realization of a single photonic quantum memristor. The paper does not present new derivations, simulations, or benchmarks, so its value lies in framing a research direction rather than establishing technical results.

major comments (3)

[Possible implementations with current quantum devices] The statement that 'the same protocols employed in the fast-developing realm of scalable quantum error correction, for error detection and correction via measurement and feedforward [29], may be directly employed for deploying a scalable network of quantum memristors' is an unsupported leap that is load-bearing for the paper's main promise. Quantum error correction is designed to suppress measurement backaction and preserve logical information, whereas a learning network must use measurement outcomes to drive non-unitary, information-discarding dynamics; no mechanism is given for how the transfer would work, and no model, simulation, or experimental evidence is supplied. This claim should be either substantially tempered with explicit caveats or supported with a concrete proposal showing how QEC-style protocols would apply to a dissipative memristive network.
[Introduction] The paper asserts that a single quantum memristor's combination of unitary evolution and measurement-induced nonlinearity provides 'the basic ingredients of unitary evolution, nonlinearity provided by the measurement, and a scalable architecture,' but no evidence is provided that these ingredients are sufficient for a useful learning process. In particular, no learning rule, convergence argument, or numerical simulation is presented, and the cited experimental realization [19] demonstrates memristive hysteresis rather than learning. The central argument that networks of such units 'may enable one to scale up quantum neural networks' therefore rests on an unexamined assumption that measurement-induced nonlinearity alone suffices for learning.
[Quantum memristors for neuromorphic quantum machine learning] The claim that quantum memristor networks are 'scalable' is not substantiated. The paper cites references [22,23] for coupled quantum memristors, but it does not describe the coupling mechanism, the effects of noise and decoherence on network dynamics, or how such a network would be trained. Without a discussion of these issues, the scalability claim remains an assertion of hope rather than a reasoned argument. The author should either provide a more concrete description of the proposed network architecture or explicitly frame scalability as an open question.

minor comments (4)

[Abstract] The phrase 'may permit to realize' is grammatically awkward; consider 'may enable' or 'may make it possible to realize.'
[General] The manuscript lacks numbered sections; adding section numbers would make it easier for readers to refer to specific claims and for the author to revise targeted passages.
[Introduction] The statement 'It is apparent that a purely quantum unitary evolution is not enough for an efficient learning process' would benefit from a supporting citation, since it is a substantive premise for the rest of the argument.
[References] Reference [29] is a single experimental paper on a logical quantum processor; citing only this paper for the entire QEC measurement-and-feedforward toolbox is overly narrow, and a review reference would be more appropriate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a perspective piece whose claims rest on external experimental work and explicit speculation, not on a derivation that reduces to its own inputs.

full rationale

The paper contains no equations, no fitted parameters, and no quantitative derivation chain. Its central claim is that quantum memristors "could be useful bricks for quantum machine learning devices," supported by the observation that they combine unitary evolution with measurement-induced nonlinearity in a modular unit. This is a conceptual argument, not a reduction of an output to an input. The key supporting experimental evidence is external: the photonic quantum memristor implementation of Spagnolo et al. [19]. The paper's use of the author's own prior proposals, such as [15] and [18], is as background literature and does not function as a load-bearing uniqueness theorem or as a substitute for independent evidence. The statement that quantum-error-correction measurement-and-feedforward protocols "may be directly employed for deploying a scalable network of quantum memristors" is an unverified analogy, but an unsupported speculative step is not circularity: it does not define its conclusion into existence or fit a parameter and then rename it as a prediction. The paper also explicitly hedges its strongest claim with "It is hard to really predict whether this quantum paradigm ... will perform better than classical machine learning protocols." No passage asserts a derivation, a uniqueness result, or a fitted prediction that would be equivalent to its own assumptions by construction. Therefore the appropriate finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no free parameters, no new entities, and no new math. Its assumptions are qualitative domain claims about the necessity of nonlinearity and the scalability of memristor networks.

assumptions (4)

domain assumption Purely unitary evolution is insufficient for efficient learning; irreversibility and nonlinearity from measurement are required.
Invoked in the Introduction through citations [1,2]; no derivation is given in this paper.
domain assumption The measurement-induced nonlinearity in a quantum memristor is sufficient and appropriate for a learning process.
The paper asserts this as the reason memristors are 'promising' without a model or demonstration.
domain assumption Quantum error correction measurement-and-feedforward protocols can be directly repurposed to scale up networks of quantum memristors.
Stated in 'Possible implementations with current quantum devices'; no engineering analysis is provided.
domain assumption Classical memristor hysteresis behavior extends to the quantum memristor in the classical limit, making the neuromorphic analogy valid.
The paper relies on the prior definition [16-21]; not checked here.

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Cite this review

Pith. "Pith review of Quantum memristors for neuromorphic quantum machine learning." pith.science (2026). https://pith.science/paper/JHTBEB3Y

@misc{pith2026241218979,
  author       = {Pith},
  title        = {Pith review of: Quantum memristors for neuromorphic quantum machine learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JHTBEB3Y}},
  note         = {Machine review of arXiv:2412.18979}
}

read the original abstract

Quantum machine learning may permit to realize more efficient machine learning calculations with near-term quantum devices. Among the diverse quantum machine learning paradigms which are currently being considered, quantum memristors are promising as a way of combining, in the same quantum hardware, a unitary evolution with the nonlinearity provided by the measurement and feedforward. Thus, an efficient way of deploying neuromorphic quantum computing for quantum machine learning may be enabled.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 30 canonical work pages

[29]

Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

work page 2024
[19]

Spagnolo et al., Experimental photonic quantum memristor, Nature Phot

M. Spagnolo et al., Experimental photonic quantum memristor, Nature Phot. 16, 318 (2022)

work page 2022
[1]

Yunfei Wang and Junyu Liu, A comprehensive review of quantum machine learning: from NISQ to fault tolerance, Rep. Prog. Phys. 87, 116402 (2024)

work page 2024
[2]

Biamonte et al., Quantum machine learning, Nature 549, 074001 (2017)

J. Biamonte et al., Quantum machine learning, Nature 549, 074001 (2017)

work page 2017
[3]

Lamata, Quantum machine learning and quantum biomimetics: A perspective, Mach

L. Lamata, Quantum machine learning and quantum biomimetics: A perspective, Mach. Learn.: Sci. Technol. 1, 033002 (2020)

work page 2020
[4]

Lamata, Quantum Machine Learning Implementations: Proposals and Experiments, Adv

L. Lamata, Quantum Machine Learning Implementations: Proposals and Experiments, Adv. Quantum Technol. 6, 2300059 (2023)

work page 2023
[5]

Peruzzo et al., A variational eigenvalue solver on a photonic quantum processor, Nature Comm

A. Peruzzo et al., A variational eigenvalue solver on a photonic quantum processor, Nature Comm. 5, 4213 (2014)

work page 2014
[6]

Casanova et al., From transistor to trapped-ion computers for quantum chemistry, Sci

J. Casanova et al., From transistor to trapped-ion computers for quantum chemistry, Sci. Rep. 4, 3589 (2014)

work page 2014

Show all 32 references

[7]

Tilly et al., The Variational Quantum Eigensolver: A review of methods and best practices, Phys

J. Tilly et al., The Variational Quantum Eigensolver: A review of methods and best practices, Phys. Rep. 986, 1 (2022)

2022
[8]

M. H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko, Quantum Boltzmann machine, Physical Review X 8, 021050 (2018)

2018
[9]

Farhi, J

E. Farhi, J. Goldstone, S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028 (2014)

2014 arXiv
[10]

Lamata, Basic protocols in quantum reinforcement learning with superconducting circuits, Sci

L. Lamata, Basic protocols in quantum reinforcement learning with superconducting circuits, Sci. Rep. 7, 1609 (2017)

2017
[11]

Albarrán-Arriagada, J

F. Albarrán-Arriagada, J. C. Retamal, E. Solano, and L. Lamata, Measurement-based adaptation protocol with quantum reinforcement learning, Physical Review A 98, 042315 (2018)

2018
[12]

Yu et al., Reconstruction of a photonic qubit state with reinforcement learning, Adv

S. Yu et al., Reconstruction of a photonic qubit state with reinforcement learning, Adv. Quantum Technol. 2, 1800074 (2019)

2019
[13]

M. L. Olivera -Atencio, L. Lamata , M. Morillo, and J. Casado -Pascual, Quantum reinforcement learning in the presence of thermal dissipation, Phys. Rev. E 108, 014128 (2023)

2023
[14]

Dunjko , H

V. Dunjko , H. J. Briegel, Machine learning & artificial intelligence in the quantum domain: a review of recent progress, Rep. Prog. Phys. 81, 074001 (2018)

2018
[15]

Lamata, Memristors go quantum, Nature Phot

L. Lamata, Memristors go quantum, Nature Phot. 16, 265 (2022)

2022
[16]

Pfeiffer, I

P. Pfeiffer, I. L. Egusquiza, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors, Sci. Rep. 6, 29507 (2016)

2016
[17]

Salmilehto, F

J. Salmilehto, F. Deppe, M. Di Ventra, M. Sanz, and E. Solano, Quantum Memristors with Superconducting Circuits, Sci. Rep. 7, 42044 (2017)

2017
[18]

M. Sanz, L. Lamata, and E. Solano , Quantum Memristors in Quantum Photonics, APL Photonics 3, 080801 (2018)

2018
[20]

P. A. Forsh, S. Y. Stremoukhov, A. S. Frolova, K. Y. Khabarova, and N. N. Kolachevsky, Quantum memristors: a new approach to neuromorphic computing, Physics-Uspekhi 67, 855 (2024)

2024
[21]

Di Ventra and Y

M. Di Ventra and Y. Pershin, Memristors and Memelements (Springer Nature, 2023)

2023
[22]

Kumar et al., Entangled quantum memristors, Phys

S. Kumar et al., Entangled quantum memristors, Phys. Rev. A 104, 062605 (2021)

2021
[23]

Kumar et al., Tripartite Entanglement in Quantum Memristors, Phys

S. Kumar et al., Tripartite Entanglement in Quantum Memristors, Phys. Rev. Applied 18, 034004 (2022)

2022
[24]

Russell and P

S. Russell and P. Norvig, Artificial Intelligence: A Modern Approach (Pearson, 2020)

2020
[25]

Hassabis, Nobel Lecture, https://www.nobelprize.org/uploads/2024/12/hassabis-lecture.pdf

D. Hassabis, Nobel Lecture, https://www.nobelprize.org/uploads/2024/12/hassabis-lecture.pdf

2024
[26]

I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014)

2014
[27]

https://www.humanbrainproject.eu/en/
[28]

Browaeys, and Thierry Lahaye, Many -body physics with individually controlled Rydberg atoms, Nature Phys

A. Browaeys, and Thierry Lahaye, Many -body physics with individually controlled Rydberg atoms, Nature Phys. 16, 132 (2020)

2020
[30]

https://www.pasqal.com, https://www.quera.com/
[31]

Lamata, A

L. Lamata, A. Parra -Rodriguez, M. Sanz, and E. Solano, Digital -Analog Quantum Simulations with Superconducting Circuits, Adv. Phys.: X 3, 1457981 (2018)

2018
[32]

Lamata, Digital-Analog Quantum Machine Learning, arXiv:2411.10744 (2024)

L. Lamata, Digital-Analog Quantum Machine Learning, arXiv:2411.10744 (2024)

2024 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [29]

Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

work page 2024

[2] [19]

Spagnolo et al., Experimental photonic quantum memristor, Nature Phot

M. Spagnolo et al., Experimental photonic quantum memristor, Nature Phot. 16, 318 (2022)

work page 2022

[3] [1]

Yunfei Wang and Junyu Liu, A comprehensive review of quantum machine learning: from NISQ to fault tolerance, Rep. Prog. Phys. 87, 116402 (2024)

work page 2024

[4] [2]

Biamonte et al., Quantum machine learning, Nature 549, 074001 (2017)

J. Biamonte et al., Quantum machine learning, Nature 549, 074001 (2017)

work page 2017

[5] [3]

Lamata, Quantum machine learning and quantum biomimetics: A perspective, Mach

L. Lamata, Quantum machine learning and quantum biomimetics: A perspective, Mach. Learn.: Sci. Technol. 1, 033002 (2020)

work page 2020

[6] [4]

Lamata, Quantum Machine Learning Implementations: Proposals and Experiments, Adv

L. Lamata, Quantum Machine Learning Implementations: Proposals and Experiments, Adv. Quantum Technol. 6, 2300059 (2023)

work page 2023

[7] [5]

Peruzzo et al., A variational eigenvalue solver on a photonic quantum processor, Nature Comm

A. Peruzzo et al., A variational eigenvalue solver on a photonic quantum processor, Nature Comm. 5, 4213 (2014)

work page 2014

[8] [6]

Casanova et al., From transistor to trapped-ion computers for quantum chemistry, Sci

J. Casanova et al., From transistor to trapped-ion computers for quantum chemistry, Sci. Rep. 4, 3589 (2014)

work page 2014