Pith. sign in

REVIEW 4 major objections 5 minor 4 cited by

Large-scale quantum reservoir computing using a Gaussian Boson Sampler

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read A >400-mode Gaussian boson sampler serves as a reservoir computer whose accuracy improves by over 20 percentage points when the output layer is given photon-number correlations between modes rather than only per-mode averages.

desk verdict A genuinely useful first demonstration of >400-mode GBS reservoir computing, with correlation features clearly helping, but the squeezed-versus-coherent superiority claim depends on an underspecified simulated baseline that needs to be pinned down before it convinces. read the letter →

arxiv 2505.13695 v1 pith:UAQUED7U submitted 2025-05-19 quant-ph

Valeria Cimini , Mandar M. Sohoni , Federico Presutti , Benjamin K. Malia , Shi-Yuan Ma , Ryotatsu Yanagimoto , Tianyu Wang , Tatsuhiro Onodera
show 2 more authors
Logan G. Wright Peter L. McMahon
This is my paper · ORCID
classification quant-ph
keywords quantumreservoircomputingGaussianbosonsamplingsqueezedlightphotoncorrelationscovariancematrixmachinelearningadiabaticfrequencyconversionoptical
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 experiments using a frequency-multiplexed Gaussian boson sampler with more than 400 optical modes as the fixed reservoir in quantum reservoir computing. The authors classify classical data—synthetic non-linearly separable tasks, spoken vowels, and MNIST digits—by encoding each sample in the spectral phases of a pump pulse, measuring output photon counts per mode, and training a single classical linear classifier on the measurements. The central result is that feeding the classifier the full photon-number covariance matrix, which includes correlations between modes, gives the same or higher accuracy than feeding it only the per-mode mean photon numbers, with gains greater than 20 percentage points in several cases. They also compare squeezed light against coherent, thermal, and supercontinuum light under matched photon budgets and find squeezed light consistently at least ties the best classical accuracy. The work positions GBS as a practical hardware platform for quantum reservoir computing at large system sizes.

What carries the argument

The workhorse is the photon-number covariance matrix of the measured output modes, $\Sigma_{ij} = \langle \hat n_i \hat n_j\rangle - \langle \hat n_i\rangle\langle \hat n_j\rangle$, built from single-shot EMCCD camera frames and flattened into a feature vector for a linear classifier. The reservoir itself is an adiabatic frequency-conversion (AFC) crystal acting as a programmable frequency-domain beamsplitter unitary: classical data $x$ are encoded in the spectral phases $\phi(\lambda)$ of the pump pulse via a spatial light modulator, and the weak input optical state (squeezed vacuum from an OPA, or coherent, thermal, or supercontinuum light) is transformed by this unitary before frequency-resolved detection. The covariance's off-diagonal elements capture inter-mode correlations that the mean-field vector discards; the paper argues that these correlations are what let the linear classifier separate classes that are not linearly separable in the raw features.

What would settle it

Repeat the vowel and moons/blobs classification experiments with a coherent light source whose spectral bandwidth, loss, mode structure, and photon budget exactly match the squeezed-vacuum path; if its covariance-based accuracy reaches or exceeds the squeezed-light accuracy within error bars, the claim that squeezing itself provides the correlation advantage is refuted.

Watch

Extended reading notes

Core claim

The paper claims that a Gaussian boson sampler used as a reservoir computer produces features whose correlations are computationally useful: across every benchmark task, providing the trained linear output layer with the photon-number covariance matrix $\Sigma$ (with elements $\Sigma_{ij} = \langle \hat{n}_i \hat{n}_j\rangle - \langle \hat{n}_i\rangle \langle \hat{n}_j\rangle$) rather than only the mean-field vector $\mu$ yields equal or higher classification accuracy. For the squeezed-light reservoir, this advantage exceeded 20 percentage points in several configurations, and the accuracy gap grows with task complexity, number of modes read out, and photon budget. The paper further claims that squeezed light used as the reservoir input consistently achieves the highest or tied-highest accuracies among squeezed, coherent, thermal, and supercontinuum light when total detected photon numbers are matched, with the caveat that only a simulated same-bandwidth coherent source provides an equal-bandwidth comparison.

Load-bearing premise

The comparison between squeezed and coherent light hinges on the simulated broadband coherent reservoir faithfully representing a classical reservoir with the same mode structure, loss, and encoding as the squeezed-light experiment; if that simulation omits loss, mode overlap, or detector effects present in the real squeezed-light path, the claim that squeezing itself helps is not established.

Editorial extensions

If this is right

  • Access to correlations in the reservoir output should be built into QRC feature design; mean-field-only readouts may leave substantial accuracy on the table.
  • Larger numbers of readout modes and higher photon budgets both increase accuracy when correlations are used, so scaling GBS reservoirs in these directions should improve performance on harder tasks.
  • Squeezed light is worth retaining as a resource even though the current system's loss keeps the correlations from being unambiguously quantum; a lower-loss version could decide whether quantum correlations genuinely cause the advantage.
  • The same GBS apparatus, operated with quantum states rather than classical data as inputs, could be used to classify quantum states of light, a task where QRC might deliver a true quantum advantage.
  • On the MNIST benchmark, the achieved accuracy is comparable to a recently reported neutral-atom quantum reservoir computer, indicating that photonic GBS is a competitive large-scale QRC platform.

Reading between the lines

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

  • Beyond the paper: if correlation-based features are as informative as these experiments suggest, other multimode squeezed-light platforms could be repurposed as reservoirs without changing the training protocol, making the AFC setup one instance of a broader class of Gaussian reservoir hardware.
  • Beyond the paper: the quadratic growth of the covariance matrix with mode count predicts that correlation readouts should become increasingly valuable relative to mean-field readouts as the number of modes grows; a direct test would compare accuracy gaps at, say, 64, 128, 256, and 400 modes.
  • Beyond the paper: the authors note their system could handle time-series inputs; a testable extension is to run temporal tasks (e.g., waveform forecasting) to see whether covariance readouts also outperform mean-field readouts in the recurrent setting.
  • Beyond the paper: the loss caveat suggests a crisp experiment—inserting a lower-loss detection stage and checking whether the correlation-driven accuracy gap widens once the measured correlations are verifiably non-classical.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper reports an experimental study in which a frequency-multiplexed Gaussian boson sampler with more than 400 modes is used as a reservoir for classification tasks. Classical data are encoded in the spectral phase of the pump of an adiabatic frequency conversion process, and the reservoir output is read out either as the mean photon number per mode or as the full photon-number covariance matrix computed from EMCCD camera frames. The authors evaluate the resulting reservoir computer on synthetic nonlinear tasks, spoken-vowel classification, and MNIST digit classification. Their central claims are that using the covariance matrix instead of the mean-field vector increases classification accuracy, in several cases by more than 20 percentage points, and that a squeezed-light source gives consistently higher (or tied-highest) accuracy than the tested classical light sources under matched total photon budgets. The paper is candid about its main limitations: the classical sources did not have the same bandwidth as the squeezed source, the end-to-end loss is high, and the measured correlations are not strong enough to rule out classical generation.

Significance. If the claims hold, this is a substantial experimental step for photonic quantum reservoir computing: it demonstrates a >400-mode GBS-based reservoir with >100 programmable input dimensions, provides evidence that two-mode correlation features improve linear classification, and compares several classical optical reservoirs under matched photon budgets. The manuscript has notable strengths: the photon-budget matching in Appendix A, the robustness check across four different output classifiers in Fig. 4d, the explicit discussion of loss, classical simulability, and the impossibility of attributing the results to quantumness in Sections IV B and IV F, and the public availability of data and code (DOI in the Data Availability statement). The main weakness is that the controlled equal-bandwidth comparison between squeezed light and coherent light rests on an underspecified simulation, and some plots labeled as classical-reservoir comparisons are actually comparisons between covariance and mean-field outputs of the squeezed-light data.

major comments (4)
  1. [Section III B, Fig. 4, and Methods V A] The simulated broadband coherent-state reservoir (orange curve in Figs. 4a and 4b) is the only equal-bandwidth classical baseline, but the manuscript does not specify the simulation model. It must state how the coherent state is constructed (for example, which measured quantities determine the complex displacement amplitudes and phases), whether the AFC unitary and the approximately 60% end-to-end transmission, the 95% EMCCD quantum efficiency, the stochastic EM gain, and the per-pixel background are included, and how the simulated camera frames are generated. Without this information, the orange curve could be an idealized lossless coherent baseline, and the claim that squeezed light outperforms an equal-bandwidth coherent reservoir would not be established; please provide the model equations or pseudocode and validate the simulator against the experimental coherent-state data shown in the red curves.
  2. [Appendix C, Fig. 10, and Fig. 4c] In several places the 'classical reservoir' is not a reservoir driven by coherent light but the mean-field output computed from the squeezed-light data. The caption of Fig. 10 states that both curves are 'computed from the same measurement datasets,' and Fig. 4c similarly compares the covariance with the mean field. This confounds the choice of output feature (covariance versus mean) with the choice of input state (squeezed versus coherent), and therefore cannot support the abstract's claim that squeezed light outperforms coherent light; either perform the comparison with actual coherent-light datasets or relabel these curves and their discussion as feature-ablation results.
  3. [Section III A and Appendix D] The comparison between covariance and mean-field inputs is not symmetric. The covariance input is feature-selected using an ANOVA F-test with the number of retained features k optimized on an 8% validation set, whereas the mean-field vector is always used with all 512 components; moreover, the covariance matrix contains the diagonal elements, which carry mean-field-like information. To support the statement that inter-mode 'correlations' are responsible for the reported gains of greater than 20 percentage points, the authors should compare against diagonal-only and off-diagonal-only covariance inputs and use nested cross-validation for the feature-count selection; otherwise the advantage could be due to feature selection or to a rescaling of the diagonal information rather than to the correlations between modes.
  4. [Footnote 7 and Section IV B] The squeezed-versus-coherent advantage is described as 'consistently' higher in accuracy, while the same footnote states that the gaps are within statistical uncertainty. Since this comparison is load-bearing for the second central claim, the abstract and Section IV should either report explicit confidence intervals or combined statistical tests across tasks, or the wording should be qualified to state that the squeezed-light advantage is suggestive but not statistically established at the reported sample sizes.
minor comments (5)
  1. [Section II, setup description] The sentence 'in all cases the AFC was pump did not encode an input vector x' contains a grammatical error and should be rewritten.
  2. [Section III B] The text '30, 0000 frames' appears to be a typo; it should presumably read '30,000 frames'.
  3. [Fig. 2 and Fig. 16] The color scales and axis units for the covariance maps are not defined in the figure captions; please add colorbars and clarify whether the axes are camera-pixel indices or wavelengths.
  4. [Appendix E, Eq. (E1)] The summation in Eq. (E1) is over m instances, but the notation m is not defined at that point and the Lagrangian formulation in Eq. (E3) also uses m; please make the notation consistent.
  5. [Throughout] The terms 'mode' and 'camera pixel' are used nearly interchangeably; since the grating maps the AFC output frequencies onto pixels, please state explicitly the pixel-to-mode relation and whether adjacent pixels correspond to distinct optical modes or to an oversampled spectrum.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the paper reports measured accuracy comparisons; same-author citations provide context and apparatus characterization but are not load-bearing reductions.

full rationale

This is an experimental benchmarking paper, not a derivation, so there is no chain of equations in which an output is imposed by its inputs. The central quantitative claims—(i) covariance-based features give equal or better held-out accuracy than mean-field features, and (ii) squeezed-light input gives the highest accuracies among the tested sources under matched photon budgets—are empirical accuracies computed on test sets, not quantities fitted from the same data and renamed as predictions. The covariance-versus-mean-field comparison does give the classifier a superset of features, so the direction of the result is unsurprising, but the paper does not derive the advantage from that inclusion; it measures it, and it explicitly notes the diagonal/mean-field overlap and the role of overfitting (Sec. III A). The simulated broadband-coherent baseline (Fig. 4a/b, orange) is a modeling assumption whose faithfulness is a genuine experimental-validity concern, but it is not a circular reduction: the simulation is not obtained by fitting the target accuracies, and the paper itself cautions that bandwidths differed and that the measured correlations could in principle be classical (Secs. IV B, IV F). Same-author citations (Refs. [24], [47]) supply theoretical context and prior characterization of the AFC/squeezed-light apparatus; they are not invoked as uniqueness theorems or as the source of the measured accuracies, so they do not make the argument circular. The paper's explicit limitations—classical simulability, non-identical classical sources, and unresolved squeezed-versus-coherent statistical significance—are acknowledged rather than hidden, and they affect the strength of the conclusions, not the circularity of the reasoning.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new postulates. Its central experimental comparison rests on standard quantum-optics models of squeezed/coherent/thermal light and on the prior characterization of the AFC setup in Ref [47]. The main free parameters are data-processing choices (feature count, frame count, encoding scalings) rather than physics.

free parameters (6)
  • Number of selected covariance features k = ~15,000
    The top k covariance-matrix elements are chosen to maximize validation accuracy (Appendix D). This is a data-fitted hyperparameter affecting the reported accuracies.
  • SLM phase scaling factor = not specified
    A constant scaling applied to dataset features to keep SLM pixel values below a threshold (Sec V B). Chosen by hand, not optimized.
  • Gaussian filtering standard deviation = not specified
    Applied to the phase mask to avoid adjacent-pixel jumps (Sec V B). Selected ad hoc.
  • Number of camera frames = 5000
    Chosen as balance between noise and acquisition time (Sec II). Affects feature noise.
  • Number of PCA components for MNIST = 100
    Dimensionality reduction of MNIST images (Sec III B). Choice limits input dimension.
  • Quadratic chirp coefficient = not specified
    Fixed phase to maintain pump pulse duration (Sec V B). Part of encoding.
assumptions (5)
  • domain assumption Adiabatic frequency conversion implements a programmable unitary beamsplitter transformation on the signal modes.
    The reservoir's computation is described as a unitary mode transformation, following Ref [47] (Sec II).
  • domain assumption The EMCCD camera gives photon-number-resolved measurements of the 512 output frequency modes.
    Used to construct mean field and covariance matrix (Sec II).
  • domain assumption The squeezed-light source produces approximately 430 supermodes with at least 3 dB squeezing.
    Inferred from photon-count fits, from Ref [47] (Sec V A).
  • domain assumption The experimental system with loss is efficiently classically simulable given mean fields and two-body correlations.
    Authors cite Refs [13,62] to state this; it is not derived in this paper (Sec IV F).
  • standard math Photon statistics of coherent, thermal, supercontinuum, and squeezed states follow standard quantum optics.
    Used to compare covariance matrices and mean fields (Sec II).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Large-scale quantum reservoir computing using a Gaussian Boson Sampler." pith.science (2026). https://pith.science/paper/UAQUED7U

@misc{pith2026250513695,
  author       = {Pith},
  title        = {Pith review of: Large-scale quantum reservoir computing using a Gaussian Boson Sampler},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UAQUED7U}},
  note         = {Machine review of arXiv:2505.13695}
}
abstract

A Gaussian boson sampler (GBS) is a special-purpose quantum computer that can be practically realized at large scale in optics. Here we report on experiments in which we used a frequency-multiplexed GBS with $>400$ modes as the reservoir in the quantum-machine-learning approach of quantum reservoir computing. We evaluated the accuracy of our GBS-based reservoir computer on a variety of benchmark tasks, including spoken-vowels classification and MNIST handwritten-digit classification. We found that when the reservoir computer was given access to the correlations between measured modes of the GBS, the achieved accuracies were the same or higher than when it was only given access to the mean photon number in each mode -- and in several cases the advantage in accuracy from using the correlations was greater than 20 percentage points. This provides experimental evidence in support of theoretical predictions that access to correlations enhances the power of quantum reservoir computers. We also tested our reservoir computer when operating the reservoir with various sources of classical rather than squeezed (quantum) light and found that using squeezed light consistently resulted in the highest (or tied highest, for simple tasks) accuracies. Our work experimentally establishes that a GBS can be an effective reservoir for quantum reservoir computing and provides a practical platform for experimentally exploring the role of quantumness and correlations in quantum machine learning at very large system sizes.

Figures

Figures reproduced from arXiv: 2505.13695 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: , resulting always in a 1920 feature vector. Since the SLM pixels transmissivity is not uniform, but central pixels have higher transmissivity compared to those at the edges, we introduced a compensating function. The function is reported in blue in the plot and it is …
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p024_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p025_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p026_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p027_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p028_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p029_16.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling

    quant-ph 2025-08 conditional novelty 7.0 of 10

    Jiuzhang 4.0 performs Gaussian boson sampling with up to 3050 detected photons and 1024 input squeezed states, claiming a quantum speedup exceeding 10^54 over the best classical simulation.

  2. Quantum latent distributions in deep generative models

    cs.LG 2025-08 conditional novelty 6.0 of 10

    Quantum latent distributions from boson samplers are shown in theory to expand the output distribution class of invertible Lipschitz generators, and in GAN benchmarks on QM9 to beat Gaussian, Bernoulli, and distinguis...

  3. Quenched Quantum Feature Maps

    quant-ph 2025-08 reject novelty 5.0 of 10

    Quench dynamics of a quantum spin glass on a D-Wave annealer generate feature representations that improve several classical classifiers on small tabular datasets, though the claimed quantum-advantage level is not supported.

  4. Enhanced Image Recognition Using Gaussian Boson Sampling

    quant-ph 2025-06 conditional novelty 4.0 of 10

    A Gaussian boson sampling device is used as a random feature generator for extreme learning machines, reaching 95.86% on MNIST and 85.95% on Fashion-MNIST.

Reference graph

Works this paper leans on

69 extracted references · 45 canonical work pages · cited by 4 Pith papers

  1. [1]

    The poling is designed for broadband sum-frequency generation, where the central wavelengths are 1550 + 1033→ 620 nm, and the 1033 nm is the pump wavelength

    Pulse shaping and frequency conversion The crystal used for frequency conversion is a 3 cm poled KTP crystal (Raicol Crystals). The poling is designed for broadband sum-frequency generation, where the central wavelengths are 1550 + 1033→ 620 nm, and the 1033 nm is the pump wavelength. The spatial frequency of the poling profile varies linearly over the le...

    work page

  2. [2]

    pixel value

    Spectrometer and detection The visible light spectrometer is based on a diffraction grating (Ibsen PCG-1908/675-972) imaged by an objective lens (Olympus UPLFLN4x) onto the N¨ uV¨ u HN¨ u 512 IS EMCCD camera. The 620 nm light from the AFC is measured on the camera after appropriate filtering of the pump (Thorlabs DMLP900; Semrock FF01-632/148). A nominal ...

    work page 1908

  3. [3]

    It is engineered to support single spatial modes at near-infrared (near-IR) wavelengths

    Light sources The OPA waveguide is a 4 cm MgO-doped LN ridge waveguide (Covesion WG-1550-40 WGCK40), optimized for wavelength conversion from 1550 nm to 775 nm. It is engineered to support single spatial modes at near-infrared (near-IR) wavelengths. This device is mounted in a temperature-controlled oven (Covesion PV40) to ensure optimal performance. Addi...

    work page 1920

  4. [4]

    Zhong, H

    H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, et al., Quantum computational advantage using photons, Science 370, 1460 (2020)

    2020

  5. [5]

    L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais, T. Vincent, J. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, et al., Quantum computational advantage with a programmable photonic processor, Nature 606, 75 (2022)

    work page 2022

  6. [6]

    C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Gaussian boson sampling, Physical review letters 119, 170501 (2017)

    2017

  7. [7]

    Roslund, R

    J. Roslund, R. M. De Araujo, S. Jiang, C. Fabre, and N. Treps, Wavelength-multiplexed quantum networks with ultrafast frequency combs, Nature Photonics 8, 109 (2014)

    work page 2014

  8. [8]

    N. C. Menicucci, P. Van Loock, M. Gu, C. Weedbrook, . f. T. C. Ralph, and M. A. Nielsen, Universal quantum computation with continuous-variable cluster states, Physical Review Letters 97, 110501 (2006)

    work page 2006

Show all 69 references
  1. [9]

    H. J. Briegel, D. E. Browne, W. D¨ ur, R. Raussendorf, and M. Van den Nest, Measurement-based quantum computation, Nature Physics 5, 19 (2009)

    2009

  2. [10]

    Raussendorf, J

    R. Raussendorf, J. Harrington, and K. Goyal, Topological fault-tolerance in cluster state quantum computation, New Journal of Physics 9, 199 (2007)

    2007

  3. [11]

    Yokoyama, R

    S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J.-i. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, Ultra-large-scale continuous-variable cluster states multiplexed in the time domain, Nature Photonics 7, 982 (2013). 18

    2013

  4. [12]

    Asavanant, Y

    W. Asavanant, Y. Shiozawa, S. Yokoyama, B. Charoensombutamon, H. Emura, R. N. Alexander, S. Takeda, J.-i. Yoshikawa, N. C. Menicucci, H. Yonezawa, et al., Generation of time-domain-multiplexed two-dimensional cluster state, Science 366, 373 (2019)

    2019

  5. [13]

    M. V. Larsen, X. Guo, C. R. Breum, J. S. Neergaard-Nielsen, and U. L. Andersen, Deterministic generation of a two- dimensional cluster state, Science 366, 369 (2019)

    2019

  6. [14]

    J. Huh, G. G. Guerreschi, B. Peropadre, J. R. McClean, and A. Aspuru-Guzik, Boson sampling for molecular vibronic spectra, Nature Photonics 9, 615 (2015)

    2015

  7. [15]

    C. Oh, Y. Lim, Y. Wong, B. Fefferman, and L. Jiang, Quantum-inspired classical algorithms for molecular vibronic spectra, Nature Physics 20, 225 (2024)

    2024

  8. [16]

    C. Oh, M. Liu, Y. Alexeev, B. Fefferman, and L. Jiang, Classical algorithm for simulating experimental gaussian boson sampling, Nature Physics 20, 1461 (2024)

    2024

  9. [17]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature 549, 195 (2017)

    2017

  10. [18]

    Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018)

    J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018)

    2018

  11. [19]

    Cerezo, G

    M. Cerezo, G. Verdon, H.-Y. Huang, L. Cincio, and P. J. Coles, Challenges and opportunities in quantum machine learning, Nature Computational Science 2, 567 (2022)

    2022

  12. [20]

    Johri, S

    S. Johri, S. Debnath, A. Mocherla, A. Singk, A. Prakash, J. Kim, and I. Kerenidis, Nearest centroid classification on a trapped ion quantum computer, npj Quantum Information 7, 122 (2021)

    2021

  13. [21]

    LeCun, L

    Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE 86, 2278 (1998)

    1998

  14. [22]

    Kornjaˇ ca, H.-Y

    M. Kornjaˇ ca, H.-Y. Hu, C. Zhao, J. Wurtz, P. Weinberg, M. Hamdan, A. Zhdanov, S. H. Cantu, H. Zhou, R. A. Bravo, et al., Large-scale quantum reservoir learning with an analog quantum computer, arXiv:2407.02553 (2024)

    2024 arXiv

  15. [23]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al., Variational quantum algorithms, Nature Reviews Physics 3, 625 (2021)

    2021

  16. [24]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications 9, 4812 (2018)

    2018

  17. [25]

    Fujii and K

    K. Fujii and K. Nakajima, Harnessing disordered-ensemble quantum dynamics for machine learning, Physical Review Applied 8, 024030 (2017)

    2017

  18. [26]

    Fujii and K

    K. Fujii and K. Nakajima, Quantum reservoir computing: a reservoir approach toward quantum machine learning on near-term quantum devices, Reservoir Computing: Theory, Physical Implementations, and Applications , 423 (2021)

    2021

  19. [27]

    L. G. Wright and P. L. McMahon, The capacity of quantum neural networks, arXiv:1908.01364 (2019)

    2019 arXiv

  20. [28]

    Garc´ ıa-Beni, G

    J. Garc´ ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Scalable photonic platform for real-time quantum reservoir computing, Physical Review Applied 20, 014051 (2023)

    2023

  21. [29]

    Suprano, D

    A. Suprano, D. Zia, L. Innocenti, S. Lorenzo, V. Cimini, T. Giordani, I. Palmisano, E. Polino, N. Spagnolo, F. Sciarrino, et al. , Experimental property reconstruction in a photonic quantum extreme learning machine, Physical Review Letters 132, 160802 (2024)

    2024

  22. [30]

    Garc´ ıa-Beni, G

    J. Garc´ ıa-Beni, G. Luca Giorgi, M. C. Soriano, and R. Zambrini, Squeezing as a resource for time series processing in quantum reservoir computing, Optics Express 32, 6733 (2024)

    2024

  23. [31]

    Nerenberg, O

    S. Nerenberg, O. D. Neill, G. Marcucci, and D. Faccio, Photon number-resolving quantum reservoir computing, arXiv:2402.06339 (2024)

    2024 arXiv

  24. [32]

    D. Zia, L. Innocenti, G. Minati, S. Lorenzo, A. Suprano, R. Di Bartolo, N. Spagnolo, T. Giordani, V. Cimini, G. M. Palma, et al., Quantum extreme learning machines for photonic entanglement witnessing, arXiv:2502.18361 (2025)

    2025

  25. [33]

    Spagnolo, J

    M. Spagnolo, J. Morris, S. Piacentini, M. Antesberger, F. Massa, A. Crespi, F. Ceccarelli, R. Osellame, and P. Walther, Experimental photonic quantum memristor, Nature Photonics 16, 318 (2022)

    2022

  26. [34]

    Selimovi´ c, I

    M. Selimovi´ c, I. Agresti, M. Siemaszko, J. Morris, B. Daki´ c, R. Albiero, A. Crespi, F. Ceccarelli, R. Osellame, M. Stobi´ nska, et al., Experimental neuromorphic computing based on quantum memristor, arXiv:2504.18694 (2025)

    2025 arXiv

  27. [35]

    Yasuda, Y

    T. Yasuda, Y. Suzuki, T. Kubota, K. Nakajima, Q. Gao, W. Zhang, S. Shimono, H. I. Nurdin, and N. Yamamoto, Quantum reservoir computing with repeated measurements on superconducting devices, arXiv:2310.06706 (2023)

    2023 arXiv

  28. [36]

    Senanian, S

    A. Senanian, S. Prabhu, V. Kremenetski, S. Roy, Y. Cao, J. Kline, T. Onodera, L. G. Wright, X. Wu, V. Fatemi, et al., Microwave signal processing using an analog quantum reservoir computer, Nature Communications 15, 7490 (2024)

    2024

  29. [37]

    F. Hu, S. A. Khan, N. T. Bronn, G. Angelatos, G. E. Rowlands, G. J. Ribeill, and H. E. T¨ ureci, Overcoming the coherence time barrier in quantum machine learning on temporal data, Nature Communications 15, 7491 (2024)

    2024

  30. [38]

    R. A. Bravo, K. Najafi, X. Gao, and S. F. Yelin, Quantum reservoir computing using arrays of rydberg atoms, PRX Quantum 3, 030325 (2022)

    2022

  31. [39]

    G. R. Steinbrecher, J. P. Olson, D. Englund, and J. Carolan, Quantum optical neural networks, npj Quantum Information 5, 60 (2019)

    2019

  32. [40]

    Ewaniuk, J

    J. Ewaniuk, J. Carolan, B. J. Shastri, and N. Rotenberg, Imperfect quantum photonic neural networks, Advanced Quantum Technologies 6, 2200125 (2023)

    2023

  33. [41]

    Z. Yin, I. Agresti, G. de Felice, D. Brown, A. Toumi, C. Pentangelo, S. Piacentini, A. Crespi, F. Ceccarelli, R. Osellame, et al., Experimental quantum-enhanced kernels on a photonic processor, arXiv:2407.20364 (2024)

    2024 arXiv

  34. [42]

    F. Hoch, E. Caruccio, G. Rodari, T. Francalanci, A. Suprano, T. Giordani, G. Carvacho, N. Spagnolo, S. Koudia, M. Proi- etti, et al., Quantum machine learning with adaptive boson sampling via post-selection, Nature Communications 16, 902 (2025)

    2025

  35. [43]

    Fukui and S

    K. Fukui and S. Takeda, Building a large-scale quantum computer with continuous-variable optical technologies, Journal 19 of Physics B: Atomic, Molecular and Optical Physics 55, 012001 (2022)

    2022

  36. [44]

    Killoran, T

    N. Killoran, T. R. Bromley, J. M. Arrazola, M. Schuld, N. Quesada, and S. Lloyd, Continuous-variable quantum neural networks, Physical Review Research 1, 033063 (2019)

    2019

  37. [45]

    Garc´ ıa-Beni, I

    J. Garc´ ıa-Beni, I. Paparelle, V. Parigi, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Quantum machine learning via continuous-variable cluster states and teleportation, arXiv:2411.06907 (2024)

    2024 arXiv

  38. [46]

    K. Anai, S. Ikehara, Y. Yano, D. Okuno, and S. Takeda, Continuous-variable quantum kernel method on a programmable photonic quantum processor, Physical Review A 110, 022404 (2024)

    2024

  39. [47]

    Nokkala, R

    J. Nokkala, R. Mart´ ınez-Pe˜ na, G. L. Giorgi, V. Parigi, M. C. Soriano, and R. Zambrini, Gaussian states of continuous- variable quantum systems provide universal and versatile reservoir computing, Communications Physics 4, 53 (2021)

    2021

  40. [48]

    Mujal, R

    P. Mujal, R. Mart´ ınez-Pe˜ na, J. Nokkala, J. Garc´ ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Opportunities in quantum reservoir computing and extreme learning machines, Advanced Quantum Technologies 4, 2100027 (2021)

    2021

  41. [49]

    Xiong, G

    W. Xiong, G. Facelli, M. Sahebi, O. Agnel, T. Chotibut, S. Thanasilp, and Z. Holmes, On fundamental aspects of quantum extreme learning machines, arXiv:2312.15124 (2023)

    2023 arXiv

  42. [50]

    Presutti, L

    F. Presutti, L. G. Wright, S.-Y. Ma, T. Wang, B. K. Malia, T. Onodera, and P. L. McMahon, Highly multimode visible squeezed light with programmable spectral correlations through broadband up-conversion, arXiv:2401.06119 (2024)

    2024 arXiv

  43. [51]

    Lukoˇ seviˇ cius and H

    M. Lukoˇ seviˇ cius and H. Jaeger, Reservoir computing approaches to recurrent neural network training, Computer Science Review 3, 127 (2009)

    2009

  44. [52]

    Tanaka, T

    G. Tanaka, T. Yamane, J. B. H´ eroux, R. Nakane, N. Kanazawa, S. Takeda, H. Numata, D. Nakano, and A. Hirose, Recent advances in physical reservoir computing: A review, Neural Networks 115, 100 (2019)

    2019

  45. [53]

    Moses, H

    J. Moses, H. Suchowski, and F. X. K¨ artner, Fully efficient adiabatic frequency conversion of broadband ti: sapphire oscillator pulses, Optics Letters 37, 1589 (2012)

    2012

  46. [54]

    C. C. Wanjura and F. Marquardt, Fully nonlinear neuromorphic computing with linear wave scattering, Nature Physics 20, 1434 (2024)

    2024

  47. [55]

    F. Xia, K. Kim, Y. Eliezer, S. Han, L. Shaughnessy, S. Gigan, and H. Cao, Nonlinear optical encoding enabled by recurrent linear scattering, Nature Photonics 18, 1067 (2024)

    2024

  48. [56]

    Yildirim, N

    M. Yildirim, N. U. Dinc, I. Oguz, D. Psaltis, and C. Moser, Nonlinear processing with linear optics, Nature Photonics 18, 1076 (2024)

    2024

  49. [57]

    P. L. McMahon, Nonlinear computation with linear systems, Nature Physics 20, 1365 (2024)

    2024

  50. [58]

    Mitarai, M

    K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Physical Review A 98, 032309 (2018)

    2018

  51. [59]

    Schuld and N

    M. Schuld and N. Killoran, Quantum machine learning in feature hilbert spaces, Physical Review Letters 122, 040504 (2019)

    2019

  52. [60]

    Rosskopf, T

    M. Rosskopf, T. Mohr, and W. Els¨ aßer, Ghost polarization communication, Physical Review Applied 13, 034062 (2020)

    2020

  53. [61]

    Buitinck, G

    L. Buitinck, G. Louppe, M. Blondel, F. Pedregosa, A. Mueller, O. Grisel, V. Niculae, P. Prettenhofer, A. Gramfort, J. Grobler, et al. , Api design for machine learning software: experiences from the scikit-learn project, arXiv:1309.0238 (2013)

    2013 arXiv

  54. [62]

    Guan and M

    S. Guan and M. Loew, A novel intrinsic measure of data separability, Applied Intelligence 52, 17734 (2022)

    2022

  55. [63]

    Hillenbrand, L

    J. Hillenbrand, L. A. Getty, M. J. Clark, and K. Wheeler, Acoustic characteristics of american english vowels, The Journal of the Acoustical society of America 97, 3099 (1995)

    1995

  56. [64]

    Deng, The mnist database of handwritten digit images for machine learning research, IEEE Signal Processing Magazine 29, 141 (2012)

    L. Deng, The mnist database of handwritten digit images for machine learning research, IEEE Signal Processing Magazine 29, 141 (2012)

    2012

  57. [65]

    Bravyi, D

    S. Bravyi, D. Gosset, and R. Movassagh, Classical algorithms for quantum mean values, Nature Physics 17, 337 (2021)

    2021

  58. [66]

    B. J. Lawrie, P. D. Lett, A. M. Marino, and R. C. Pooser, Quantum sensing with squeezed light, ACS Photonics 6, 1307 (2019)

    2019

  59. [67]

    S. Khan, S. Prabhu, L. G. Wright, and P. L. McMahon, Quantum computational-sensing advantage, arXiv (2025)

    2025

  60. [68]

    M. Joly, A. Makowski, B. Courme, L. Porstendorfer, S. Wilksen, E. Charbon, C. Gies, H. Defienne, and S. Gigan, Harnessing photon indistinguishability in quantum extreme learning machines, arXiv:2505.11238 (2025)

    2025 arXiv

  61. [69]

    N. O. F. Elssied, O. Ibrahim, and A. H. Osman, A novel feature selection based on one-way anova f-test for e-mail spam classification, Research Journal of Applied Sciences, Engineering and Technology 7, 625 (2014). 20 APPENDICES Appendix A: Resources count To ensure a fair com...

    2014

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.