Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

By encoding several past inputs at once into separate qubits, a quantum extreme learning machine keeps circuit depth constant as the time series grows, turning the quadratic cost of standard quantum reservoir computing into a linear one and

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-02 21:01 UTC pith:RQ5OUXI3

load-bearing objection Real hardware numbers on a credible extension, but the 'outperforms QRC' claim only holds against a baseline the authors' own prior work superseded. the 3 major comments →

arxiv 2602.21544 v2 pith:RQ5OUXI3 submitted 2026-02-25 quant-ph

Efficient time-series prediction on NISQ devices via time-delayed quantum extreme learning machine

Mio Kawanabe , Saud Cindrak , Kathy Ludge , Jun-ichi Shirakashi , Tetsuo Shibuya , Hiroshi Imai This is my paper
classification quant-ph
keywords time-delayed quantum extreme learning machinequantum reservoir computingtime-series predictionNARMA10NISQ hardwarenoise robustnessshallow circuitsTrotterized Ising reservoir
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the time-delayed quantum extreme learning machine (TD-QELM), which encodes a fixed window of past inputs in parallel into separate qubits before a single reservoir evolution. This makes the quantum circuit identical at every timestep, so circuit depth is independent of sequence length and total cost is linear rather than quadratic. On the NARMA10 benchmark, a six-qubit TD-QELM is claimed to consistently outperform the standard restarting-protocol quantum reservoir computer, reaching roughly an order of magnitude lower error and staying stable as sequence length grows. The paper runs the comparison in noiseless simulation, in a noisy hardware model, and on a 127-qubit superconducting processor, and finds that hardware noise can even improve TD-QELM accuracy. A sympathetic reader would care because it suggests a concrete, shallow-circuit design for practical time-series learning on current noisy devices.

Core claim

On the paper's own terms, the central discovery is that the dominant cost and noise burden of quantum reservoir computing on sequential data comes from the restarting protocol, not from the reservoir dynamics. TD-QELM removes that burden by re-initializing to |00...0> at each step and encoding the current plus N-1 delayed inputs into six qubits, so each prediction uses exactly one encoding and one evolution. The measured consequence is that TD-QELM's NMSE on a real 127-qubit processor stays roughly flat at 0.86-1.58e-3 as input length M grows to 1000, while QRC's error rises to 8.61e-3 by M=500 and cannot be run further within the paper's resource limits. The paper further claims that the re

What carries the argument

The central object is the time-delayed encoding map, which loads six past inputs (s_t, s_{t-1}, s_{t-2}, s_{t-9}, s_{t-10}, s_{t-11}) into six qubits as |psi(s)> = sqrt(1-s)|0> + sqrt(s)|1>, followed by one Trotterized step of a transverse-field Ising Hamiltonian whose two-qubit couplings follow the device's connectivity. This produces a fixed, shallow feature circuit U(theta) = prod R_z(2h) prod R_XX(2J); the readout is a linear regression on Pauli-z expectations over multiplexed times. The same circuit is repeated at every timestep, so noise does not accumulate with sequence length, and the memory necessary for NARMA10 is supplied by the input-delay structure rather than by the reservoir's

Load-bearing premise

The load-bearing premise is that 'conventional quantum reservoir computing' means the restarting implementation that re-encodes the entire past history from scratch at each timestep; if the baseline is instead a constant-depth QRC variant (which the paper's own references describe), the linear-versus-quadratic and noise-accumulation advantages are no longer structural, and the performance gap may shrink.

What would settle it

A head-to-head NARMA10 run on the same 127-qubit processor comparing TD-QELM with a QRC implementation whose per-step circuit depth is held constant via a fixed memory window or periodic reset, matched for qubit count and readout dimension, would settle the matter: if the constant-depth QRC matches or beats TD-QELM's NMSE for long sequences, then the paper's attribution of QRC's failure to restarting-induced noise is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • In noiseless simulation, six-qubit TD-QELM reaches NMSE 2.73e-4 on NARMA10 at readout dimension 600, versus 1.59e-3 for the restarting QRC baseline.
  • On 127-qubit hardware, TD-QELM error stays within 0.86-1.58e-3 as M goes from 100 to 1000, while QRC degrades to 8.61e-3 at M=500 and becomes computationally impractical beyond that.
  • Total circuit executions scale as M instead of M(M+1)/2, so longer time series become feasible on NISQ devices.
  • Restricting the reservoir's memory window does not hurt; it induces nonlinear features that improve prediction, consistent with artificial-memory-restriction results.
  • Hardware noise can improve TD-QELM accuracy, so the method is positioned to exploit, not just tolerate, NISQ noise.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The complexity advantage is defined against the restarting QRC protocol; measuring against constant-depth QRC variants already proposed in the paper's own references (e.g., artificial memory restriction, periodic resets, feedback) could shrink or erase the reported gap. The authors do not make that comparison.
  • The specific delay taps (1, 2, 9, 10, 11) are chosen for NARMA10; for other tasks a principled delay-selection rule would be needed, and the paper does not provide one.
  • Because hardware noise helps in these experiments, TD-QELM could serve as a testbed for identifying which error channels assist learning, but the paper does not isolate that mechanism.
  • A matched comparison against a classical reservoir with the same delay taps and readout would clarify how much of the performance is quantum; the paper includes a linear model but not a classical echo-state or reservoir baseline.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces the time-delayed quantum extreme learning machine (TD-QELM), a QRC/QELM hybrid in which each timestep is processed by a single shallow circuit that encodes a fixed window of N delayed inputs, rather than sequentially re-encoding the entire past history. The authors compare TD-QELM against the standard 'restarting' QRC protocol on the NARMA10 task, using noiseless simulation, the FakeKawasaki noise model, and the IBM Quantum ibm_kawasaki device. They report that TD-QELM achieves lower NMSE than QRC in almost all settings and, crucially, that its error stays roughly constant with input length M while QRC degrades, attributing this to noise accumulation in the restarting protocol. The computational cost is claimed to be O(M) for TD-QELM versus O(M^2) for the restarting QRC protocol.

Significance. If the central claims are established, the paper is a useful contribution to the NISQ time-series literature: it gives a clean complexity argument (Eqs. 6 and 8), provides a straightforward implementation on real IBM hardware, and documents an interesting noise-assisted effect in which the hardware implementation outperforms the noiseless simulation. The explicit error-bar tables and the derivation in Appendix A are also strengths. However, the significance of the headline claim—'TD-QELM consistently outperforms conventional QRC'—is substantially weakened by the choice of baseline, as detailed below. The paper is technically coherent, but the claimed advantage is structural only against the restarting protocol, not against constant-depth QRC variants that already exist in the cited literature.

major comments (3)
  1. [Quantum reservoir computing, Eqs. (2)–(6); Results, Fig. 3 and Tables I–II] The paper equates 'conventional QRC' with the restarting protocol in which each timestep re-initializes the whole history, leading to O(M^2) circuit evolutions. However, the Introduction itself cites refs. [30,31,33,34] as strategies that avoid full re-initialization: artificial memory restriction (ref. [30], same group, explicitly 'solving the time-complexity problem'), repeated measurements [31], weak/projective resets [33], and feedback [34]. TD-QELM is essentially a fixed-window parallel-encoding scheme and therefore belongs to the same design class as the memory-restricted QRC of ref. [30]. No numerical comparison is run against any of these constant-depth QRC alternatives, nor against a classical TD-ELM baseline. Consequently, the complexity advantage of Eq. (8) over Eq. (6) and the noise-accumulation explanation of Fig. 3 are not established as advantages over the relevant state o
  2. [Tables II–III and Fig. 3] The statistical support for 'consistently outperforms' is weaker than the text suggests. Several comparisons have overlapping error bars: for example, at M=100 in the noiseless simulation, TD-QELM gives NMSE 2.56e-3 with standard deviation 1.48e-3, while QRC gives 3.05e-3 with standard deviation 3.68e-4; on ibm_kawasaki at M=500, QRC shows NMSE 8.61e-3 with standard deviation 3.36e-3. In addition, Table II has no QRC entries for M=1000 (and no FakeKawasaki entry at M=500), so the claim that QRC degrades with M on hardware rests on a small number of points. The authors should provide per-realization paired differences or confidence intervals and extend the hardware comparison where feasible.
  3. [Results, paragraph beginning 'Overall, these results suggest' and Conclusion] The paper states that the restricted memory 'induces rich nonlinear features... consistent with the findings reported in [30]'. Ref. [30] is the same group's previous work, so this is not independent validation. The mechanism is also not tested by ablations: the authors do not compare the chosen delay set {0,1,2,9,10,11} against other windows, nor do they demonstrate that the nonlinear unitary evolution is necessary beyond a classical linear model with the same features. Adding such an ablation would substantially strengthen the claim that TD-QELM provides a quantum benefit.
minor comments (5)
  1. [Eq. (10)] The notation is inconsistent: the vector s_t is introduced as an ordered tuple, but Eq. (10) writes components as |ψ(s_t)⟩, |ψ(s_{t-1})⟩, etc. Please use a consistent subscript notation and define τ_i explicitly.
  2. [Fig. 3 / Table II] The text says QRC 'could be executed up to 300 timesteps' with FakeKawasaki and 'up to 500 timesteps' on real hardware, but the reason given is 'computational resource limitations.' This conflates classical simulation cost with quantum-device scalability; please clarify whether the limitation is the exponential classical simulation of the density matrix or an actual hardware constraint.
  3. [Eq. (13)] The product notation in Eq. (13) is ambiguous: the second product runs over all i,j including non-edges, while the hardware Hamiltonian is defined on E2. Specify that the R_XX gates are applied only for edges in E, and define the ordering of the products.
  4. [References] Ref. [40] is only a URL to IBM Quantum Platform; please cite the specific device and the date of access, and include a reference for the FakeKawasaki noise model if one is available.
  5. [Appendix B] The standard deviations in Table III are useful, but the text in the main body refers to 'error bars' in Fig. 3 without specifying that they are min–max ranges. Clarify in the caption whether the error bars are min–max or standard deviation.

Circularity Check

0 steps flagged

No significant circularity: the reported NMSE values and the O(M) vs O(M^2) complexity counts are measured or arithmetic, and the main results do not reduce to a fitted parameter or to a self-citation chain.

full rationale

The paper's central empirical claims are direct measurements: NMSE values are computed on a held-out test split after training readout weights by least squares (Eqs. 4-5, 11), and the hardware results in Fig. 3 and Tables I-II are experimental outputs rather than predictions derived from fitted parameters. The complexity claim is an explicit arithmetic comparison of two defined protocols: the restarting QRC protocol of Eqs. (1)-(6) costs sum_{n=1}^M n = M(M+1)/2, while TD-QELM costs M (Eqs. 6, 8). That reduction is by construction of the respective protocols, not by fitting or relabeling, and it does not presuppose the performance results. The paper does cite the authors' own prior work [30] to explain why restricted memory improves nonlinear feature extraction and to note that [30] already solved the time-complexity problem by artificial memory restriction. This is a contextual or mechanistic citation, and the present hardware/simulation numbers stand independently of whether [30]'s interpretation is correct, so it is not load-bearing circularity. The more serious concern raised by the comparison baseline -- that constant-depth QRC variants already exist in [30,31,33,34] and are not used as baselines -- is a scientific criticism about whether 'conventional QRC' is representative, not a circularity in the derivation chain: the paper does not define QRC in terms of TD-QELM's target, nor does it fit QRC's degradation and then call it a prediction. Thus, while the baseline choice may weaken the generality of the performance claim, no specific equation or fitted parameter reduces to its own input, so the circularity score is low.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

TD-QELM invents no new physical entity: it composes an existing transverse-field Ising reservoir, a standard angle encoding, and a linear readout. The free parameters are reservoir settings (h, J bounds, implied T) and the task-informed delay set; the axioms are the expressive-power of the shallow Trotter circuit, the transferability of NARMA10 results, the noise-as-regularizer effect, and the feasibility of time-multiplexing within a single Trotter step.

free parameters (5)
  • External field h = 5
    Set by hand in Eq. (12); standard QRC setting, but not justified or varied, and it shapes the nonlinear feature map.
  • Coupling sampling bound for J_ij = uniform in [-5,5]
    Random couplings drawn per reservoir; bound chosen by hand; 10 realizations averaged, seeds not given.
  • Evolution time T (Trotter step) = 1 (implicit in angles 2h, 2J of Eq. 13)
    One-step Trotterization fixes T=1; not scanned, yet the nonlinear features produced by the reservoir depend on it.
  • Input delay set tau = {0,1,2,9,10,11}
    Chosen from NARMA10's known structure via Kubota's IPC analysis (refs [41,42]); task-specific and in-sample with respect to the benchmark.
  • Readout settings = N_V in {5,10,20,50,100}; N_shots=8192; split 10/70/20
    Experimental settings; N_V is scanned in Table I with no reported selection rule; split is conventional.
axioms (5)
  • domain assumption The 1-step Trotterized TFI reservoir U(theta) (Eq. 13) with h=5, J in [-5,5] provides a sufficiently expressive, non-concentrating nonlinear feature map.
    Ref [39] is invoked to justify avoiding random circuits, but no concentration or expressivity metric is computed for this specific circuit.
  • ad hoc to paper Memory restriction (a fixed 6-input window) produces richer readout features than full reservoir memory.
    Asserted in Results as 'consistent with the findings reported in [30]' (a same-group prior paper); not derived here.
  • domain assumption NARMA10 is a representative benchmark whose results transfer to general time-series tasks.
    Supports the 'practical and scalable framework' claim in the abstract; only one task is tested.
  • domain assumption Hardware noise on ibm_kawasaki acts as a beneficial regularizer for TD-QELM.
    Borrowed as a known effect from refs [10,24,26,28]; reported here but not controlled for drift or calibration state.
  • ad hoc to paper Time-multiplexed readouts at N_V times are realizable within a single one-step Trotter circuit.
    Methods do not specify how N_V in {5,...,100} mid-circuit readouts are extracted from a circuit with roughly fifteen two-qubit gates, yet Table I depends on it.

pith-pipeline@v1.3.0-alltime-deepseek · 10383 in / 30149 out tokens · 251668 ms · 2026-08-02T21:01:47.659438+00:00 · methodology

0 comments
read the original abstract

We proposed a time-delayed quantum extreme learning machine (TD-QELM) for efficient time-series prediction on noisy intermediate-scale quantum (NISQ) devices. By encoding multiple past inputs simultaneously, TD-QELM achieves shallow circuit depth independent of sequence length, thereby, mitigating noise accumulation and reducing computational complexity. Experiments using the NARMA benchmark on both noiseless simulations and IBM's 127-qubit processor demonstrate that TD-QELM consistently outperforms conventional quantum reservoir computing in prediction accuracy and noise robustness. These results highlight TD-QELM as a practical and scalable framework for time-series learning on current NISQ hardware.

Figures

Figures reproduced from arXiv: 2602.21544 by Hiroshi Imai, Jun-ichi Shirakashi, Kathy Ludge, Mio Kawanabe, Saud Cindrak, Tetsuo Shibuya.

Figure 1
Figure 1. Figure 1: FIG. 1. Conceptual Diagrams of QRC and TD-QELM. (a) [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Connectivity map of the qubits used in the ex [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Average NMSE of TD-QELM and QRC as a function [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

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

  1. Measurement-enabled online quantum processing with amplitude encoding

    quant-ph 2026-06 unverdicted novelty 6.0

    A new protocol for online amplitude-encoded quantum reservoir computing is proposed that uses mid-circuit measurement and reset to implement partial-trace dynamics and indirect measurements for observables.

Reference graph

Works this paper leans on

48 extracted references · 5 linked inside Pith · cited by 1 Pith paper

  1. [1]

    M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, Quantum Computation as Geometry, Science311, 1133 (2006)

    2006

  2. [2]

    AbuGhanem, IBM quantum computers: evolution, performance, and future directions, J

    M. AbuGhanem, IBM quantum computers: evolution, performance, and future directions, J. Supercomput81, 687 (2025)

    2025

  3. [3]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    2018

  4. [4]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brand˜ ao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, 6 B. Foxen, A. Fowler,et al., Quantum supremacy using a programmable superconducting processor, Nature574, 505 (2019)

    2019

  5. [5]

    Schuld, I

    M. Schuld, I. Sinayskiy, and F. Petruccione, An introduc- tion to quantum machine learning, Contemp. Phys.56, 172 (2015)

    2015

  6. [6]

    Biamonte, P

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Na- ture549, 195 (2017)

    2017

  7. [7]

    Cerezo, G

    M. Cerezo, G. Verdon, H. Huang, L. Cincio, and P. J. Coles, Challenges and opportunities in quantum machine learning, Nat. Comput. Sci.2, 567 (2022)

    2022

  8. [8]

    Fujii and K

    K. Fujii and K. Nakajima, Harnessing disordered- ensemble quantum dynamics for machine learning, Phys. Rev. Applied8, 024030 (2017)

    2017

  9. [9]

    J. Chen, H. I. Nurdin, and N. Yamamoto, Temporal in- formation processing on noisy quantum computers, Phys. Rev. Applied14, 024065 (2020)

    2020

  10. [10]

    Suzuki, Q

    Y. Suzuki, Q. Gao, K. C. Pradel, K. Yasuoka, and N. Ya- mamoto, Natural quantum reservoir computing for tem- poral information processing, Sci. Rep.12, 1353 (2022)

    2022

  11. [11]

    Nakajima, K

    K. Nakajima, K. Fujii, M. Negoro, K. Mitarai, and M. Kitagawa, Boosting computational power through spatial multiplexing in quantum reservoir computing, Phys. Rev. Applied11, 034021 (2019)

    2019

  12. [12]

    Garcia-Beni, G

    J. Garcia-Beni, G. L. Giorgi, M. C. Soriano, and R. Zam- brini, Scalable photonic platform for real-time quan- tum reservoir computing, Phys. Rev. Applied20, 014051 (2023)

    2023

  13. [13]

    Mujal, R

    P. Mujal, R. Martinez-Pena, J. Nokkala, J. Garcia-Beni, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Oppor- tunities in quantum reservoir computing and extreme learning machines, Adv. Quantum Technol.4, 2100027 (2021)

    2021

  14. [14]

    A. H. Abbas, H. Abdel-Ghani, and I. S. Maksymov, Clas- sical and quantum physical reservoir computing for on- board artificial intelligence systems: a perspective, Dy- namics4, 643 (2024)

    2024

  15. [15]

    Fujii and K

    K. Fujii and K. Nakajima, Quantum reservoir comput- ing: a reservoir approach toward quantum machine learn- ing on near-term quantum devices, inReservoir Com- puting: Theory, Physical Implementations, and Applica- tions, edited by K. Nakajima and I. Fischer (Springer Singapore, Singapore, 2021) pp. 423–450

    2021

  16. [16]

    Nakajima, Physical reservoir computing—an intro- ductory perspective, Jpn

    K. Nakajima, Physical reservoir computing—an intro- ductory perspective, Jpn. J. Appl. Phys.59, 060501 (2020)

    2020

  17. [17]

    Pfeffer, F

    P. Pfeffer, F. Heyder, and J. Schumacher, Reduced-order modeling of two-dimensional turbulent rayleigh-b´ enard flow by hybrid quantum-classical reservoir computing, Phys. Rev. Research5, 043242 (2023)

    2023

  18. [18]

    G¨ otting, S

    N. G¨ otting, S. Wilksen, A. Steinhoff, F. Lohof, and C. Gies, Connection between memory performance and optical absorption in quantum reservoir computing, Phys. Rev. Lett.135, 240403 (2025)

    2025

  19. [19]

    Vetrano, G

    M. Vetrano, G. Lo Monaco, L. Innocenti, S. Lorenzo, and G. M. Palma, State estimation with quantum ex- treme learning machines beyond the scrambling time, npj Quantum Inf11, 1 (2025)

    2025

  20. [20]

    Fake” in the legend), and a real NISQ device (ibm kawasaki, denoted as “ibm

    and at the edge of quantum chaos [21]. Furthermore, [22, 23] introduced a measure based on Krylov complex- ity, showing near-perfect correlations with data expres- sivity in QRC, thus linking computational performance with insights into complex quantum systems. Although noise is often detrimental in quantum algo- rithms, specific types of noise have been ...

    Pith/arXiv arXiv 2026

  21. [21]

    Mart ´ ınez-Pe˜ na, G

    R. Mart ´ ınez-Pe˜ na, G. L. Giorgi, J. Nokkala, M. C. So- riano, and R. Zambrini, Dynamical phase transitions in quantum reservoir computing, Phys. Rev. Lett.127, 100502 (2021)

    2021

  22. [22]

    Kobayashi and Y

    K. Kobayashi and Y. Motome, Edge of many-body quan- tum chaos in quantum reservoir computing, Phys. Rev. Lett.136, 040602 (2026)

    2026

  23. [23]

    ˇCindrak, K

    S. ˇCindrak, K. L¨ udge, and L. C. Jaurigue, From krylov complexity to observability: Capturing phase space di- mension with applications in quantum reservoir comput- ing, Phys. Rev. Research7, L042039 (2025)

    2025

  24. [24]

    ˇCindrak, L

    S. ˇCindrak, L. C. Jaurigue, and K. L¨ udge, Engineering quantum reservoirs through krylov complexity, expres- sivity, and observability, Phys. Rev. Research7, 043190 (2025)

    2025

  25. [25]

    Kubota, Y

    T. Kubota, Y. Suzuki, S. Kobayashi, Q. H. Tran, N. Ya- mamoto, and K. Nakajima, Temporal information pro- cessing induced by quantum noise, Phys. Rev. Research 5, 023057 (2023)

    2023

  26. [26]

    Domingo, G

    L. Domingo, G. Carlo, and F. Borondo, Taking advantage of noise in quantum reservoir computing, Sci. Rep.13, 8790 (2023)

    2023

  27. [27]

    Sannia, R

    A. Sannia, R. Mart ´ ınez-Pe˜ na, M. C. Soriano, G. L. Giorgi, and R. Zambrini, Dissipation as a resource for Quantum Reservoir Computing, Quantum8, 1291 (2024)

    2024

  28. [28]

    Monzani, E

    F. Monzani, E. Ricci, L. Nigro, and E. Prati, Non- unital noise in a superconducting quantum computer as a computational resource for reservoir computing, arXiv:2409.07886 (2025)

    Pith/arXiv arXiv 2025

  29. [29]

    Franceschetto, M

    G. Franceschetto, M. P lodzie´ n, M. Lewenstein, A. Ac ´ ın, and P. Mujal, Harnessing quantum back-action for time- series processing, arXiv:2411.03979 (2024)

    Pith/arXiv arXiv 2024

  30. [30]

    D. Fry, A. Deshmukh, S. Y. Chen, V. Rastunkov, and V. Markov, Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series predic- tion, Sci. Rep.13, 19326 (2023)

    2023

  31. [31]

    ˇCindrak, B

    S. ˇCindrak, B. Donvil, K. L¨ udge, and L. C. Jaurigue, Enhancing the performance of quantum reservoir com- puting and solving the time-complexity problem by arti- ficial memory restriction, Phys. Rev. Research6, 013051 (2024)

    2024

  32. [32]

    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 measure- ments on superconducting devices, arXiv:2310.06706 (2023)

    Pith/arXiv arXiv 2023

  33. [33]

    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, Nat. Commun.15, 7491 (2024)

    2024

  34. [34]

    Mujal, R

    P. Mujal, R. Mart ´ ınez-Pe˜ na, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Time-series quantum reservoir comput- ing with weak and projective measurements, npj Quan- tum Inf.9, 16 (2023)

    2023

  35. [35]

    Kobayashi, K

    K. Kobayashi, K. Fujii, and N. Yamamoto, Feedback- driven quantum reservoir computing for time-series anal- ysis, PRX Quantum5, 040325 (2024)

    2024

  36. [36]

    Pfeffer, F

    P. Pfeffer, F. Heyder, and J. Schumacher, Hybrid quantum-classical reservoir computing of thermal con- vection flow, Phys. Rev. Research4, 033176 (2022)

    2022

  37. [37]

    J. B. Butcher, D. Verstraeten, B. Schrauwen, C. R. Day, and P. W. Haycock, Reservoir computing and extreme learning machines for non-linear time-series data analy- sis, Neural Netw.38, 76 (2013)

    2013

  38. [38]

    Innocenti, S

    L. Innocenti, S. Lorenzo, I. Palmisano, A. Ferraro, M. Pa- ternostro, and G. M. Palma, Potential and limitations of quantum extreme learning machines, Commun. Phys.6, 1 (2023). 7

    2023

  39. [39]

    De Lorenzis, M

    A. De Lorenzis, M. P. Casado, M. P. Estarellas, N. Lo Gullo, T. Lux, F. Plastina, A. Riera, and J. Settino, Harnessing quantum extreme learning machines for im- age classification, Phys. Rev. Applied23, 044024 (2025)

    2025

  40. [40]

    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)

    Pith/arXiv arXiv 2023

  41. [41]

    IBM, IBM Quantum Platform,https:// quantum-computing.ibm.com/

  42. [42]

    Kubota, H

    T. Kubota, H. Takahashi, and K. Nakajima, Unifying framework for information processing in stochastically driven dynamical systems, Phys. Rev. Research3, 043135 (2021)

    2021

  43. [43]

    Dambre, D

    J. Dambre, D. Verstraeten, B. Schrauwen, and S. Massar, Information processing capacity of dynamical systems, Sci. Rep.2, 514 (2012)

    2012

  44. [44]

    J. Lin, F. L. Chung, and S. Wang, A fast parametric and structural transfer leaky integrator echo state network for reservoir computing, IEEE Trans. Syst. Man Cybern. Syst.54, 3257 (2024)

    2024

  45. [45]

    Picco, L

    E. Picco, L. C. Jaurigue, K. L¨ udge, and S. Massar, Effi- cient optimisation of physical reservoir computers using only a delayed input, Commun. Eng.4, 3 (2025)

    2025

  46. [46]

    Owen-Newns, L

    D. Owen-Newns, L. C. Jaurigue, J. Robertson, A. Adair, J. A. Jaurigue, K. L¨ udge, and A. Hurtado, Photonic spik- ing neural network built with a single vcsel for high-speed time series prediction, Commun. Phys.8, 110 (2025)

    2025

  47. [47]

    Kandala, A

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets, Nature549, 242 (2017)

    2017

  48. [48]

    M. N. Ivaki, A. Lazarides, and T. Ala-Nissila, Quantum reservoir computing on random regular graphs, Phys. Rev. A112, 012622 (2025). Appendix A: Relationship between error definitions In this appendix, we derive the relationship be- tween the signal-energy normalized NMSE commonly used in quantum reservoir computing and the variance- normalized NMSE frequ...

    2025