Connection between memory performance and optical absorption in quantum reservoir computing

Alexander Steinhoff; Christopher Gies; Frederik Lohof; Niclas G\"otting; Steffen Wilksen

REVIEW 3 major objections 5 minor 35 references

Connection between memory performance and optical absorption in quantum reservoir computing

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read A quantum reservoir's optical absorption tracks its memory capacity, with both peaking at the same dissipation.

desk verdict The absorption–memory alignment is a genuinely useful design insight for finite-shot QRC, but the abstract's 'quantitative connection' is really a qualitative, noise-regime-dependent correspondence. read the letter →

arxiv 2501.15580 v2 pith:JDC6UJIU submitted 2025-01-26 quant-ph

Niclas Götting , Steffen Wilksen , Alexander Steinhoff , Frederik Lohof , Christopher Gies This is my paper · ORCID

classification quant-ph

keywords quantumreservoircomputingshort-termmemorycapacityopticalabsorptiontransverse-fieldIsingmodelLindbladmasterequationdissipationengineeringlinearresponseopensystems

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 reservoir computers need a fading memory, and in an open quantum system that memory is supplied by dissipation. This paper claims that, for a coherently driven transverse-field Ising reservoir with tunable qubit decay, the reservoir's optical absorption spectrum is quantitatively tied to its short-term memory capacity: as the decay rate is swept, the average resonant absorption and the linear memory capacity rise, peak, and fall together, both maximizing near $\gamma\approx 1$. If true, the absorption spectrum becomes a physically measurable proxy for memory performance, turning an abstract information-theoretic benchmark into a quantity accessible in the lab. The authors show the qualitative agreement holds across coupling strengths, system sizes, and topologies, and use it to explain the known 'sweet spot' of dissipation in quantum reservoir computing.

What carries the argument

The central object is the average resonant absorption $\bar\alpha_\gamma$, obtained by computing the linear-response dipole autocorrelation spectrum (Eq. 6) at the pump frequency for each input strength $s$ and averaging over the uniform distribution of testing signals. Its partner is the linear short-term memory capacity $C_1 = \sum_{\tau=0}^{\tau_{\max}} C_1^\tau$, where each $C_1^\tau$ is the squared Pearson correlation between the reservoir readout and a delayed input (Eq. 5). Both quantities are computed from the same Gorini–Kossakowski–Sudarshan–Lindblad master equation (Eq. 3), with the qubit decay $\gamma$ as the control parameter; their shared bell shape in $\gamma$ is the paper's evidence for the connection.

What would settle it

Run the same 3-qubit reservoir at $\gamma=10^2$ with zero measurement noise and record the linear short-term memory capacity $C_1$: it stays near one while the resonant absorption $\alpha(0)$ is near zero, which directly contradicts the claim that a reservoir cannot remember what it cannot absorb; a complementary test is to compare $C_1(\gamma)$ with $\alpha_{s,\gamma}(0)$ at one fixed signal strength $s$ to see whether the peak alignment survives without averaging over $s$.

Watch

Extended reading notes

Core claim

This paper establishes that for a three-qubit transverse-field Ising reservoir driven by a coherent input and damped by identical qubit decay, the average resonant optical absorption and the linear short-term memory capacity are aligned as functions of the decay rate: both rise from negligible values near $\gamma\approx 10^{-2}$, peak near $\gamma\approx 1$, and fall to zero near $\gamma\approx 10^{2}$ (Figs. 3 and 4). The optical absorption of the reservoir thus acts as a physical proxy for its ability to remember past inputs, and the previously reported 'sweet spot' in quantum reservoir computing is explained as the dissipation regime where absorption at the pump frequency is maximal. The authors state the link as a quantitative connection between a physical metric and an information-theoretic benchmark, while noting that a formal derivation connecting the two expressions is not yet available.

Load-bearing premise

The paper assumes that the average amount of light the reservoir absorbs at the drive frequency is what determines how well it remembers past inputs, and nothing in the paper proves that link in general; the curves stop matching once measurement noise is removed, so the alignment depends on that noisy setting.

Editorial extensions

If this is right

A lab measurement of resonant absorption at the pump frequency can locate the dissipation strength where a coherent-input quantum reservoir computer has maximal linear memory, without running the full training benchmark.
Tuning qubit decay toward the absorption maximum becomes a concrete design rule for coherently driven dissipative quantum reservoirs.
The qualitative absorption–memory alignment persists for different coupling strengths, for four-qubit systems, and for all-to-all versus ring topologies (Supplementary Fig. 8).
Higher-order memory capacities show the same trend under finite shot noise, so absorption tuning may affect nonlinear information processing even though the paper focuses on the linear short-term memory capacity.

Reading between the lines

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

If the alignment is causal, absorption at the drive frequency could serve as a training-free, physics-based diagnostic for quantum reservoir computer hardware; the paper suggests but does not prove this.
The zero-shot-noise data in Supplementary Fig. 7 indicate the absorption–memory alignment is a finite-shot-noise effect: with perfect measurements, linear short-term memory survives at large $\gamma$ where absorption vanishes, so the operative link may be signal-to-noise efficiency rather than storage capacity in principle.
The same signal-averaged response logic could be applied to other input-dependent susceptibilities, such as dispersive or nonlinear response, in photonic and Rydberg reservoir platforms, where a 'response peak equals memory peak' relation would be a testable extension.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, the useful idea: the authors identify optical absorption, computed by linear response, as a physical correlate of the short-term memory capacity of a coherently driven dissipative TFIM reservoir, and show both peak at the same dissipation strength. The sweet spot in γ was known before—refs 6, 13, 20 report it—but tying it to absorption is new and practically relevant. If you are building a QRC, this gives a physical knob: maximize resonant absorption, get good memory. Second, the abstract overstates the result. 'Quantitative connection' is not what the evidence supports; the match is qualitative, visual similarity of two curves with no correlation measure. And the paper's own supplementary undercuts the causal story in the ideal limit.

The model is clean: 3-qubit TFIM, coherent input encoding, qubit decay, GKSL evolution, STMC via Pearson correlation, absorption via the normalized dipole correlation spectrum, averaged over signal strengths. The supplementary is honest in important ways: Supp. Fig. 7 shows that in the infinite-shot limit, linear STMC stays near 1 for decays up to γ=10^3, while absorption has vanished by γ=10^2. So in the noiseless case, the reservoir does remember without absorbing. The large-γ drop of STMC in Fig. 3 is a measurement-resolution effect, not a physical one. The authors include that figure but do not let it revise the abstract, and the 'cannot remember if it cannot absorb' intuition only holds once shot noise is in the picture. The small-γ side is robust, and the peak location near γ≈1 is robust, so the sweet-spot physics survives; the universal law does not.

Three soft spots, in proportion. (1) The central claim is framed as quantitative and universal, one step too strong; a correlation coefficient or scatter plot plus an explicit statement of the noise regime would fix it. (2) The signal-strength averaging is reasonable given uniform test inputs, but the comparison depends on that distribution; absorption peaks move by orders of magnitude in γ with s, so the average is doing real work. (3) The authors admit no formal connection exists—fine, but then the conclusion should not lean so hard on causal language. The citation pattern is fine; the prior sweet-spot reports are properly credited, and the generality checks across J0, system size, and topology (Supp. Fig. 8) are a genuine plus.

Who this is for: anyone in QRC or quantum ML who wants an experimentally accessible design rule, and quantum-optics people interested in the memory–response link. It deserves a serious referee, but the referee should push for a reframed, noise-regime-qualified claim and a quantitative comparison. I would send it to review, expecting major revision.

Referee Report

3 major / 5 minor

Summary. The paper considers a three-qubit transverse-field Ising model as a quantum reservoir, with coherent input injection and tunable qubit decay γ. It computes the short-term memory capacity (STMC) via the Pearson correlation of reconstructed past inputs (Eq. 5) and the resonant optical absorption via the dipole-correlation spectrum (Eq. 6). For finite shot noise (10^6 shots), both the linear STMC C1(γ) and the signal-averaged absorption ᾱγ rise near γ≈10^-2, peak near γ≈1, and fall to zero near γ≈10^2 (Figs. 3 and 4). The paper claims this reveals a quantitative connection, with maximal absorption coinciding with optimal memory, and interprets it as 'cannot remember if it cannot absorb.' The supplementary material shows that in the ideal infinite-shot limit, the linear STMC remains near unity at large γ while absorption vanishes.

Significance. If the connection were established, it would offer an experimentally measurable physical proxy for QRC memory performance and a design principle for dissipation engineering. The paper has real strengths: no parameters are fitted to align the curves; the authors explicitly acknowledge that no formal connection between Eq. (6) and Eq. (5) is established; and the supplementary checks across coupling strengths, system sizes, and topologies (Supp. Fig. 8) indicate that the qualitative sweet spot is not a single-model accident. However, the central claim as stated in the abstract and conclusion is not supported by the evidence: the match is only qualitative, and the high-γ drop of STMC is a finite-shot-noise artifact rather than a reflection of the intrinsic absorption. The paper can be revised to make the claim precise and to condition it on the measurement-noise setting.

major comments (3)

[Abstract and Conclusion; Figs. 3 and 4] The abstract and conclusion state that a 'quantitative connection' is established and that 'optimal STMC aligns directly with maximal absorption,' but no quantitative measure of the alignment is provided. The main text itself describes the similarity as 'qualitatively very similar' and states that 'there exists a significant correlation' without reporting a correlation coefficient, a scatter plot of ᾱγ versus C1(γ), or error bars across the 15 random system realizations. Since both quantities are computed from the same GKSL dynamics (Eq. (3)), a quantitative comparison statistic (e.g., Pearson or Spearman correlation over the γ grid, with a permutation baseline) is needed to substantiate the claimed connection.
[Supplementary Fig. 7; Section 'Bounds of Dissipation'] The large-γ falloff of the linear STMC in Fig. 3, which is central to the claimed alignment with absorption, is not a property of the noiseless reservoir dynamics. Supplementary Fig. 7 shows that with zero shot noise the linear STMC remains at almost exactly one for γ up to 10^3, while Fig. 4 shows the average absorption vanishes by γ≈10^2. Thus the observed drop in C1 at large γ arises from the finite-shot-noise threshold and the τ_max truncation, not from a physical inability to absorb. The statement 'the system cannot possibly remember any information if it is not able to absorb it in the first place' is therefore not supported. The central claim should be explicitly conditioned on finite measurement noise, or the paper should identify why finite-shot behavior is the operative regime.
[Section 'Connection to physical reservoir properties', Eq. (6)] The comparison relies on a specific averaging of the absorption over signal strengths: ᾱγ is the uniform average of α_{s,γ}(0) over ten values of s, justified by the statement that 'the 1000 testing input signals are uniformly chosen.' This averaging is an assumption, not a derivation: the STMC is a nonlinear functional of the full input sequence and the trained output weights, and it is not shown that the uniform average of the linear-response absorption is the appropriate physical quantity. The authors should either derive this correspondence or test its robustness by, for example, computing capacities for fixed s and comparing them with α_{s,γ}(0), or by showing that the alignment is insensitive to the choice of averaging (geometric mean, weighted mean, or median).

minor comments (5)

[Section 'Bounds of Dissipation'] The word 'capcities' in the paragraph below Eq. (5) should be 'capacities'.
[Section 'Bounds of Dissipation'] The sentence 'we cut the sequence at that τ and receive the maximum delay τ_max' is awkward; 'receive' should be 'obtain'.
[Section 'Bounds of Dissipation'] The phrase 'we restrain the following discussion to the linear STMC' should use 'restrict' instead of 'restrain'.
[Figure 4 caption] The color-bar labels 'α avg' and 's =' appear truncated; the caption should clearly state that the color coding indicates the signal strength s and that the thick blue line is the average over s.
[Figure 2 caption] The caption refers to 'In light red (right axis)' but does not explicitly identify which curve corresponds to the input signal; this should be clarified.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: STMC and absorption are computed from independent definitions, with no fitted parameter forcing their alignment. The only self-citation is background and not load-bearing.

full rationale

The paper's central comparison is between the linear short-term memory capacity, obtained from the Pearson correlation in Eq. (5) applied to GKSL reservoir outputs, and the resonant optical absorption, obtained from the dipole-correlation Fourier spectrum in Eq. (6). These are distinct, independently defined quantities: neither equation is defined in terms of the other, and no parameter is fitted to make the two curves agree. The averaging of absorption over signal strengths is motivated by the uniform distribution of the testing inputs, and the removal of the elastic-scattering tail is a standard external correction, not an input-specific fit. The only self-citation ([6]) appears as background for the previously reported 'sweet-spot' behavior and is not load-bearing: the present calculations are performed fresh from the GKSL dynamics rather than imported from that citation. The paper explicitly states that a direct formal connection between Eq. (6) and Eq. (5) is not established, which is an admission of an explanatory gap but not evidence of circularity. The finite-shot-noise dependence of the STMC falloff and the infinite-shot behavior in Supplementary Fig. 7 raise concerns about the universality of the claimed alignment, but that is a robustness and correctness issue, not a circular-reasoning issue. Accordingly, no circular step can be exhibited from the paper's own equations, and the score is at the non-circular end of the scale.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard open-quantum-system and linear-response formalism plus a few simulation choices (J0, shot noise, noise threshold, signal-strength averaging). The most consequential input is the finite-shot-noise setting: without it, the STMC-absorption alignment breaks at large γ. No new physical entities are postulated.

free parameters (3)

Coupling strength J0 = 0.5
Chosen by hand; the main text states 'we set the coupling strength to J0 = 0.5 for all following calculations' (Section 2). The qualitative result is claimed to hold for J0 = 0.25 and 1.0 in the supplementary, so it is a chosen simulation parameter rather than a fitted constant.
Shot noise level (10^6 shots) = 10^6 shots
The STMC results in Fig. 3 use measurement noise corresponding to 10^6 shots. This choice is load-bearing for the large-γ alignment: with zero shot noise, linear STMC remains near unity where absorption vanishes (Supplementary Fig. 7).
STMC noise threshold C_thresh = Max over 500 random target correlations
The τ_max cutoff is determined by the largest capacity from 500 random-signal correlations. This ad hoc procedure defines the reported total capacities and affects the shape of the STMC curve.

assumptions (5)

domain assumption GKSL master equation models the reservoir dynamics with Markovian qubit decay
Eq. (3) assumes Gorini-Kossakowski-Sudarshan-Lindblad dynamics with weak, Markovian coupling to the environment, which is standard for NISQ models but not derived here.
standard math Linear response (dipole correlation) formula gives the optical absorption
Eq. (6) uses the normalized two-time dipole correlation function in the steady state, following standard Kubo-style linear response (refs 28, 29).
domain assumption Averaging absorption over signal strengths represents the mean reservoir response relevant to STMC
The authors average α_{s,γ}(0) over 10 signal strengths because the test inputs are uniformly chosen. This mapping from signal-averaged absorption to input-averaged memory is assumed, not derived.
domain assumption The constant tail of the correlation function is elastic pump scattering and can be subtracted
The delta peak at the pump frequency is attributed to Mollow elastic scattering (ref 30) and removed by subtracting the constant tail, a modeling choice shown in Fig. 5 of the supplementary.
domain assumption The dissipative reservoir reaches a unique steady state without a washout sequence
Section 2 assumes the system relaxes to a known steady state to arbitrary precision, relying on common-signal-induced synchronization (ref 23).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Connection between memory performance and optical absorption in quantum reservoir computing." pith.science (2026). https://pith.science/paper/JDC6UJIU

@misc{pith2026250115580,
  author       = {Pith},
  title        = {Pith review of: Connection between memory performance and optical absorption in quantum reservoir computing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JDC6UJIU}},
  note         = {Machine review of arXiv:2501.15580}
}

read the original abstract

The fading memory property is a key requirement for reservoir computers -- a specific type of recurrent neural network with fixed internal weights. While mostly undesired in gate-based quantum computing, dissipation due to material imperfections or coupling to the environment acts as a natural mechanism intrinsically providing fading memory to reservoir computers based on dynamical open quantum systems. In this work, we unravel a connection between the physical metric of optical absorption and the performance of quantum reservoir computers in terms of their short-term memory capacity. We establish this link by considering a coherent input encoding in conjunction with tunable qubit decay, giving precise control over the fading memory in the quantum reservoir computer. Our analysis enables us to identify a sweet-spot regime for the dissipation strength at which memory performance is maximized.

Figures

Figures reproduced from arXiv: 2501.15580 by the authors.

**Figure 2.** FIG. 2. Time evolution of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. First three degrees of the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4. Resonant absorption [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5. Absorption spectra for qubit decays [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Absorption spectra for a 3-qubit reservoir computer with a coupling strength [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7. The first three [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: FIG. 8. The [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

35 extracted references · 24 canonical work pages

[1]

J. L. Elman, Finding Structure in Time, Cognitive Science 14, 179 (1990)

work page 1990
[2]

M. I. Jordan,Serial Order: A Parallel Distributed Process- ing Approach. Technical Report, June 1985-March 1986, Tech. Rep. AD-A-173989/5/XAB; ICS-8604 (California Univ., San Diego, La Jolla (USA). Inst. for Cognitive Science, 1986)

work page 1985
[3]

Echo State

H. Jaeger, The “Echo State” Approach to Analysing and Training Recurrent Neural Networks, GMD-Report 148, German National Research Institute for Computer Science (2001)

work page 2001
[4]

Maass, T

W. Maass, T. Natschl¨ ager, and H. Markram, Real-time computing without stable states: A new framework for neural computation based on perturbations, Neural Com- putation14, 2531 (2002)

2002
[5]

Ghosh, A

S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, Reconstructing Quantum States With Quantum Reservoir Networks, IEEE Transactions on Neu- ral Networks and Learning Systems32, 3148 (2021)

work page 2021
[6]

G¨ otting, F

N. G¨ otting, F. Lohof, and C. Gies, Exploring quantumness in quantum reservoir computing, Physical Review A108, 052427 (2023)

work page 2023
[7]

M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information, 10th ed. (Cambridge Univer- sity Press, Cambridge ; New York, 2010)

work page 2010
[8]

Sugiura, R

S. Sugiura, R. Ariizumi, T. Asai, and S.-I. Azuma, Nonessentiality of Reservoir’s Fading Memory for Uni- versality of Reservoir Computing, IEEE Transactions on Neural Networks and Learning Systems35, 16801 (2024)

work page 2024

Show all 35 references

[9]

T. L. Carroll, Optimizing Memory in Reservoir Comput- ers, Chaos: An Interdisciplinary Journal of Nonlinear Science32, 023123 (2022), arXiv:2201.01605 [cs]

2022 arXiv
[10]

Fujii and K

K. Fujii and K. Nakajima, Harnessing Disordered- Ensemble Quantum Dynamics for Machine Learning, Physical Review Applied8, 024030 (2017)

2017
[11]

Mart ´ ınez-Pe˜ na, J

R. Mart ´ ınez-Pe˜ na, J. Nokkala, G. L. Giorgi, R. Zambrini, and M. C. Soriano, Information Processing Capacity of Spin-Based Quantum Reservoir Computing Systems, Cog- nitive Computation 10.1007/s12559-020-09772-y (2020)

2020 doi
[12]

Palacios, R

A. Palacios, R. Mart ´ ınez-Pe˜ na, M. C. Soriano, G. L. Giorgi, and R. Zambrini, Role of coherence in many-body Quantum Reservoir Computing, Communications Physics 7, 1 (2024)

2024
[13]

Monzani, E

F. Monzani, E. Ricci, L. Nigro, and E. Prati, Leverag- ing non-unital noise for gate-based quantum reservoir computing (2024), arXiv:2409.07886 [quant-ph]

2024 arXiv
[14]

M. L. Olivera-Atencio, L. Lamata, and J. Casado-Pascual, Benefits of Open Quantum Systems for Quantum Machine Learning, Advanced Quantum Technologies , 2300247 (2023)

2023
[15]

Sannia, R

A. Sannia, R. Mart ´ ınez-Pe˜ na, M. C. Soriano, G. L. Giorgi, and R. Zambrini, Dissipation as a resource for Quan- tum Reservoir Computing, Quantum8, 1291 (2024), arXiv:2212.12078 [quant-ph]

2024 arXiv
[16]

Domingo, G

L. Domingo, G. Carlo, and F. Borondo, Taking advan- tage of noise in quantum reservoir computing, Scientific Reports13, 8790 (2023)

2023
[17]

X. Han, Y. Zhao, and M. Small, Revisiting the memory capacity in reservoir computing of directed acyclic net- work, Chaos: An Interdisciplinary Journal of Nonlinear Science31, 033106 (2021). 6

2021
[18]

Sannia, G

A. Sannia, G. L. Giorgi, S. Longhi, and R. Zam- brini, Skin effect in quantum neural networks (2024), arXiv:2406.14112 [quant-ph]

2024 arXiv
[19]

ˇCindrak, B

S. ˇCindrak, B. Donvil, K. L¨ udge, and L. Jaurigue, Enhanc- ing the performance of quantum reservoir computing and solving the time-complexity problem by artificial memory restriction, Physical Review Research6, 013051 (2024)

2024
[20]

Kurokawa, J

Y. Kurokawa, J. Takahashi, and Y. Yamanaka, Quantum Reservoir Computing Using Bose-Einstein Condensate with Damping (2024), arXiv:2408.09577 [cond-mat]

2024 arXiv
[21]

Pfeuty and R

P. Pfeuty and R. J. Elliott, The Ising model with a trans- verse field. II. Ground state properties, Journal of Physics C: Solid State Physics4, 2370 (1971)

1971
[22]

Manzano, A short introduction to the Lindblad master equation, AIP Advances10, 025106 (2020)

D. Manzano, A short introduction to the Lindblad master equation, AIP Advances10, 025106 (2020)

2020
[23]

Inubushi, K

M. Inubushi, K. Yoshimura, Y. Ikeda, and Y. Nagasawa, On the Characteristics and Structures of Dynamical Sys- tems Suitable for Reservoir Computing, inReservoir Com- puting: Theory, Physical Implementations, and Applica- tions, edited by K. Nakajima and I. Fischer (Springer, S...

2021
[24]

Jaeger,Short Term Memory in Echo State Networks (GMD Forschungszentrum Informationstechnik, 2001)

H. Jaeger,Short Term Memory in Echo State Networks (GMD Forschungszentrum Informationstechnik, 2001)

2001
[25]

noise capacities

or the maximally well reproducible functions of the reservoir – the so-calledeigentasks[26, 27]. Here, it suffices to consider a reduced form of the IPCs, which quantifies the ability of the QRC to reproduce legendre polynomials of the input sequence up to a cer- tain degree. ...
[26]

Dambre, D

J. Dambre, D. Verstraeten, B. Schrauwen, and S. Massar, Information Processing Capacity of Dynamical Systems, Scientific Reports2, 514 (2012)

2012
[27]

F. Hu, G. Angelatos, S. A. Khan, M. Vives, E. T¨ ureci, L. Bello, G. E. Rowlands, G. J. Ribeill, and H. E. T¨ ureci, Tackling Sampling Noise in Physical Systems for Ma- chine Learning Applications: Fundamental Limits and Eigentasks, Physical Review X13, 041020 (2023)

2023
[28]

A. M. Polloreno, Limits to Reservoir Learning (2023), arXiv:2307.14474 [cs, math]

2023 arXiv
[29]

Chang and J

T.-M. Chang and J. Skinner, Non-Markovian population and phase relaxation and absorption lineshape for a two- level system strongly coupled to a harmonic quantum bath, Physica A: Statistical Mechanics and its Applications193, 483 (1993)

1993
[30]

D. A. McQuarrie,Statistical Mechanics(2000)

2000
[31]

B. R. Mollow, Power Spectrum of Light Scattered by Two-Level Systems, Physical Review188, 1969 (1969)

1969
[32]

Garc ´ ıa-Beni, G

J. Garc ´ ıa-Beni, G. L. Giorgi, M. C. Soriano, and R. Zam- brini, Scalable Photonic Platform for Real-Time Quan- tum Reservoir Computing, Physical Review Applied20, 014051 (2023)

2023
[33]

L. C. G. Govia, G. J. Ribeill, G. E. Rowlands, H. K. Krovi, and T. A. Ohki, Quantum reservoir computing with a single nonlinear oscillator, Physical Review Research3, 013077 (2021)

2021
[34]

R. A. Bravo, K. Najafi, X. Gao, and S. F. Yelin, Quantum Reservoir Computing Using Arrays of Rydberg Atoms, PRX Quantum3, 030325 (2022)

2022
[35]

Ebadi, T

S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semegh- ini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletic, and M. D. Lukin, Quantum Phases of Matter on a 256- Atom Programmable Quantum Simulator, Nature595, 227 (2021),...

2021 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

J. L. Elman, Finding Structure in Time, Cognitive Science 14, 179 (1990)

work page 1990

[2] [2]

M. I. Jordan,Serial Order: A Parallel Distributed Process- ing Approach. Technical Report, June 1985-March 1986, Tech. Rep. AD-A-173989/5/XAB; ICS-8604 (California Univ., San Diego, La Jolla (USA). Inst. for Cognitive Science, 1986)

work page 1985

[3] [3]

Echo State

H. Jaeger, The “Echo State” Approach to Analysing and Training Recurrent Neural Networks, GMD-Report 148, German National Research Institute for Computer Science (2001)

work page 2001

[4] [4]

Maass, T

W. Maass, T. Natschl¨ ager, and H. Markram, Real-time computing without stable states: A new framework for neural computation based on perturbations, Neural Com- putation14, 2531 (2002)

2002

[5] [5]

Ghosh, A

S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, Reconstructing Quantum States With Quantum Reservoir Networks, IEEE Transactions on Neu- ral Networks and Learning Systems32, 3148 (2021)

work page 2021

[6] [6]

G¨ otting, F

N. G¨ otting, F. Lohof, and C. Gies, Exploring quantumness in quantum reservoir computing, Physical Review A108, 052427 (2023)

work page 2023

[7] [7]

M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information, 10th ed. (Cambridge Univer- sity Press, Cambridge ; New York, 2010)

work page 2010

[8] [8]

Sugiura, R

S. Sugiura, R. Ariizumi, T. Asai, and S.-I. Azuma, Nonessentiality of Reservoir’s Fading Memory for Uni- versality of Reservoir Computing, IEEE Transactions on Neural Networks and Learning Systems35, 16801 (2024)

work page 2024