Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Experimental demonstration of enhanced quantum tomography via quantum reservoir processing

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read By learning a bosonic cavity's real dynamics from a minimal measurement set, quantum reservoir processing reconstructs continuous-variable states at over 91 percent fidelity, versus 59 percent for an idealized model.

desk verdict First QRP-based CV state reconstruction on cQED, with real promise and a simulation-dependence caveat that needs referee attention. read the letter →

arxiv 2412.11015 v2 pith:ORGQJMXC submitted 2024-12-15 quant-ph

Tanjung Krisnanda , Pengtao Song , Adrian Copetudo , Clara Yun Fontaine , Tomasz Paterek , Timothy C. H. Liew , Yvonne Y. Gao This is my paper · ORCID
classification quant-ph
keywords quantumreservoirprocessingstatetomographyprocesscontinuous-variableinformationcircuitelectrodynamicsbosonicreconstructionBayesianestimationkittenstates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports a laboratory demonstration of a machine-learning approach to tomography of a bosonic mode, the continuous-variable quantum system used in many error-correction schemes. The method, quantum reservoir processing, does not require a precise Hamiltonian model; instead it learns the actual map from input states to measurement outcomes from a small training set, then inverts that learnt map to reconstruct unknown states. On four 'kitten' states, small-amplitude superpositions of coherent states that were not part of the training data, the learnt map reconstructed states with fidelity above 91 percent, while a map computed from an idealized model of the device reached 59 percent. The authors claim this closes the gap left by device imperfections such as imperfect pulses, decoherence, and systematic measurement errors, making reliable bosonic state and process reconstruction practical on real hardware.

What carries the argument

The load-bearing object is the linear map $\beta = [\vec{V}, M]$ that connects a vectorised description $\vec{Y}$ of the input state to the measured observables $\vec{X}$ through $\vec{X} = \beta [1; \vec{Y}]$. Because the device's real dynamics together with the measurement is still a completely positive, trace-preserving process, this linear relation survives even when the idealised parity model fails; training states provide labelled pairs $(\vec{Y}, \vec{X})$ from which ridge regression fixes $\beta$ using the minimum $D^2$ states and $D^2-1$ observables. Once $\beta$ is learnt, an unknown state is estimated by inverting the relation and passing the result through Bayesian inference to obtain a physical density matrix. The displacements preceding each parity measurement are chosen by gradient descent to keep the map's condition number small, controlling how measurement noise amplifies into the reconstructed state.

What would settle it

Perform full Wigner tomography of the four kitten states immediately after preparation and compare the measured density matrices with the simulated training targets; if the average fidelity between them falls well below the reported $\approx 0.97$, the learnt map is trained on incorrect labels and the claimed reconstruction fidelities are not supported.

Watch

Extended reading notes

Core claim

The central experimental claim is that a learnt process map, fixed by ridge regression from measurement outcomes of 36 known input states, captures the true dynamics of the device's displacement-and-parity measurement better than any parameter-based model the authors could construct. Tested on four kitten states in a six-dimensional truncation, the learnt map gives reconstruction fidelities above 91 percent, while the idealised map, computed by assuming a perfect parity mapping, gives around 59 percent. The gap is traced mainly to coherent errors in the $\pi/2$-wait-$\pi/2$ Ramsey parity sequence and to qubit dephasing; because the learnt map absorbs these errors into the linear map $\beta$, it also outperforms a simulated map whose fidelity is volatile under realistic parameter uncertainty. The paper therefore claims that quantum reservoir processing turns an imperfect, partly unknown device into a usable tomography instrument for continuous-variable states.

Load-bearing premise

The load-bearing premise is that the simulated density matrices used as training labels match the states actually prepared in the device, because if the simulation misrepresents those states, the learnt map is trained on incorrect ground truth and the reported fidelities could be inflated.

Editorial extensions

If this is right

  • For a fixed truncation dimension $D$, tomography uses only $D^2$ training states and $D^2-1$ observables, the theoretical minimum, so the overhead is set by the state's dimension rather than by detailed assumptions about the device.
  • The same linear-map machinery yields process tomography of an unknown dynamics, not just state tomography, because the paper shows how to isolate the underlying dynamical map from the learnt $\beta$.
  • Because the learnt map absorbs coherent pulse errors, qubit dephasing, and systematic readout offsets, it stays accurate without re-calibrating each imperfection separately.
  • The method applies in principle to arbitrary states within the truncation dimension, not only to the kitten states used as an out-of-sample test, and the authors project that faster cavity reset could shrink the whole learning run to about a minute.

Reading between the lines

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

  • The element-wise deviation between idealised and learnt maps grows with truncation dimension, so a comparison of the two maps could serve as a diagnostic that identifies which operations drift furthest from the model.
  • The protocol should transfer to other bosonic platforms, such as mechanical, photonic, or trapped-ion systems, because it assumes only a linear displacement-like operation followed by a parity-type measurement, though the training labels would need independent validation on each platform.
  • A decisive benchmark would be to retrain the map using states characterized by an independent method, such as full Wigner tomography, in place of simulated labels; if reported fidelities survive that substitution, the method no longer depends on trust in the pulse simulation.
  • The linearity assumption ties the learnt map to the truncation dimension used in training, so scaling to larger Hilbert spaces would require retraining rather than extrapolating a low-dimensional map.
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

3 major / 5 minor

Summary. The manuscript reports an experimental demonstration of quantum reservoir processing (QRP) for continuous-variable state reconstruction on a bosonic circuit-QED platform. The method learns a linear process map from measurement outcomes of a training set of states (Fock states and superpositions) prepared by GRAPE-optimized pulses, then inverts the map and applies Bayesian inference to reconstruct four previously unseen kitten states. The authors report reconstruction fidelities greater than 91% with the learnt map, compared to about 59% with an idealized model map, and attribute the improvement to the learnt map's ability to capture physical non-idealities such as dynamical errors, decoherence, and systematic measurement errors. The manuscript also compares the learnt map with a simulated map based on a detailed Hamiltonian model and provides a full description of the experimental setup and analysis procedures.

Significance. If the central claim holds, the work demonstrates a practical and resource-efficient QRP-based tomography scheme for bosonic systems using minimal measurements and a single qubit-cavity device. The manuscript has notable strengths: the learnt map is tested on out-of-sample states not used in training; bootstrap error bars are reported; the data and code are publicly available on GitHub; and the comparison against both an idealized map and a detailed simulated map provides context for the improvement. The protocol uses the theoretical minimum number of observables, which is valuable for scalability. However, the central validation is weakened by the fact that both the training labels and the test targets are obtained from GRAPE simulations of state preparation rather than from an independent experimental characterization, making the reported fidelities potentially sensitive to common-mode simulation error.

major comments (3)
  1. [Results, 'Quantum process reconstruction' and Fig. 5a] The training set {Y_n(rho_n), X_n} and the test targets rho_± and rho_y± are both obtained from GRAPE simulations of the state preparation, rather than from an independent characterization of the actually prepared states. The reported fidelities therefore measure agreement with the simulated states. If the real prepared states differ systematically from the simulation (e.g., due to pulse distortions, calibration errors, or unmodelled Hamiltonian terms), ridge regression can absorb part of that preparation discrepancy into the learnt map, and the claimed >91% fidelity would be inflated relative to the true physical states. The statement in the text that the simulated density matrices are close to the ideal states (average fidelity ≈0.97) does not establish that the simulation is close to the experimental states. The authors should add an independent validation of the prepared states (e.g., Wigner tomography or a second tomographic method), or otherwise demonstrate the simulation's accuracy, before the main claim that the map captures the device's true imperfect dynamics can be accepted.
  2. [Fig. 4 and Eq. (2)] The observable MSE plotted in Fig. 4 is computed with the same simulated Y vectors for both the idealised and learnt maps. Because both the training and test Y are simulation-derived, a systematic preparation error would appear as a common-mode bias in this metric. The lower MSE for the learnt map could reflect the map's ability to reproduce the simulated coordinates rather than the true physical process, so this comparison cannot separate preparation errors from dynamical errors. The text's claim that the learning protocol addresses all imperfections except random measurement errors is therefore not fully supported by the presented data.
  3. [Fig. 5a and Appendix 'Simulated map'] The simulated-map comparison does not break the common-mode dependence. The blue shaded region in Fig. 5a is generated from a Hamiltonian model and is evaluated against the same GRAPE-simulated kitten-state targets. While the volatility of the simulated map under parameter perturbations is a useful sanity check, it does not validate the learnt map against an independently known ground truth. The conclusion that 'the learnt map achieves reconstruction fidelities comparable to the best case scenarios of the simulated maps' is conditional on the simulation model being accurate; the authors should either provide an independent measurement of the prepared states or clearly state that the reported fidelities are relative to the simulated states in both the main text and the abstract.
minor comments (5)
  1. [Appendix 'Learning with ridge regression', Eq. (5)] The regularization coefficient ν is described as 'selected to optimize the balance between overfitting and underfitting from noisy data', but no value or selection procedure is given. If ν is tuned on the test states, this would introduce circularity; if it is chosen by cross-validation on the training data, that procedure should be described explicitly.
  2. [Fig. 3 and surrounding text] The definition of the element-wise MSE is presented ambiguously: the sentence 'averaged over all D^4 - D^2 elements' with the displayed denominator D^2(D^2 - 1) is confusing because these expressions are not obviously equal. Please clarify the normalization used in Fig. 3a.
  3. [Main text, 'Implementation in cQED'] The abstract and introduction state that the scheme does not require precise control over the quantum system, but the protocol relies on GRAPE-optimized 2 µs state-preparation pulses and precisely timed displacement and Ramsey sequences. This apparent tension should be addressed in the introduction to avoid overstating the relaxation of control requirements.
  4. [Results, 'Quantum state reconstruction'] The text states that the simulated density matrices for the training set are close to ideal with fidelity ≈0.97, but the corresponding fidelity for the test kitten states is not reported. Please report the simulated-to-ideal fidelities for the four test states, since they are the targets in Eq. (3).
  5. [Throughout] The term 'true dynamical process' and 'accurate process map' are used in the conclusion, but given the simulation-based validation, these claims are stronger than what the data establish. Please soften the wording or add the caveat about simulation-dependent validation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the learnt map is trained on measured observables with simulated state labels and tested on distinct kitten states, so the reported fidelities are empirical rather than fitted; the main caveat is common-mode simulation dependence, which is a robustness concern, not a circular reduction.

full rationale

The derivation chain is self-contained. The learnt map β_L is obtained by ridge regression, β_L = X Y^T (Y Y^T + ν I)^-1 (Eq. 5), from measured observables X_n and state-parameter vectors Y_n; the test kitten states are explicitly not part of the training set, and their measured observables are new experimental data. Thus the claim that the learnt map outperforms the idealised map is not a fitted prediction reducible to the training inputs. The idealised map β_I is computed from the assumed perfect parity and displacement model (Eqs. 6-8), so the comparison is a genuine empirical benchmark. The simulated-map comparison in Fig. 5a is an auxiliary consistency check, not the source of the learnt map. The main weakness is model dependence in the labels: the paper states that the training set uses "the density matrix simulated from GRAPE pulses taking into account decoherence" and that test states "simulated from GRAPE pulses are denoted ρ_± and ρ_y±"; fidelities are therefore computed against simulated target states rather than independently characterized preparation. If the GRAPE simulation is biased, the learnt map may absorb preparation errors and the reported fidelities could be inflated. This is an external-validity caveat, not a circularity, because the map's outputs are not equal to its inputs by construction and the good test performance is an empirical outcome. Several foundational references are self-citations (e.g., Refs. [18], [27], [51], [54]), but they supply background, prior proposals, and the standard linear-response formalism; the paper provides data and code and does not invoke any uniqueness theorem from those works to rule out alternatives. Accordingly, no step in the derivation reduces to its own input, and the circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard linear-inversion tomography assumptions and on the accuracy of GRAPE simulations used as ground truth for training states. No new physical entities are introduced; the method uses a conventional transmon-cavity cQED system.

free parameters (3)
  • Ridge regularization coefficient nu = not stated
    Chosen to balance overfitting and underfitting in Eq. (5); affects the learnt map but is not fitted to the test-state fidelities.
  • Displacement amplitudes {alpha_k} = optimized per truncation dimension D via gradient descent
    Selected to minimize the condition number of the idealized inversion matrix M; a protocol design choice, not fitted to the reported reconstruction results.
  • Bayesian inference hyperparameters (alpha=1, sigma=1/N, MCMC samples 2^10, thinning 2^7) = as listed in Appendix
    Settings for the pseudo-likelihood BME estimator from Ref [63]; standard values, not fitted to the central claim.
assumptions (4)
  • domain assumption The device dynamics, including all imperfections, can be modeled as a CPTP map, preserving the linear relation X = beta [1;Y].
    Used in 'The General Protocol' and Appendix 'The process tomography' to justify learning a linear map from measurements.
  • domain assumption Truncating the bosonic Hilbert space to dimension D=6 contains both the prepared states and the dynamics.
    The kitten states are stated to be well contained within D=6; truncation is required because the full Hilbert space is infinite.
  • domain assumption GRAPE-simulated density matrices of the training states accurately describe the states actually prepared in the experiment.
    Training labels are computed from simulated rho_n; the simulation is stated to have average fidelity 0.97 to ideal states, but no independent experimental tomography validates it.
  • standard math The D^2-1 displaced parity measurements provide informationally complete data, so M is invertible.
    Based on the completeness condition det(M^dagger M) != 0 and the minimum measurement count for D-dimensional states.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Experimental demonstration of enhanced quantum tomography via quantum reservoir processing." pith.science (2026). https://pith.science/paper/ORGQJMXC

@misc{pith2026241211015,
  author       = {Pith},
  title        = {Pith review of: Experimental demonstration of enhanced quantum tomography via quantum reservoir processing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ORGQJMXC}},
  note         = {Machine review of arXiv:2412.11015}
}
read the original abstract

Quantum machine learning is a rapidly advancing discipline that leverages the features of quantum mechanics to enhance the performance of computational tasks. Quantum reservoir processing, which allows efficient optimization of a single output layer without precise control over the quantum system, stands out as one of the most versatile and practical quantum machine learning techniques. Here we experimentally demonstrate a quantum reservoir processing approach for continuous-variable state reconstruction on a bosonic circuit quantum electrodynamics platform. The scheme learns the true dynamical process through a minimum set of measurement outcomes of a known set of initial states. We show that the map learnt this way achieves high reconstruction fidelity for several test states, offering significantly enhanced performance over using a map calculated based on an idealised model of the system. This is due to a key feature of reservoir processing which accurately accounts for physical non-idealities such as decoherence, spurious dynamics, and systematic errors. Our results present a valuable tool for robust bosonic state and process reconstruction, concretely demonstrating the power of quantum reservoir processing in enhancing real-world applications.

Figures

Figures reproduced from arXiv: 2412.11015 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: b to illustrate the performance of the learnt and idealised maps. We note that, in general, the learnt map significantly outperforms the idealised map due to the capability of QRP to accurately account for complex dynamics in the system. While the simulated map offers …
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Near-term Application Engineering Challenges in Emerging Superconducting Qudit Processors

    quant-ph 2025-06 conditional novelty 2.0 of 10

    A review identifying near-term application opportunities and hardware engineering challenges for transmon-cavity qudit processors, with no new experimental or theoretical result.

Reference graph

Works this paper leans on

63 extracted references · 60 canonical work pages · cited by 1 Pith paper

  1. [1]

    A practical guide to applying echo state networks,

    Mantas Lukoˇ seviˇ cius, “A practical guide to applying echo state networks,” inNeural Networks: Tricks of the Trade: Second Edition(Springer, 2012) pp. 659–686

    work page 2012

  2. [2]

    Parallel photonic information process- ing at gigabyte per second data rates using transient states,

    Daniel Brunner, Miguel C Soriano, Claudio R Mirasso, and Ingo Fischer, “Parallel photonic information process- ing at gigabyte per second data rates using transient states,” Nature Communications4, 1364 (2013)

    work page 2013

  3. [3]

    Experimental demonstration of reservoir computing on a silicon photonics chip,

    Kristof Vandoorne, Pauline Mechet, Thomas Van Vaerenbergh, Martin Fiers, Geert Morthier, David Verstraeten, Benjamin Schrauwen, Joni Dambre, and Peter Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nature Communications5, 3541 (2014)

    work page 2014

  4. [4]

    High-speed photonic reservoir com- puting using a time-delay-based architecture: Million words per second classification,

    Laurent Larger, Antonio Bayl´ on-Fuentes, Romain Mar- tinenghi, Vladimir S Udaltsov, Yanne K Chembo, and Maxime Jacquot, “High-speed photonic reservoir com- puting using a time-delay-based architecture: Million words per second classification,” Physical Review X7, 011015 (2017)

    work page 2017

  5. [5]

    Harnessing nonlinear- ity: Predicting chaotic systems and saving energy in wire- less communication,

    Herbert Jaeger and Harald Haas, “Harnessing nonlinear- ity: Predicting chaotic systems and saving energy in wire- less communication,” Science304, 78–80 (2004)

    work page 2004

  6. [6]

    Model-free prediction of large spatiotemporally chaotic systems from data: A reser- voir computing approach,

    Jaideep Pathak, Brian Hunt, Michelle Girvan, Zhixin Lu, and Edward Ott, “Model-free prediction of large spatiotemporally chaotic systems from data: A reser- voir computing approach,” Physical Review Letters120, 024102 (2018)

    work page 2018

  7. [7]

    Large-scale optical reservoir computing for spatiotemporal chaotic systems prediction,

    Mushegh Rafayelyan, Jonathan Dong, Yongqi Tan, Flo- rent Krzakala, and Sylvain Gigan, “Large-scale optical reservoir computing for spatiotemporal chaotic systems prediction,” Physical Review X10, 041037 (2020)

    work page 2020

  8. [8]

    Information processing via physical soft body,

    Kohei Nakajima, Helmut Hauser, Tao Li, and Rolf Pfeifer, “Information processing via physical soft body,” Scientific reports5, 10487 (2015)

    work page 2015

Show all 63 references
  1. [9]

    Design and anal- ysis of a neuromemristive reservoir computing architec- ture for biosignal processing,

    Dhireesha Kudithipudi, Qutaiba Saleh, Cory Merkel, James Thesing, and Bryant Wysocki, “Design and anal- ysis of a neuromemristive reservoir computing architec- ture for biosignal processing,” Frontiers in Neuroscience 9, 502 (2016)

    2016

  2. [10]

    Reservoir computing using dynamic memristors for temporal information pro- cessing,

    Chao Du, Fuxi Cai, Mohammed A Zidan, Wen Ma, Se- ung Hwan Lee, and Wei D Lu, “Reservoir computing using dynamic memristors for temporal information pro- cessing,” Nature Communications8, 2204 (2017)

    2017

  3. [11]

    Artificial neural network (ann) to spiking neural network (snn) converters based on diffusive memristors,

    Rivu Midya, Zhongrui Wang, Shiva Asapu, Saumil Joshi, Yunning Li, Ye Zhuo, Wenhao Song, Hao Jiang, Navnidhi Upadhay, Mingyi Rao,et al., “Artificial neural network (ann) to spiking neural network (snn) converters based on diffusive memristors,” Advanced Electronic Materials 5, ...

    2019

  4. [12]

    Physical reservoir com- puting with origami and its application to robotic crawl- ing,

    Priyanka Bhovad and Suyi Li, “Physical reservoir com- puting with origami and its application to robotic crawl- ing,” Scientific Reports11, 13002 (2021)

    2021

  5. [13]

    Reservoir com- puting with magnetic thin films,

    Matthew Dale, David Griffin, Richard FL Evans, Sarah Jenkins, Simon O’keefe, Angelika Sebald, Susan Stepney, Fernando Torre, and Martin Trefzer, “Reservoir com- puting with magnetic thin films,” International Journal of Unconventional Computing19, 63 (2024)

    2024

  6. [14]

    A perspective on physical reservoir computing with nanomagnetic de- vices,

    Dan A Allwood, Matthew OA Ellis, David Griffin, Thomas J Hayward, Luca Manneschi, Mohammad F Musameh, Simon O’Keefe, Susan Stepney, Charles Swindells, Martin A Trefzer,et al., “A perspective on physical reservoir computing with nanomagnetic de- vices,” Applied Physics Letters1...

    2023

  7. [15]

    Polaritonic neuromorphic computing out- performs linear classifiers,

    Dario Ballarini, Antonio Gianfrate, Riccardo Panico, An- drzej Opala, Sanjib Ghosh, Lorenzo Dominici, Vincenzo Ardizzone, Milena De Giorgi, Giovanni Lerario, Giuseppe Gigli,et al., “Polaritonic neuromorphic computing out- performs linear classifiers,” Nano Letters20, 3506–3512 (2020)

    2020

  8. [16]

    Neuromorphic binarized polariton networks,

    Rafa l Mirek, Andrzej Opala, Paolo Comaron, Magdalena Furman, Mateusz Kr´ ol, Krzysztof Tyszka, Bart lomiej Seredy´ nski, Dario Ballarini, Daniele Sanvitto, Timo- thy CH Liew,et al., “Neuromorphic binarized polariton networks,” Nano Letters21, 3715–3720 (2021)

    2021

  9. [17]

    Harnessing disordered-ensemble quantum dynamics for machine learning,

    Keisuke Fujii and Kohei Nakajima, “Harnessing disordered-ensemble quantum dynamics for machine learning,” Physical Review Applied8, 024030 (2017)

    2017

  10. [18]

    Quantum reservoir processing,

    Sanjib Ghosh, Andrzej Opala, Micha l Matuszewski, Tomasz Paterek, and Timothy CH Liew, “Quantum reservoir processing,” npj Quantum Information5, 35 (2019)

    2019

  11. [19]

    Opportunities in quantum reser- voir computing and extreme learning machines,

    Pere Mujal, Rodrigo Mart ´ ınez-Pe˜ na, Johannes Nokkala, Jorge Garc ´ ıa-Beni, Gian Luca Giorgi, Miguel C Soriano, and Roberta Zambrini, “Opportunities in quantum reser- voir computing and extreme learning machines,” Ad- vanced Quantum Technologies4, 2100027 (2021)

    2021

  12. [20]

    Quantum reservoir computing: a reservoir approach toward quantum ma- chine learning on near-term quantum devices,

    Keisuke Fujii and Kohei Nakajima, “Quantum reservoir computing: a reservoir approach toward quantum ma- chine learning on near-term quantum devices,” Reservoir Computing: Theory, Physical Implementations, and Ap- plications , 423–450 (2021)

    2021

  13. [21]

    Dy- namical phase transitions in quantum reservoir comput- ing,

    Rodrigo Mart ´ ınez-Pe˜ na, Gian Luca Giorgi, Johannes Nokkala, Miguel C Soriano, and Roberta Zambrini, “Dy- namical phase transitions in quantum reservoir comput- ing,” Physical Review Letters127, 100502 (2021)

    2021

  14. [22]

    Potential and limitations of quantum ex- treme learning machines,

    Luca Innocenti, Salvatore Lorenzo, Ivan Palmisano, Alessandro Ferraro, Mauro Paternostro, and G Mas- 11 simo Palma, “Potential and limitations of quantum ex- treme learning machines,” Communications Physics6, 118 (2023)

    2023

  15. [23]

    State esti- mation with quantum extreme learning machines beyond the scrambling time,

    Marco Vetrano, Gabriele Lo Monaco, Luca Innocenti, Salvatore Lorenzo, and G Massimo Palma, “State esti- mation with quantum extreme learning machines beyond the scrambling time,” npj Quantum Information11, 20 (2025)

    2025

  16. [24]

    Superpolyno- mial quantum enhancement in polaritonic neuromorphic computing,

    Huawen Xu, Tanjung Krisnanda, Wouter Verstraelen, Timothy CH Liew, and Sanjib Ghosh, “Superpolyno- mial quantum enhancement in polaritonic neuromorphic computing,” Physical Review B103, 195302 (2021)

    2021

  17. [25]

    Optimizing a quantum reservoir computer for time se- ries prediction,

    Aki Kutvonen, Keisuke Fujii, and Takahiro Sagawa, “Optimizing a quantum reservoir computer for time se- ries prediction,” Scientific Reports10, 14687 (2020)

    2020

  18. [26]

    Time-series quantum reservoir computing with weak and projective measurements,

    Pere Mujal, Rodrigo Mart ´ ınez-Pe˜ na, Gian Luca Giorgi, Miguel C Soriano, and Roberta Zambrini, “Time-series quantum reservoir computing with weak and projective measurements,” npj Quantum Information9, 16 (2023)

    2023

  19. [27]

    Reconstruct- ing quantum states with quantum reservoir networks,

    Sanjib Ghosh, Andrzej Opala, Micha l Matuszewski, Tomasz Paterek, and Timothy CH Liew, “Reconstruct- ing quantum states with quantum reservoir networks,” IEEE Transactions on Neural Networks and Learning Systems32, 3148–3155 (2020)

    2020

  20. [28]

    Reservoir computing approach to quantum state measurement,

    Gerasimos Angelatos, Saeed A Khan, and Hakan E T¨ ureci, “Reservoir computing approach to quantum state measurement,” Physical Review X11, 041062 (2021)

    2021

  21. [29]

    Phase mea- surement beyond the standard quantum limit using a quantum neuromorphic platform,

    Tanjung Krisnanda, Sanjib Ghosh, Tomasz Paterek, Wies law Laskowski, and Timothy CH Liew, “Phase mea- surement beyond the standard quantum limit using a quantum neuromorphic platform,” Physical Review Ap- plied18, 034011 (2022)

    2022

  22. [30]

    Quantum neuromorphic platform for quantum state preparation,

    Sanjib Ghosh, Tomasz Paterek, and Timothy CH Liew, “Quantum neuromorphic platform for quantum state preparation,” Physical Review Letters123, 260404 (2019)

    2019

  23. [31]

    Dy- namical learning of a photonics quantum-state engi- neering process,

    Alessia Suprano, Danilo Zia, Emanuele Polino, Taira Giordani, Luca Innocenti, Alessandro Ferraro, Mauro Pa- ternostro, Nicol` o Spagnolo, and Fabio Sciarrino, “Dy- namical learning of a photonics quantum-state engi- neering process,” Advanced Photonics3, 066002–066002 (2021)

    2021

  24. [32]

    Realising and compressing quantum circuits with quantum reservoir computing,

    Sanjib Ghosh, Tanjung Krisnanda, Tomasz Paterek, and Timothy CH Liew, “Realising and compressing quantum circuits with quantum reservoir computing,” Communi- cations Physics4, 105 (2021)

    2021

  25. [33]

    Gaussian states of continuous-variable quan- tum systems provide universal and versatile reservoir computing,

    Johannes Nokkala, Rodrigo Mart ´ ınez-Pe˜ na, Gian Luca Giorgi, Valentina Parigi, Miguel C Soriano, and Roberta Zambrini, “Gaussian states of continuous-variable quan- tum systems provide universal and versatile reservoir computing,” Communications Physics4, 53 (2021)

    2021

  26. [34]

    Machine learning with controllable quantum dynamics of a nuclear spin ensemble in a solid,

    Makoto Negoro, Kosuke Mitarai, Keisuke Fujii, Kohei Nakajima, and Masahiro Kitagawa, “Machine learning with controllable quantum dynamics of a nuclear spin ensemble in a solid,” arXiv:1806.10910 (2018)

    2018 arXiv

  27. [35]

    Quantum reservoir computing implementation on co- herently coupled quantum oscillators,

    Julien Dudas, Baptiste Carles, Erwan Plouet, Frank Al- ice Mizrahi, Julie Grollier, and Danijela Markovi´ c, “Quantum reservoir computing implementation on co- herently coupled quantum oscillators,” npj Quantum In- formation9, 64 (2023)

    2023

  28. [36]

    Experimental property reconstruction in a pho- tonic quantum extreme learning machine,

    Alessia Suprano, Danilo Zia, Luca Innocenti, Salvatore Lorenzo, Valeria Cimini, Taira Giordani, Ivan Palmisano, Emanuele Polino, Nicol` o Spagnolo, Fabio Sciarrino, et al., “Experimental property reconstruction in a pho- tonic quantum extreme learning machine,” Physical Re- vi...

    2024

  29. [37]

    Quantum extreme learning machines for photonic entanglement witnessing,

    Danilo Zia, Luca Innocenti, Giorgio Minati, Salvatore Lorenzo, Alessia Suprano, Rosario Di Bartolo, Nicol` o Spagnolo, Taira Giordani, Valeria Cimini, G Massimo Palma,et al., “Quantum extreme learning machines for photonic entanglement witnessing,” arXiv preprint arXiv:2502.18...

    2025

  30. [38]

    Determinis- tic generation of a two-dimensional cluster state,

    Mikkel V Larsen, Xueshi Guo, Casper R Breum, Jonas S Neergaard-Nielsen, and Ulrik L Andersen, “Determinis- tic generation of a two-dimensional cluster state,” Science 366, 369–372 (2019)

    2019

  31. [39]

    Genera- tion of time-domain-multiplexed two-dimensional cluster state,

    Warit Asavanant, Yu Shiozawa, Shota Yokoyama, Baramee Charoensombutamon, Hiroki Emura, Rafael N Alexander, Shuntaro Takeda, Jun-ichi Yoshikawa, Nico- las C Menicucci, Hidehiro Yonezawa,et al., “Genera- tion of time-domain-multiplexed two-dimensional cluster state,” Science366,...

    2019

  32. [40]

    Macroscopically distinct quantum- superposition states as a bosonic code for amplitude damping,

    Paul T Cochrane, Gerard J Milburn, and William J Munro, “Macroscopically distinct quantum- superposition states as a bosonic code for amplitude damping,” Physical Review A59, 2631 (1999)

    1999

  33. [41]

    Encoding a qubit in an oscillator,

    Daniel Gottesman, Alexei Kitaev, and John Preskill, “Encoding a qubit in an oscillator,” Physical Review A 64, 012310 (2001)

    2001

  34. [42]

    New class of quantum error-correcting codes for a bosonic mode,

    Marios H Michael, Matti Silveri, RT Brierley, Victor V Albert, Juha Salmilehto, Liang Jiang, and Steven M Girvin, “New class of quantum error-correcting codes for a bosonic mode,” Physical Review X6, 031006 (2016)

    2016

  35. [43]

    Quantum error correction of a qubit encoded in grid states of an oscilla- tor,

    Philippe Campagne-Ibarcq, Alec Eickbusch, Steven Touzard, Evan Zalys-Geller, Nicholas E Frattini, Volodymyr V Sivak, Philip Reinhold, Shruti Puri, Shyam Shankar, Robert J Schoelkopf,et al., “Quantum error correction of a qubit encoded in grid states of an oscilla- tor,” Nature...

    2020

  36. [44]

    Ex- tending the lifetime of a quantum bit with error correc- tion in superconducting circuits,

    Nissim Ofek, Andrei Petrenko, Reinier Heeres, Philip Reinhold, Zaki Leghtas, Brian Vlastakis, Yehan Liu, Luigi Frunzio, Steven M Girvin, Liang Jiang,et al., “Ex- tending the lifetime of a quantum bit with error correc- tion in superconducting circuits,” Nature536, 441–445 (2016)

    2016

  37. [45]

    Beating the break-even point with a discrete-variable-encoded logical qubit,

    Zhongchu Ni, Sai Li, Xiaowei Deng, Yanyan Cai, Libo Zhang, Weiting Wang, Zhen-Biao Yang, Haifeng Yu, Fei Yan, Song Liu,et al., “Beating the break-even point with a discrete-variable-encoded logical qubit,” Nature616, 56–60 (2023)

    2023

  38. [46]

    Real-time quantum error correction beyond break-even,

    Volodymyr V Sivak, Alec Eickbusch, Baptiste Royer, Shraddha Singh, Ioannis Tsioutsios, Suhas Ganjam, Alessandro Miano, BL Brock, AZ Ding, Luigi Frun- zio,et al., “Real-time quantum error correction beyond break-even,” Nature616, 50–55 (2023)

    2023

  39. [47]

    Quantitative tomography for continu- ous variable quantum systems,

    Olivier Landon-Cardinal, Luke CG Govia, and Aashish A Clerk, “Quantitative tomography for continu- ous variable quantum systems,” Physical Review Letters 120, 090501 (2018)

    2018

  40. [48]

    Effi- cient multimode Wigner tomography,

    Kevin He, Ming Yuan, Yat Wong, Srivatsan Chakram, Alireza Seif, Liang Jiang, and David I Schuster, “Effi- cient multimode Wigner tomography,” Nature Commu- nications15, 4138 (2024)

    2024

  41. [49]

    Mul- timode photon blockade,

    Srivatsan Chakram, Kevin He, Akash V Dixit, Andrew E Oriani, Ravi K Naik, Nelson Leung, Hyeokshin Kwon, Wen-Long Ma, Liang Jiang, and David I Schuster, “Mul- timode photon blockade,” Nature Physics18, 879–884 (2022). 12

    2022

  42. [50]

    Optimized tomography of continuous variable systems using excitation counting,

    Chao Shen, Reinier W Heeres, Philip Reinhold, Luyao Jiang, Yi-Kai Liu, Robert J Schoelkopf, and Liang Jiang, “Optimized tomography of continuous variable systems using excitation counting,” Physical Review A 94, 052327 (2016)

    2016

  43. [51]

    Demonstrating efficient and robust bosonic state reconstruction via optimized excitation counting,

    Tanjung Krisnanda, Clara Yun Fontaine, Adrian Copetudo, Pengtao Song, Kai Xiang Lee, Ni-Ni Huang, Fernando Valadares, Timothy CH Liew, and Yvonne Y Gao, “Demonstrating efficient and robust bosonic state reconstruction via optimized excitation counting,” PRX Quantum6, 010303 (2025)

    2025

  44. [52]

    Experimental neural network enhanced quantum tomography,

    Adriano Macarone Palmieri, Egor Kovlakov, Federico Bianchi, Dmitry Yudin, Stanislav Straupe, Jacob D Bia- monte, and Sergei Kulik, “Experimental neural network enhanced quantum tomography,” npj Quantum Informa- tion6, 20 (2020)

    2020

  45. [53]

    Experimental quantum homodyne tomography via machine learning,

    Egor S Tiunov, VV Tiunova, Alexander E Ulanov, AI Lvovsky, and Aleksey K Fedorov, “Experimental quantum homodyne tomography via machine learning,” Optica7, 448–454 (2020)

    2020

  46. [54]

    Tomographic completeness and ro- bustness of quantum reservoir networks,

    Tanjung Krisnanda, Huawen Xu, Sanjib Ghosh, and Timothy CH Liew, “Tomographic completeness and ro- bustness of quantum reservoir networks,” Physical Re- view A107, 042402 (2023)

    2023

  47. [55]

    Implementing a universal gate set on a log- ical qubit encoded in an oscillator,

    Reinier W Heeres, Philip Reinhold, Nissim Ofek, Luigi Frunzio, Liang Jiang, Michel H Devoret, and Robert J Schoelkopf, “Implementing a universal gate set on a log- ical qubit encoded in an oscillator,” Nature Communica- tions8, 94 (2017)

    2017

  48. [56]

    Method for direct measurement of the Wigner function in cavity qed and ion traps,

    LG Lutterbach and L Davidovich, “Method for direct measurement of the Wigner function in cavity qed and ion traps,” Physical Review Letters78, 2547 (1997)

    1997

  49. [57]

    Direct measurement of the Wigner function of a one-photon fock state in a cav- ity,

    Patrice Bertet, Alexia Auffeves, Paolo Maioli, Stefano Osnaghi, Tristan Meunier, Michel Brune, Jean-Michel Raimond, and Serge Haroche, “Direct measurement of the Wigner function of a one-photon fock state in a cav- ity,” Physical Review Letters89, 200402 (2002)

    2002

  50. [58]

    Roger A Horn and Charles R Johnson,Matrix analysis (Cambridge University Press, 2012)

    2012

  51. [59]

    Cavity quan- tum electrodynamics for superconducting electrical cir- cuits: An architecture for quantum computation,

    Alexandre Blais, Ren-Shou Huang, Andreas Wallraff, Steven M Girvin, and R Jun Schoelkopf, “Cavity quan- tum electrodynamics for superconducting electrical cir- cuits: An architecture for quantum computation,” Phys- ical Review A69, 062320 (2004)

    2004

  52. [60]

    96 (Oxford University Press, 2014) pp

    Steven M Girvin,Circuit QED: superconducting qubits coupled to microwave photons, Vol. 96 (Oxford University Press, 2014) pp. 113–256

    2014

  53. [61]

    Optimal, reliable estimation of quantum states,

    Robin Blume-Kohout, “Optimal, reliable estimation of quantum states,” New Journal of Physics12, 043034 (2010)

    2010

  54. [62]

    How long does it take to obtain a physical density matrix?

    Lukas Knips, Christian Schwemmer, Klein. Nico, Jonas Reuter, Geza Toth, and Harald Weinfurter, “How long does it take to obtain a physical density matrix?” arXiv:1512.06866 (2015)

    2015 arXiv

  55. [63]

    A practical and efficient approach for Bayesian quantum state estimation,

    Joseph M Lukens, Kody JH Law, Ajay Jasra, and Pavel Lougovski, “A practical and efficient approach for Bayesian quantum state estimation,” New Journal of Physics22, 063038 (2020)

    2020

Pith tools

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