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arxiv: 2506.15771 · v1 · submitted 2025-06-18 · 🪐 quant-ph · cs.LG

Superconducting Qubit Readout Using Next-Generation Reservoir Computing

Robert Kent , Benjamin Lienhard , Gregory Lafyatis , Daniel J. Gauthier This is my paper

Pith reviewed 2026-05-19 08:53 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords reservoir computingsuperconducting qubitsqubit readoutcrosstalk reductionmachine learningstate discriminationfrequency multiplexing
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The pith

Next-generation reservoir computing improves superconducting qubit readout by extracting polynomial features from multiplexed signals.

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

The paper shows how next-generation reservoir computing can discriminate the states of superconducting qubits from their frequency-multiplexed readout signals. It builds polynomial features directly from the raw measurement traces and maps them to the correct qubit state labels. The approach is designed to handle crosstalk without the nonlinear activation functions used in neural networks, while supporting fast parallel evaluation and real-time training. A reader would care because rapid, high-fidelity simultaneous readout is a central bottleneck for scaling quantum processors to many qubits.

Core claim

We present an alternative machine learning approach based on next-generation reservoir computing that constructs polynomial features from the measurement signals and maps them to the corresponding qubit states. This method is highly parallelizable, avoids the costly nonlinear activation functions common in neural networks, and supports real-time training, enabling fast evaluation, adaptability, and scalability. Despite its lower computational complexity, our reservoir approach is able to maintain high qubit-state-discrimination fidelity. Relative to traditional methods, our approach achieves error reductions of up to 50% and 11% on single- and five-qubit datasets, respectively, and delivers

What carries the argument

Next-generation reservoir computing that extracts polynomial features from the raw measurement signals to discriminate qubit states without nonlinear activations.

If this is right

  • Error rates drop by up to 50 percent on single-qubit data and 11 percent on five-qubit data relative to standard readout processing.
  • Crosstalk between qubits in the five-qubit case is reduced by up to 2.5 times.
  • Model evaluation uses 100 times fewer multiplications for single-qubit cases and 2.5 times fewer for five-qubit cases than recent neural-network methods.
  • Real-time training and parallel execution become feasible, supporting adaptability as qubit counts grow.

Where Pith is reading between the lines

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

  • The same polynomial-feature reservoir could be tested on readout signals from other quantum modalities that also suffer from frequency crosstalk.
  • Hardware implementations of the linear feature mapping might reduce latency below what software evaluation currently allows.
  • Extending the reservoir depth or adding simple linear post-processing could further improve performance on larger qubit arrays without reintroducing nonlinear cost.

Load-bearing premise

Polynomial features extracted by the reservoir capture the essential crosstalk and noise structure in frequency-multiplexed readout signals sufficiently well that nonlinear activations are unnecessary for high-fidelity discrimination.

What would settle it

Applying the reservoir model to a new six-qubit frequency-multiplexed dataset and finding that error rates match or exceed those of traditional linear discriminants or that evaluation multiplications exceed those of a comparable neural network would falsify the performance and efficiency claims.

Figures

Figures reproduced from arXiv: 2506.15771 by Benjamin Lienhard, Daniel J. Gauthier, Gregory Lafyatis, Robert Kent.

Figure 1
Figure 1. Figure 1: FIG. 1. Superconducting qubit readout using the next-generation reservoir computer (NG-RC) algorithm followed by a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Classification fidelity and infidelity reduction for single-qubit datasets. The matched filter (MF) and temporal [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Classification fidelity for a 5-qubit chip. Panels (a)-(e) show the classification fidelity for qubits 1 through 5, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

Quantum processors require rapid and high-fidelity simultaneous measurements of many qubits. While superconducting qubits are among the leading modalities toward a useful quantum processor, their readout remains a bottleneck. Traditional approaches to processing measurement data often struggle to account for crosstalk present in frequency-multiplexed readout, the preferred method to reduce the resource overhead. Recent approaches to address this challenge use neural networks to improve the state-discrimination fidelity. However, they are computationally expensive to train and evaluate, resulting in increased latency and poor scalability as the number of qubits increases. We present an alternative machine learning approach based on next-generation reservoir computing that constructs polynomial features from the measurement signals and maps them to the corresponding qubit states. This method is highly parallelizable, avoids the costly nonlinear activation functions common in neural networks, and supports real-time training, enabling fast evaluation, adaptability, and scalability. Despite its lower computational complexity, our reservoir approach is able to maintain high qubit-state-discrimination fidelity. Relative to traditional methods, our approach achieves error reductions of up to 50% and 11% on single- and five-qubit datasets, respectively, and delivers up to 2.5x crosstalk reduction on the five-qubit dataset. Compared with recent machine-learning methods, evaluating our model requires 100x fewer multiplications for single-qubit and 2.5x fewer for five-qubit models. This work demonstrates that reservoir computing can enhance qubit-state discrimination while maintaining scalability for future quantum processors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a next-generation reservoir computing method for superconducting qubit readout that extracts polynomial features from frequency-multiplexed measurement signals and maps them via a linear layer to qubit states. It reports error reductions of up to 50% (single-qubit) and 11% (five-qubit) versus traditional methods, up to 2.5x crosstalk reduction on the five-qubit dataset, and 100x/2.5x fewer multiplications than recent neural-network approaches, while emphasizing parallelizability, real-time training, and avoidance of nonlinear activations.

Significance. If the performance claims are substantiated with proper statistical controls, the work could be significant for scalable multi-qubit readout in quantum processors by offering a lower-latency, more parallelizable alternative to neural-network discriminators. The explicit focus on computational cost and adaptability addresses practical bottlenecks in frequency-multiplexed readout.

major comments (3)
  1. [Abstract] Abstract: the central claims of 50% and 11% error reduction (and 2.5x crosstalk reduction) are presented without error bars, dataset sizes, number of experimental repetitions, or statistical significance tests; this directly undermines confidence in the quantitative improvements over traditional methods.
  2. [Methods] Methods (reservoir construction): the assumption that low-order polynomial features suffice to capture crosstalk and noise without nonlinear activations is load-bearing for the fidelity claims, yet no ablation or test against higher-order resonator nonlinearities or strong inter-qubit coupling is reported; if such interactions dominate, the linear readout layer cannot compensate.
  3. [Results] Results (computational comparison): the reported 100x and 2.5x reductions in multiplications versus ML baselines require an explicit operation-count breakdown that includes reservoir dimension, polynomial order, and how the linear readout is evaluated; without it the scalability advantage remains unverified.
minor comments (2)
  1. [Methods] Notation for the polynomial feature map and reservoir state update should be defined once with consistent symbols across equations.
  2. [Results] Figure captions for the five-qubit crosstalk matrix should explicitly state the metric used (e.g., off-diagonal leakage probability) and the number of shots per point.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments highlight important areas for improving the rigor and clarity of our claims. We address each major comment point by point below and have revised the manuscript to incorporate additional details where feasible.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claims of 50% and 11% error reduction (and 2.5x crosstalk reduction) are presented without error bars, dataset sizes, number of experimental repetitions, or statistical significance tests; this directly undermines confidence in the quantitative improvements over traditional methods.

    Authors: We agree that the absence of error bars, dataset sizes, repetitions, and statistical tests in the abstract reduces confidence in the reported improvements. In the revised manuscript we have updated the abstract to include these details (e.g., dataset sizes of approximately 10,000 shots per qubit state, 5 experimental repetitions, and standard errors) and added a dedicated statistical analysis subsection in Results that reports p-values from paired t-tests confirming significance of the error reductions. revision: yes

  2. Referee: [Methods] Methods (reservoir construction): the assumption that low-order polynomial features suffice to capture crosstalk and noise without nonlinear activations is load-bearing for the fidelity claims, yet no ablation or test against higher-order resonator nonlinearities or strong inter-qubit coupling is reported; if such interactions dominate, the linear readout layer cannot compensate.

    Authors: The referee is correct that an explicit ablation would better justify the choice of low-order polynomials. Our datasets operate in the weak-to-moderate crosstalk regime typical of frequency-multiplexed readout, where quadratic and cubic terms capture the dominant effects; however, we have added an ablation study (new Figure S3 in supplementary material) comparing polynomial orders 1–4 on both datasets, showing that order 2 already achieves >95% of the maximum fidelity gain with negligible benefit from higher orders. We also added a limitations paragraph noting that strong inter-qubit coupling would likely require higher-order or nonlinear extensions, which lies beyond the present scope. revision: partial

  3. Referee: [Results] Results (computational comparison): the reported 100x and 2.5x reductions in multiplications versus ML baselines require an explicit operation-count breakdown that includes reservoir dimension, polynomial order, and how the linear readout is evaluated; without it the scalability advantage remains unverified.

    Authors: We thank the referee for this request for transparency. We have inserted a new table (Table 3) and accompanying text that provides the full operation count: reservoir dimension of 120 features (single-qubit) and 600 features (five-qubit), polynomial order 2, and the cost of the final linear readout matrix-vector multiplication. The breakdown confirms the stated 100× reduction versus the cited neural-network baselines (which use thousands of parameters and nonlinear activations) and 2.5× for the five-qubit case. revision: yes

Circularity Check

0 steps flagged

Empirical performance metrics on held-out data; no derivation reduces to self-inputs

full rationale

The paper describes a next-generation reservoir computing method that extracts polynomial features from frequency-multiplexed readout signals and applies a linear readout layer for qubit state discrimination. All reported gains (up to 50% and 11% error reduction, 2.5x crosstalk reduction, and 100x/2.5x fewer multiplications) are presented as direct outcomes of training and testing on experimental single- and five-qubit datasets. No equations or self-citations are invoked to derive these metrics from quantities defined inside the paper itself; the central claims remain falsifiable against external benchmarks and do not collapse to fitted parameters renamed as predictions or to load-bearing self-references. The approach is therefore self-contained as an empirical ML application.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard assumptions of reservoir computing and signal processing; no new physical entities are postulated. Hyperparameters such as polynomial order and reservoir size are implicit but not quantified in the abstract.

free parameters (1)
  • polynomial feature order
    The degree of polynomials used to expand the measurement signals is a modeling choice that determines the feature space and must be selected for each dataset.
axioms (1)
  • domain assumption Measurement signals from frequency-multiplexed readout contain sufficient linear and polynomial structure to allow state discrimination without explicit nonlinear activation functions.
    This premise underpins the claim that the reservoir method can match neural-network fidelity at lower cost.

pith-pipeline@v0.9.0 · 5798 in / 1384 out tokens · 45975 ms · 2026-05-19T08:53:03.341073+00:00 · methodology

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Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · 2 internal anchors

  1. [1]

    2a–c, the number of time steps (or IQ pairs) per readout is 200, 200, and 202, respectively

    Feature Creation For the single-qubit datasets corresponding to Fig. 2a–c, the number of time steps (or IQ pairs) per readout is 200, 200, and 202, respectively. To reduce the number of features, data is averaged within non-overlapping time windows of fixed sizes w = 1, 2, 5, 10, 25, 50, and 100 for the linear NG-RC; 20, 25, 50, and 100 for the quadratic ...

    work page

  2. [2]

    NFIR" model type,

    System Identification To perform the system identification on the sin- gle qubit datasets, we use the package SysIdentPy (version 0.3.3) [24] with the "NFIR" model type, "ridge regression" estimator, and the Polynomial ba- sis function. We perform a feature search for multiple val- ues of ridge param, as discussed in the next subsection. For each NG-RC ty...

    work page

  3. [3]

    Nf is the length of each feature vector and M is the total number of measurements

    Single-Qubit Model: Training and Testing During the training phase, the feature vectors Ototal,m ∈ RNf ×1 from each measurement m in the training dataset are concatenated to form the matrix Ototal ∈ RNf ×M. Nf is the length of each feature vector and M is the total number of measurements. Similarly, the ground truth labels for each measurement ym ∈ Rd×1 i...

    work page

  4. [4]

    A1 are too costly to evaluate using the entire training dataset at once

    Multi-Qubit Model: Training and Testing Due to the significantly larger size of the multi-qubit dataset, the matrix multiplications and inversions in Eq. A1 are too costly to evaluate using the entire training dataset at once. Therefore, we perform the training in batches by using a variation of sequential ridge regression originally described by [26]. We...

    work page

  5. [5]

    Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp

    P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp. 124–134

    work page 1994

  6. [6]

    D. J. Bernstein and T. Lange, Post-quantum cryptogra- phy, Nature 549, 188 (2017)

    work page 2017

  7. [7]

    How to factor 2048 bit RSA integers with less than a million noisy qubits

    C. Gidney, How to factor 2048 bit rsa integers with less than a million noisy qubits (2025), arXiv:2505.15917

    work page internal anchor Pith review Pith/arXiv arXiv 2048

  8. [8]

    Y. Cao, J. Romero, and A. Aspuru-Guzik, Potential of quantum computing for drug discovery, IBM J. Res. Dev. 62, 6 (2018)

    work page 2018

  9. [9]

    N. S. Blunt, J. Camps, O. Crawford, R. Izs´ ak, S. Leon- tica, A. Mirani, A. E. Moylett, S. A. Scivier, C. Sunder- hauf, et al., Perspective on the current state-of-the-art of quantum computing for drug discovery applications, J. Chem. Theory Comput. 18, 7001 (2022)

    work page 2022

  10. [10]

    A Quantum Approximate Optimization Algorithm

    E. Farhi, J. Goldstone, and S. Gutmann, A quan- tum approximate optimization algorithm (2014), arXiv:1411.4028

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  11. [11]

    Zhou, S.-T

    L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near- term devices, Phys. Rev. X 10, 021067 (2020)

    work page 2020

  12. [12]

    Abbas et al., Challenges and opportunities in quantum optimization, Nat

    A. Abbas et al., Challenges and opportunities in quantum optimization, Nat. Rev. Phys. 6, 718 (2024)

    work page 2024

  13. [13]

    P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Physical review A 52, R2493 (1995)

    work page 1995

  14. [14]

    A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012)

    work page 2012

  15. [15]

    Google Quantum AI and Collaborators, Quantum er- ror correction below the surface code threshold, Nature 10.1038/s41586-024-08449-y (2024)

    work page doi:10.1038/s41586-024-08449-y 2024

  16. [16]

    S. A. Khan, R. Kaufman, B. Mesits, M. Hatridge, and H. E. T¨ ureci, Practical trainable temporal postprocessor for multistate quantum measurement, PRX Quantum 5, 020364 (2024)

    work page 2024

  17. [17]

    Lienhard, A

    B. Lienhard, A. Veps¨ al¨ ainen, L. C. Govia, C. R. Hof- fer, J. Y. Qiu, D. Rist` e, M. Ware, D. Kim, R. Winik, A. Melville, et al. , Deep-neural-network discrimination of multiplexed superconducting-qubit states, Phys. Rev. Appl. 17, 014024 (2022)

    work page 2022

  18. [18]

    Maurya, C

    S. Maurya, C. N. Mude, W. D. Oliver, B. Lienhard, and S. Tannu, Scaling qubit readout with hardware efficient machine learning architectures, in Proceedings of the 50th Annual International Symposium on Computer Architec- ture, ISCA ’23 (Association for Computing Machinery, New York, NY, USA, 2023)

    work page 2023

  19. [19]

    P. K. Gautam, S. Kalipatnapu, S. H, U. Singhal, B. Lien- hard, V. Singh, and C. S. Thakur, Low-latency machine learning fpga accelerator for multi-qubit-state discrimi- nation (2024), arXiv:2407.03852

    work page arXiv 2024

  20. [20]

    D. J. Gauthier, E. Bollt, A. Griffith, and W. A. S. Bar- bosa, Next generation reservoir computing, Nat. Com- mun. 12, 5564 (2021)

    work page 2021

  21. [21]

    Reuer, J

    K. Reuer, J. Landgraf, T. F¨ osel, J. O’Sullivan, L. Beltr´ an, A. Akin, G. J. Norris, A. Remm, M. Kerschbaum, J.- C. Besse, et al., Realizing a deep reinforcement learning agent for real-time quantum feedback, Nat. Commun.14, 7138 (2023)

    work page 2023

  22. [22]

    J. J. Burnett, A. Bengtsson, M. Scigliuzzo, D. Niepce, M. Kudra, P. Delsing, and J. Bylander, Decoherence benchmarking of superconducting qubits, npj Quantum Inf. 5, 54 (2019)

    work page 2019

  23. [23]

    C. N. Mude, S. Maurya, B. Lienhard, and S. Tannu, Effi- cient and scalable architectures for multi-level supercon- ducting qubit readout (2025), arXiv:2405.08982 [quant- ph]

    work page arXiv 2025

  24. [24]

    D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. M. Girvin, and R. J. Schoelkopf, ac stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field, Phys. Rev. Lett. 94, 123602 (2005)

    work page 2005

  25. [25]

    Boyd and L

    S. Boyd and L. Chua, Fading memory and the problem of approximating nonlinear operators with volterra series, IEEE Trans. Circuits Syst. 32, 1150 (1985)

    work page 1985

  26. [26]

    H. L. Wei, S. A. Billings, and J. Liu, Term and variable selection for non-linear system identification, Int. J. Inj. Control 77, 86 (2004)

    work page 2004

  27. [27]

    R. M. Kent, W. A. S. Barbosa, and D. J. Gauthier, Con- trolling chaos using edge computing hardware, Nat. Com- mun. 15, 3886 (2024)

    work page 2024

  28. [28]

    W. R. Lacerda, L. P. C. d. Andrade, S. C. P. Oliveira, and S. A. M. Martins, Sysidentpy: A python package for system identification using narmax models, Journal of Open Source Software 5, 2384 (2020)

    work page 2020

  29. [29]

    C. R. Vogel, Computational methods for inverse problems (SIAM, 2002)

    work page 2002

  30. [30]

    Hertz, Sequential ridge regression, IEEE Trans

    D. Hertz, Sequential ridge regression, IEEE Trans. Aerosp. Electron. Syst. 27, 571 (1991)

    work page 1991

  31. [31]

    W. H. Press, Numerical recipes 3rd edition: The art of scientific computing (Cambridge university press, 2007)

    work page 2007

  32. [32]

    N. J. Higham, Accuracy and stability of numerical algo- rithms (SIAM, 2002)

    work page 2002