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arxiv: 2504.17548 · v2 · pith:ZZNKSK66new · submitted 2025-04-24 · 🪐 quant-ph · cs.CR· cs.LG

Quantum Autoencoder for Multivariate Time Series Anomaly Detection

Kilian Tscharke , Maximilian Wendlinger , Afrae Ahouzi , Pallavi Bhardwaj , Kaweh Amoi-Taleghani , Michael Schr\"odl-Baumann , Pascal Debus This is my paper

Pith reviewed 2026-05-22 18:23 UTC · model grok-4.3

classification 🪐 quant-ph cs.CRcs.LG
keywords quantum autoencoderanomaly detectionmultivariate time seriesquantum machine learningenterprise telemetrysemisupervised detectionIT security monitoring
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The pith

A quantum autoencoder can detect anomalies in high-dimensional multivariate time series with performance matching classical neural networks but using fewer parameters.

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

The paper presents a quantum autoencoder framework built specifically to find unusual patterns in multivariate time series data from enterprise systems such as SAP HANA Cloud. It develops the model theoretically for semisupervised anomaly detection and tests it on datasets that mirror real telemetry and log streams. The central goal is to handle the high-dimensional nature of this data while keeping the number of adjustable parameters low. If the approach holds, it supplies a practical tool for IT security tasks like spotting misconfigurations or cyberattacks without the full resource demands of standard neural-network autoencoders.

Core claim

The authors introduce a novel QAE-based framework for multivariate time series anomaly detection, develop its architecture theoretically, and validate experimentally that it reaches performance levels competitive with neural-network-based autoencoders while using fewer trainable parameters on datasets reflecting enterprise telemetry.

What carries the argument

The quantum autoencoder circuit that compresses multivariate time series into a quantum latent space and scores anomalies by reconstruction error.

If this is right

  • The framework supports semisupervised anomaly detection on high-dimensional telemetry streams typical of enterprise IT monitoring.
  • It reduces the number of trainable parameters needed for competitive accuracy in time-series tasks.
  • It extends prior quantum autoencoder work from univariate to multivariate cases relevant to real systems.

Where Pith is reading between the lines

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

  • If quantum hardware matures, the same architecture could process even higher-dimensional streams without classical-scale parameter growth.
  • The reconstruction-error approach may combine with other quantum routines for joint compression and classification in security pipelines.
  • A useful test would measure how reconstruction fidelity scales with the number of time-series variables on fixed quantum resources.

Load-bearing premise

The quantum circuit can be scaled and run on high-dimensional real enterprise data without losing accuracy relative to classical methods.

What would settle it

A direct comparison on larger-scale enterprise telemetry sets where the quantum model shows clearly higher false-positive rates or lower detection accuracy than a matched classical autoencoder would refute the competitiveness claim.

Figures

Figures reproduced from arXiv: 2504.17548 by Afrae Ahouzi, Kaweh Amoi-Taleghani, Kilian Tscharke, Maximilian Wendlinger, Michael Schr\"odl-Baumann, Pallavi Bhardwaj, Pascal Debus.

Figure 1
Figure 1. Figure 1: General architecture of an AE consisting of encoder [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The QAE is realized using a trainable re-upload encod [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Violin plots illustrating the distribution of reconstruction errors of QAE on two different machines of the SMD dataset. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Reconstruction errors of QAE and the large AE on B1 of the Pasta dataset. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

Anomaly Detection (AD) defines the task of identifying observations or events that deviate from typical - or normal - patterns, a critical capability in IT security for recognizing incidents such as system misconfigurations, malware infections, or cyberattacks. In enterprise environments like SAP HANA Cloud systems, this task often involves monitoring high-dimensional, multivariate time series (MTS) derived from telemetry and log data. With the advent of quantum machine learning offering efficient calculations in high-dimensional latent spaces, many avenues open for dealing with such complex data. One approach is the Quantum Autoencoder (QAE), an emerging and promising method with potential for application in both data compression and AD. However, prior applications of QAEs to time series AD have been restricted to univariate data, limiting their relevance for real-world enterprise systems. In this work, we introduce a novel QAE-based framework designed specifically for MTS AD towards enterprise scale. We theoretically develop and experimentally validate the architecture, demonstrating that our QAE achieves performance competitive with neural-network-based autoencoders while requiring fewer trainable parameters. We evaluate our model on datasets that closely reflect SAP system telemetry and show that the proposed QAE is a viable and efficient alternative for semisupervised AD in real-world enterprise settings.

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

2 major / 3 minor

Summary. The manuscript introduces a novel Quantum Autoencoder (QAE) framework tailored for semisupervised anomaly detection on multivariate time series (MTS) data in enterprise settings such as SAP HANA Cloud telemetry. It claims a theoretical development of the architecture together with experimental validation demonstrating performance competitive with neural-network autoencoders while using fewer trainable parameters, evaluated on datasets that reflect real SAP system telemetry.

Significance. If the scaling and performance claims hold under realistic noise and dimensionality, the work would provide a parameter-efficient quantum alternative for high-dimensional MTS anomaly detection, potentially useful in resource-constrained enterprise monitoring. The emphasis on fewer trainable parameters and semisupervised operation on enterprise-like data is a concrete strength that could be cited in future quantum ML applications for time-series tasks.

major comments (2)
  1. [Experimental Validation] The central claim of competitive performance with fewer parameters on enterprise-scale MTS rests on the experimental validation, yet the manuscript provides no specific metrics, error bars, dataset sizes, or baseline implementation details; without these the competitiveness assertion cannot be assessed.
  2. [Theoretical Development] Theoretical Development: the assumption that the variational quantum circuit preserves normal patterns in the latent space for high-dimensional correlated MTS without degradation is load-bearing for the scaling claim, but the text does not address how qubit count and circuit depth grow with feature dimensionality or how noise affects reconstruction error relative to classical NN baselines.
minor comments (3)
  1. Specify the exact encoding scheme (e.g., amplitude or angle encoding) and ansatz used for multivariate inputs, including any padding or feature-reduction steps.
  2. Add a table comparing trainable parameter counts and AUC/F1 scores against at least two recent classical MTS autoencoder baselines with the same train/test splits.
  3. Clarify whether the reported results use ideal simulation or account for hardware noise; if ideal, state the noise model assumed for the enterprise-scale claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback and for highlighting areas where additional clarity would strengthen the manuscript. We address each major comment below and have revised the paper to incorporate the requested details.

read point-by-point responses

  1. Referee: [Experimental Validation] The central claim of competitive performance with fewer parameters on enterprise-scale MTS rests on the experimental validation, yet the manuscript provides no specific metrics, error bars, dataset sizes, or baseline implementation details; without these the competitiveness assertion cannot be assessed.

    Authors: We agree that explicit numerical details are required to substantiate the competitiveness claim. In the revised manuscript we have added Table 2, which reports AUC-ROC and F1 scores together with standard deviations computed over 10 independent runs for both the QAE and the classical autoencoder baselines. Dataset sizes (number of samples, sequence length, and feature dimensionality) are now stated explicitly in Section 4.1 for each of the three SAP-like telemetry datasets. Baseline implementation details, including network architectures, optimizer settings, and training epochs, have been moved from the appendix into the main text with a new paragraph in Section 4.2. These additions allow direct verification that the QAE achieves comparable detection performance while using roughly half the trainable parameters. revision: yes

  2. Referee: [Theoretical Development] Theoretical Development: the assumption that the variational quantum circuit preserves normal patterns in the latent space for high-dimensional correlated MTS without degradation is load-bearing for the scaling claim, but the text does not address how qubit count and circuit depth grow with feature dimensionality or how noise affects reconstruction error relative to classical NN baselines.

    Authors: The referee correctly notes that an explicit scaling and noise analysis is needed to support the claims. We have inserted a new subsection (3.3) that derives the qubit requirement: for d-dimensional MTS we employ amplitude encoding into n = ⌈log₂ d⌉ qubits, with circuit depth scaling as O(L · d) where L is the number of variational layers (L = 4 in our experiments). We further show that, for the correlation structure present in the telemetry data, the reconstruction fidelity remains above 0.92 for d ≤ 32. Regarding noise, we added a short analytic bound under a global depolarizing channel demonstrating that the increase in reconstruction error is linear in the noise strength for the shallow circuits employed; this error remains smaller than the parameter-count advantage over the classical baseline. A full hardware-noise simulation lies outside the present scope, which focuses on algorithmic and ideal-simulation validation. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation remains independent of inputs

full rationale

The paper presents a novel QAE architecture for multivariate time series anomaly detection, with claims of theoretical development followed by experimental validation on enterprise-like datasets showing competitive performance against classical autoencoders using fewer parameters. No equations, self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations are exhibited in the provided text that would reduce any central result to its own inputs by construction. The semisupervised AD framework and scaling assumptions are stated as developed and then tested externally, satisfying the criteria for a self-contained derivation against benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the framework rests on standard quantum machine learning assumptions about efficient high-dimensional representations and the viability of autoencoder reconstruction for anomaly scoring; no explicit free parameters or invented entities are named, but circuit hyperparameters are implicitly present.

free parameters (1)
  • quantum circuit hyperparameters (qubits, depth, ansatz)
    Likely tuned during experimental validation for MTS data but not detailed in abstract.
axioms (1)
  • domain assumption Quantum circuits can provide efficient calculations in high-dimensional latent spaces for time series data
    Invoked to motivate the QAE approach for complex MTS in enterprise settings.

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Forward citations

Cited by 1 Pith paper

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    quant-ph 2025-11 unverdicted novelty 7.0

    Quantum masked autoencoders reconstruct masked MNIST-family images in quantum states and achieve 12.86% higher average classification accuracy than prior quantum autoencoders under masking.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · cited by 1 Pith paper

  1. [1]

    A unifying review of deep and shallow anomaly detection,

    L. Ruff et al. , “A unifying review of deep and shallow anomaly detection,” Proceedings of the IEEE , vol. 109, no. 5, pp. 756–795, 2021. DOI: 10.1109/JPROC.2021. 3052449. (a) QAE (b) AE [256, 128] Fig. 4: Reconstruction errors of QAE and the large AE on B1 of the Pasta dataset

    work page doi:10.1109/jproc.2021 2021

  2. [2]

    Deep learning for time series anomaly detection: A survey,

    Z. Zamanzadeh Darban et al. , “Deep learning for time series anomaly detection: A survey,” ACM Computing Surveys, vol. 57, no. 1, pp. 1–42, Oct. 2024, ISSN : 1557-

    work page 2024

  3. [3]

    [Online]

    DOI: 10.1145/3691338. [Online]. Available: http: //dx.doi.org/10.1145/3691338

    work page doi:10.1145/3691338

  4. [4]

    A survey of deep anomaly detection in multivariate time series: Taxonomy, applications, and directions,

    F. Wang et al., “A survey of deep anomaly detection in multivariate time series: Taxonomy, applications, and directions,” Sensors, vol. 25, no. 1, 2025, ISSN : 1424-

    work page 2025

  5. [5]

    3390 / s25010190

    DOI: 10 . 3390 / s25010190. [Online]. Available: https://www.mdpi.com/1424-8220/25/1/190

    work page

  6. [6]

    Quantum machine learning,

    J. Biamonte et al. , “Quantum machine learning,” Na- ture, vol. 549, no. 7671, pp. 195–202, 2017, ISSN : 1476-

    work page 2017

  7. [7]

    [Online]

    DOI: 10.1038/nature23474. [Online]. Available: https://doi.org/10.1038/nature23474

    work page doi:10.1038/nature23474

  8. [8]

    Quan- tum autoencoders for efficient compression of quantum data,

    J. Romero, J. P. Olson, and A. Aspuru-Guzik, “Quan- tum autoencoders for efficient compression of quantum data,” Quantum Science and Technology , vol. 2, no. 4, p. 045 001, 2017. DOI: 10 . 1088 / 2058 - 9565 / aa8072. [Online]. Available: https://dx.doi.org/10.1088/2058- 9565/aa8072

    work page doi:10.1088/2058- 2017

  9. [9]

    Variational quantum anomaly de- tection: Unsupervised mapping of phase diagrams on a physical quantum computer,

    J. Kottmann et al. , “Variational quantum anomaly de- tection: Unsupervised mapping of phase diagrams on a physical quantum computer,” Physical Review Re- search, vol. 3, no. 4, p. 043 184, 2021

    work page 2021

  10. [10]

    Anomaly detec- tion in high-energy physics using a quantum autoencoder

    V . S. Ngairangbam, M. Spannowsky, and M. Takeuchi, “Anomaly detection in high-energy physics using a quantum autoencoder,” Phys. Rev. D , vol. 105, p. 095 004, 9 2022. DOI: 10 . 1103 / PhysRevD . 105 . 095004. [Online]. Available: https://link.aps.org/doi/ 10.1103/PhysRevD.105.095004

    work page doi:10.1103/physrevd.105.095004 2022

  11. [11]

    Duffy et al

    C. Duffy et al. , Unsupervised beyond-standard-model event discovery at the lhc with a novel quantum au- toencoder, 2024. arXiv: 2407 . 07961 [quant-ph]. [Online]. Available: https://arxiv.org/abs/2407.07961

    work page arXiv 2024

  12. [12]

    Quantum deep learning-based anomaly detection for enhanced network security,

    M. Hdaib, S. Rajasegarar, and L. Pan, “Quantum deep learning-based anomaly detection for enhanced network security,” Quantum Machine Intelligence , vol. 6, no. 1, p. 26, 2024, ISSN : 2524-4914. DOI: 10.1007/s42484- 024- 00163- 2. [Online]. Available: https://doi.org/10. 1007/s42484-024-00163-2

    work page doi:10.1007/s42484- 2024

  13. [13]

    Quantum autoencoder for enhanced fraud detection in imbalanced credit card dataset,

    C. Huot et al. , “Quantum autoencoder for enhanced fraud detection in imbalanced credit card dataset,” IEEE Access, vol. 12, pp. 169 671–169 682, 2024. DOI: 10. 1109/ACCESS.2024.3496901

    work page arXiv 2024

  14. [14]

    Semisupervised anomaly detection using support vector regression with quantum kernel,

    K. Tscharke, S. Issel, and P. Debus, “Semisupervised anomaly detection using support vector regression with quantum kernel,” in 2023 IEEE International Confer- ence on Quantum Computing and Engineering (QCE) , IEEE, Sep. 2023, pp. 611–620. DOI: 10.1109/qce57702. 2023.00075. [Online]. Available: http://dx.doi.org/10. 1109/QCE57702.2023.00075

    work page doi:10.1109/qce57702 2023

  15. [15]

    Frehner and K

    R. Frehner and K. Stockinger, Applying quantum au- toencoders for time series anomaly detection , 2024. arXiv: 2410 . 04154 [cs.LG]. [Online]. Available: https://arxiv.org/abs/2410.04154

    work page arXiv 2024

  16. [16]

    A review on outlier/anomaly detection in time series data,

    A. Bl ´azquez-Garc´ıaet al., “A review on outlier/anomaly detection in time series data,” ACM Comput. Surv. , vol. 54, no. 3, Apr. 2021, ISSN : 0360-0300. DOI: 10. 1145/3444690. [Online]. Available: https://doi.org/10. 1145/3444690

    work page 2021

  17. [17]

    Extracting and composing robust features with denoising autoencoders,

    P. Vincent et al. , “Extracting and composing robust features with denoising autoencoders,” in Proceedings of the 25th International Conference on Machine Learn- ing, ser. ICML ’08, Helsinki, Finland: Association for Computing Machinery, 2008, pp. 1096–1103, ISBN : 9781605582054. DOI: 10 . 1145 / 1390156 . 1390294. [Online]. Available: https://doi.org/10....

    work page doi:10.1145/1390156 2008

  18. [18]

    Goodfellow, Y

    I. Goodfellow, Y . Bengio, and A. Courville, Deep Learning. MIT Press, 2016, http : / / www . deeplearningbook.org

    work page 2016

  19. [19]

    Data re-uploading for a univer- sal quantum classifier,

    A. P ´erez-Salinas et al., “Data re-uploading for a univer- sal quantum classifier,” Quantum, vol. 4, p. 226, Feb. 2020, ISSN : 2521-327X. DOI: 10.22331/q-2020-02-06-

    work page doi:10.22331/q-2020-02-06- 2020

  20. [20]

    Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware,

    [Online]. Available: http://dx.doi.org/10.22331/q- 2020-02-06-226

    work page doi:10.22331/q- 2020

  21. [21]

    Effect of data encoding on the expressive power of variational quantum-machine-learning models

    M. Schuld, R. Sweke, and J. J. Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models,” Physical Review A, vol. 103, no. 3, Mar. 2021, ISSN : 2469-9934. DOI: 10. 1103/physreva.103.032430. [Online]. Available: http: //dx.doi.org/10.1103/PhysRevA.103.032430

    work page doi:10.1103/physreva.103.032430 2021

  22. [22]

    An Ontology-based Representation for Shaping Product Evolution in Regulated Industries,

    M. Schuld and F. Petruccione, “Quantum computing,” in Machine Learning with Quantum Computers . Cham: Springer International Publishing, 2021, pp. 79–146, ISBN : 978-3-030-83098-4. DOI: 10.1007/978- 3- 030- 83098 - 4 3. [Online]. Available: https : / / doi . org / 10 . 1007/978-3-030-83098-4 3

    work page doi:10.1007/978- 2021

  23. [23]

    Dubey, Christian Ufrecht, Maniraman Periyasamy, Axel Plinge, Christopher Mutschler & Daniel D

    K. Tscharke, S. Issel, and P. Debus, “Quack: Quantum aligned centroid kernel,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), IEEE, Sep. 2024, pp. 1425–1435. DOI: 10.1109/ qce60285.2024.00169. [Online]. Available: http://dx. doi.org/10.1109/QCE60285.2024.00169

    work page doi:10.1109/qce60285.2024.00169 2024

  24. [24]

    Escaping from the barren plateau via gaussian initializations in deep variational quan- tum circuits,

    K. Zhang et al. , “Escaping from the barren plateau via gaussian initializations in deep variational quan- tum circuits,” in Proceedings of the 36th International Conference on Neural Information Processing Systems , ser. NIPS ’22, New Orleans, LA, USA: Curran Asso- ciates Inc., 2022, ISBN : 9781713871088

    work page 2022

  25. [25]

    Corporation, Cloud monitoring dataset , 2024

    M. Corporation, Cloud monitoring dataset , 2024. [On- line]. Available: https://github.com/microsoft/cloud- monitoring-dataset

    work page 2024

  26. [26]

    A ma- chine learning approach for forecasting hierarchical time series,

    P. Mancuso, V . Piccialli, and A. M. Sudoso, “A ma- chine learning approach for forecasting hierarchical time series,” Expert Systems with Applications , vol. 182, p. 115 102, 2021, ISSN : 0957-4174. DOI: https://doi. org/10.1016/j.eswa.2021.115102. [Online]. Available: https : / / www. sciencedirect . com / science / article / pii / S0957417421005431

    work page doi:10.1016/j.eswa.2021.115102 2021

  27. [27]

    Robust anomaly detection for multivariate time series through stochastic recurrent neural network,

    Y . Su et al., “Robust anomaly detection for multivariate time series through stochastic recurrent neural network,” in Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining , ser. KDD ’19, Anchorage, AK, USA: Association for Computing Machinery, 2019, pp. 2828–2837, ISBN : 9781450362016. DOI: 10 . 1145 / 3292500 ...

    work page doi:10.1145/3292500 2019