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Evaluating the Potential of Quantum Machine Learning in Cybersecurity: A Case-Study on PCA-based Intrusion Detection Systems

Armando Bellante, Tommaso Fioravanti, Michele Carminati, Stefano Zanero, Alessandro Luongo

arXiv:2502.11173v1quant-phcs.CRcs.LGcs.NI

TL;DR

The paper asks how QML could affect cybersecurity beyond cryptography, given limited evidence about fault-tolerant QML on realistic security datasets. It develops an assessment methodology and applies it to PCA-based quantum models for network intrusion detection, finding that quantum advantage appears only beyond large problem sizes and remains constrained by hardware slowdowns.

  • Problem

    QML’s long-term impact on cybersecurity remains poorly explored because near-term heuristics lack theoretical guarantees and current hardware and simulators limit prediction on realistic datasets.

    Source: §1 · p. 2

  • Method

    The paper develops a theoretical methodology for assessing quantum advantage in machine learning and applies it to quantum clustering and dimensionality reduction for intrusion detection using numerical simulations of key quantum subroutines.

    Source: §1 · p. 2, §6 · p. 20

  • Results

    Quantum methods are unlikely to outperform classical intrusion-detection methods on small datasets, while query-complexity advantage appears beyond 4 ∗106 samples and 50 features.

    Source: §6 · p. 20

  • Takeaways & Limitations

    Hardware slowdowns shift any advantage toward larger datasets, requiring more physical qubits and making near-term advantage unlikely.

    Source: §6 · p. 21

    The evaluation framework is cautious and may miss advantageous QML candidates because its decision assumptions can exclude them; its criteria for selecting quantum algorithms also need further elaboration.

    Source: §4.2.1 · p. 12

Abstract

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Quantum computing promises to revolutionize our understanding of the limits of computation, and its implications in cryptography have long been evident. Today, cryptographers are actively devising post-quantum solutions to counter the threats posed by quantum-enabled adversaries. Meanwhile, quantum scientists are innovating quantum protocols to empower defenders. However, the broader impact of quantum computing and quantum machine learning (QML) on other cybersecurity domains still needs to be explored. In this work, we investigate the potential impact of QML on cybersecurity applications of traditional ML. First, we explore the potential advantages of quantum computing in machine learning problems specifically related to cybersecurity. Then, we describe a methodology to quantify the future impact of fault-tolerant QML algorithms on real-world problems. As a case study, we apply our approach to standard methods and datasets in network intrusion detection, one of the most studied applications of machine learning in cybersecurity. Our results provide insight into the conditions for obtaining a quantum advantage and the need for future quantum hardware and software advancements.

1. Introduction

Quantum computing and QML may extend cybersecurity beyond cryptography, but their long-term impact on practical security tasks remains insufficiently understood. This paper develops an evaluation framework and applies it to PCA-based quantum methods for network intrusion detection.

Motivation

  • QML’s long-term impact on cybersecurity remains largely unexplored because near-term heuristics lack theoretical guarantees and current hardware limits realistic evaluation.The paper therefore focuses on fault-tolerant QML algorithms with provable guarantees.Source: §1 · p. 2

Contributions

  • The paper introduces a framework that compares quantum and classical running times while assessing how QML approximation errors affect model performance.Its goal is to identify conditions under which a fault-tolerant QML algorithm outperforms a classical counterpart.Source: §1 · p. 2
  • The framework is intended to provide a fair benchmarking tool for cybersecurity practitioners evaluating future QML solutions.It supports assessment of whether quantum algorithms can address specific practical problems effectively.Source: §1 · p. 2

Case study

  • The case study evaluates quantum clustering and quantum dimensionality reduction for network intrusion detection using simulated amplitude estimation, phase estimation, and pure-state tomography.These subroutines represent essential building blocks for simulating existing QML algorithms.Source: §1 · p. 2

Contributions

  • The study contributes a theoretical assessment of QML advantages together with a PCA-based intrusion-detection case study addressing performance and real-world feasibility.The paper positions the methodology as broader than the individual case study.Source: §1 · p. 2

2. Quantum machine learning algorithms for computer security

Cybersecurity research has explored QML mainly through near-term heuristic methods, but their performance is difficult to guarantee or assess at realistic scale. The paper consequently emphasizes fault-tolerant algorithms with provable guarantees and studies their potential relevance to large cybersecurity problems.

Current research trends

  • Near-term QML research targets cybersecurity tasks such as intrusion, botnet, denial-of-service, supply-chain, and Trojan detection, often using variational circuits on NISQ devices.These approaches use parameterized gates optimized with a classical computer, but remain constrained by hardware limitations.Source: §2.2 · pp. 3–4, §2.4 · p. 4
  • Variational QML methods generally lack provable performance guarantees, while hardware and simulator constraints limit experiments on realistic dataset dimensions.These limitations make their scaling and practical performance difficult to predict.Source: §2.2 · p. 4

Fault-tolerant opportunities

  • Fault-tolerant QML algorithms derived from quantum linear algebra seek shorter running times than classical methods, including for clustering, PCA, nearest-neighbor, regression, and deep-learning tasks.The paper focuses on algorithms whose guarantees permit future-impact analysis without requiring quantum hardware or simulators.Source: §2.3 · p. 4
  • With quantum access to data, many fault-tolerant algorithms have polylogarithmic dependence on the number of data points, contrasting with at least linear classical dependence.This distinction motivates evaluating their potential on realistic cybersecurity datasets.Source: §2.3 · p. 4

Motivation and relevance to cybersecurity

  • The paper proposes a reusable evaluation framework and PCA-based intrusion-detection case study to assess when fault-tolerant QML may achieve meaningful advantages.The broader methodology is intended to extend beyond this case study as quantum hardware advances.Source: §2.4 · p. 5

3. Quantum computing background

Quantum computing uses qubits, quantum gates, and measurement to process information, but practical quantum advantage depends on hardware overheads and complexity measures that capture more than oracle queries alone.

Qubits and registers

  • Qubits can occupy superpositions, while multi-qubit registers represent states in exponentially large spaces and may exhibit correlations.Measurement collapses the quantum state to a definite computational outcome.Source: §3 · p. 5

Quantum algorithms

  • Quantum algorithms repeatedly evolve an initial state with quantum gates and measure it to obtain computational outcomes.Source: §3 · p. 5

Quantum advantage

  • Current quantum prototypes have hundreds of qubits and thousands of executable gates but lack provable practical advantage for problems of real interest.Some architectures have nevertheless outperformed classical computers on purely theoretical tasks.Source: §3.1 · pp. 5–6

Quantum hardware

  • Quantum software incurs overhead from compilation, gate decomposition, error correction, and hardware connectivity constraints.Error correction increases qubit and operation requirements, while limited connectivity can require additional swap operations.Source: §3.1 · p. 6

Complexity measures

  • Query complexity counts oracle calls but can conceal implementation and inter-query costs, so it is not always a reliable proxy for gate or time complexity.Grover’s search illustrates a query advantage that extends to gate complexity, whereas the hidden subgroup example shows the opposite pattern.Source: §3.2 · pp. 6–7, §3.3 · p. 8

4. Evaluating the quantum advantage

The evaluation framework assesses fault-tolerant QML by modeling approximation errors, data-loading costs, and quantum-versus-classical running times. It identifies when quantum advantage may be plausible while warning that resource overheads and conservative assumptions can exclude beneficial candidates.

Framework scope

  • The framework evaluates QML impact by analyzing fault-tolerant algorithms, data-loading costs, and running-time comparisons on real-world cybersecurity problems.Its methodology is intended to be adaptable beyond cybersecurity applications.Source: §4 · p. 8, §4.1 · p. 8

Data-loading costs

  • Classical data loading and preprocessing can erase expected exponential speedups, although polynomial advantages may remain when training or inference is polynomial-time.Source: §4.1.1 · p. 9

Complexity and accuracy

  • Quantum advantage depends on dataset parameters such as condition number and approximation error, with advantage indicated when the tolerated error satisfies ϵ ∈Ω(1/d).Too much error can misclassify anomalies, whereas too little error can make the quantum algorithm slower than its classical counterpart.Source: §4.1.2 · pp. 9–10

Evaluation procedure

  • A preliminary query-complexity analysis can identify promising QML applications and rule out tasks without requiring quantum simulation or immediate detailed resource estimation.This can help practitioners evaluate large, realistic datasets more quickly.Source: §4.2 · p. 11, §4.2.1 · p. 12

Advantages and limitations

  • Fault-tolerant resource overheads and assumptions about comparable quantum and classical clock speeds make the framework cautious and capable of missing advantageous candidates.Further resource estimation is needed after query-level advantage appears plausible, and classical architectures may also improve.Source: §4.2 · p. 12, §4.2.1 · p. 12
  • The paper defines advantage as greater speed with comparable performance, while noting that robustness and adversarial resilience require further study.Source: §4.2.1 · p. 12

5. Case study: PCA-based network IDSs

The case study evaluates three PCA-based anomaly detection methods and focuses on whether quantum PCA model extraction can reduce the training bottleneck while preserving detection performance.

Case-study scope

  • The study compares quantum and classical PCA model-extraction costs for the Principal Component Classifier, Reconstruction Loss, and Ensemble PCC methods.PCA features are extracted from normal training data and then used by all three detectors.Source: §5 · p. 12, §5.1 · pp. 13, 15
  • PCA model extraction is treated as the main classical computational bottleneck, although preprocessing and fine-tuning can sometimes cost more.Equivalent quantum methods for those other stages remain necessary for a complete end-to-end comparison.Source: §5 · pp. 12–13

Anomaly detection algorithms

  • PCC flags an observation when either major- or minor-component score exceeds its validation-set threshold, with false alarm rate α controlling the threshold trade-off.The major-component-only variant omits the minor-component score and threshold.Source: §5.1 · pp. 13–14
  • Ensemble PCC runs dot-product, cosine-similarity, and correlation variants of PCC and labels a sample anomalous if any model exceeds its threshold.The paper reports that this ensemble improves PCC performance.Source: §5.1 · p. 14
  • Reconstruction Loss projects a sample into the principal-component space and back, using the resulting squared reconstruction error as the anomaly score.Samples whose error exceeds a threshold are labeled anomalies.Source: §5.1 · pp. 14–15

PCA model extraction

  • Quantum PCA extraction uses threshold search for selected variance followed by quantum extraction of eigenvalues and principal components.The required routines and input parameters are summarized in the quantum PCA pipeline.Source: §5.1 · p. 15, Figure 3 · p. 15

5.2. Experimental settings

Experiments simulate quantum subroutine errors on public intrusion-detection datasets and compare detection performance and theoretical running times with classical PCA methods.

Experimental settings

  • Quantum errors are simulated by modifying scikit-learn PCA implementations to model amplitude-estimation, phase-estimation, tomography, and singular-vector-extraction routines.Theoretical QML routines show running-time advantages over classical counterparts for high-dimensional data.Source: §5.2 · pp. 15–16
  • The evaluation uses KDDCUP99, CIC-IDS2017, and DARKNET to identify feature-and-sample ranges that could enable quantum advantage.The analysis varies dataset parameters while fixing quantum error parameters and seeks a working point matching classical performance with lower execution time.Source: §5.2 · p. 16

Experimental scope

  • The study excludes data-acquisition time into quantum-readable memory because it is performed once and is treated as necessary in both approaches.The datasets are acknowledged to have limitations, especially KDDCUP99, and are used for long-term classical-versus-quantum comparison.Source: §5.2 · p. 16

PCC over KDDCUP99

  • For major components, quantum PCA matches classical PCC performance on KDDCUP99 while its query-complexity advantage appears only for sufficiently large datasets.The advantage becomes evident after approximately 4 × 10^6 samples and 50 features; small datasets favor neither quantum speedup nor the reported advantage.Source: §5.3 · p. 17, Table 3 · p. 17

Running-time comparison

  • The major-component comparison uses randomized PCA with complexity O(ndk log(k)), whereas extracting both major and minor components requires comparison with full SVD complexity O(min(nd^2, n^2d)).These alternatives correspond to whether the detection method needs only major components or both component sets.Source: Table 2 · p. 16, §5.3 · p. 17

5.4. PCC and Ensemble over CICIDS2017

On CICIDS2017, quantum PCC matches classical performance under selected errors, while Ensemble PCC improves recall and F1-score; quantum running-time advantages appear only at very large dataset sizes and are weakened for minor-component extraction.

Performance analysis

  • QPCA-70 matches the classical PCC performance on CICIDS2017 under the reported error parameters, although both perform worse than KDDCUP99 with major components only.The comparison uses QPCA70 with major and minor components and varying false alarm rates.Source: §5.4 · p. 17, Table 4 · p. 18
  • The ensemble model improves PCC, particularly recall and accuracy, and raises overall F1-score by using six attack-classification criteria instead of two.The recall gain reduces false negatives but increases false positives, while precision decreases.Source: §5.4 · p. 17

Running time analysis

  • A quantum query-complexity advantage emerges after approximately 2 ∗10^9 samples and 100 features for CICIDS2017 PCC with major and minor components.The quantum estimate includes binary search, top-k singular-vector extraction, and least-q singular-vector extraction, increasing its running time relative to simpler settings.Source: §5.4 · p. 18, §5.5 · p. 19

Limitations

  • Extracting minor components with full classical SVD shows no quantum advantage at approximately 3 ∗10^7 samples and 500 features, and MCA would likely reduce the advantage further.This limits the practical case for quantum methods on problems requiring minor-component extraction.Source: §5.4 · p. 18

Reconstruction loss

  • For reconstruction-loss PCA on CICIDS2017, QPCA matches classical performance at δ = 0.01, while increasing δ tends to classify more points as attacks.The reported matching parameters are ϵθ = ϵ = 0.3 and η = 0.00075.Source: §5.5 · p. 18, Table 5 · p. 19

5.6. Reconstruction loss over DARKNET

On DARKNET reconstruction loss, the quantum model nearly matches classical performance under a tomography heuristic and shows a query-complexity advantage at 10^8 samples, but practical deployment remains constrained by resource and hardware requirements.

Experimental setup

  • The DARKNET model uses 34 principal components retaining p = 99.65% of the variance, with d = 85 normalized and scaled features.The classical hyperparameter search optimized F1-score and selected the shorter-running configuration.Source: §5.6 · p. 19

Performance analysis

  • The quantum model achieves almost the classical performance with the tomography heuristic and theoretical singular-vector error δ = 0.1.The heuristic obtains δ = 0.01 by using s/100 samples, sacrificing provable guarantees.Source: §5.6 · p. 19

Running time analysis

  • A quantum query-complexity advantage appears at 10^8 samples for datasets with up to hundreds of features.This running-time comparison uses parameters obtained from the hyperparameter search.Source: §5.6 · p. 19, Table 6 · p. 19

Practical scope

  • The theoretical advantage is practical mainly for organizations able to process massive datasets, although high generalization from subsets of approximately 5,000 or 50,000 samples makes such dataset sizes seemingly unnecessary here.The paper therefore questions whether the required data volume is realistic for this PCA-based application.Source: §5.7 · pp. 19–20

Resource estimation

  • Under optimistic QRAM assumptions, one query requires approximately 1.07 ms and 2.08 × 10^14 physical qubits, while less favorable parameters require 28.1 ms and 7.31 × 10^16 qubits.These access times are far slower than classical RAM and can outweigh a theoretical two-order-of-magnitude operation advantage.Source: §5.8 · p. 20

6. Conclusions

The paper introduces an evaluation methodology for QML in cybersecurity and applies it to network intrusion detection. It finds that quantum advantage is constrained to massive-scale problems and is unlikely soon without major hardware advances.

6. Conclusions

  • The evaluation methodology assesses QML’s potential impact on specific cybersecurity problems and demonstrates the approach using fundamental network-intrusion-detection algorithms.The framework is intended to distinguish practical impact from hype surrounding emerging technologies.Source: §6 · pp. 20–21
  • QML techniques are unlikely to outperform classical intrusion-detection methods on small datasets, while quantum query-complexity advantages appear beyond 4 ∗106 samples and 50 features.These thresholds arise in the case study’s comparison of quantum and classical approaches.Source: §6 · p. 20
  • Hardware slowdowns shift the potential advantage toward larger datasets, requiring more physical qubits and making near-term advantage unlikely.The theoretical requirements may align with real-world datasets, but implementation overhead changes the practical boundary.Source: §6 · p. 21
  • Fault-tolerant quantum computing could provide an asymptotic running-time advantage, but likely only for massive-scale datasets beyond first-generation hardware capabilities.The paper identifies hardware technology advancement as necessary for those dataset sizes to become usable.Source: §6 · p. 21

Appendix A. Brief introduction to quantum information

Quantum information is represented in qubits and quantum registers, whose states evolve unitarily and yield limited information through measurement. Tomography reconstructs state amplitudes statistically because measurement collapses superpositions and quantum states cannot be generically copied.

Appendix A. Brief introduction to quantum information

  • A qubit is a normalized linear combination of computational-basis states, with nonzero coefficients indicating a superposition.The coefficients are complex amplitudes whose squared absolute values sum to one.Source: Appendix A · p. 25
  • A quantum register contains n qubits and spans a 2^n-dimensional computational-basis space.Its state is expressed as a normalized vector over binary-encoded basis states.Source: Appendix A · p. 25
  • Quantum algorithms evolve states with unitary matrices, which preserve norms and can be decomposed into one- and two-qubit gates.Multiplication corresponds to sequential circuits, while tensor products correspond to parallel circuits on different qubits.Source: Appendix A · p. 25
  • Measurements reveal only one computational-basis bit-string per outcome, so superposition amplitudes cannot be retrieved all at once.Measurement operators determine outcome probabilities and produce state collapse after an outcome is observed.Source: Appendix A · p. 25
  • Tomography reconstructs quantum-state amplitudes from statistics over repeated measurements because measurement destroys the original superposition and no-cloning prevents generic copying.The procedure is therefore inherently based on repeated observations rather than direct access to all amplitudes.Source: Appendix A · p. 25

Appendix B. Algorithms and subroutines implemented

The implemented algorithms define quantum access, data normalization, state-readout, spectral-estimation, and clustering procedures for the QML case study. Their performance depends on data structures, tomography precision, and matrix-dependent parameters.

Appendix B. Algorithms and subroutines implemented

  • Quantum access to matrices uses a data structure that stores entries in O(nm log(nm)), updates entries in O(log(nm)), and enables mappings in O(polylog(nm)) time.QRAM and KP-trees provide the coherent access assumed by the quantum algorithms after input preprocessing.Source: Appendix B · p. 26
  • The memory parameter µ(X) controls quantum-algorithm efficiency, with smaller values yielding more efficient algorithms and the optimal value estimable during preprocessing.The framework does not simulate quantum access itself but does estimate the best µ for the dataset.Source: Appendix B · p. 26
  • Tomography estimates a normalized vector with ℓ2 error at most δ using repeated access to a state-preparation map and its controlled version.The stated routine achieves success probability at least 1 −1/poly(m) with a measurement complexity depending on m and δ.Source: Appendix B · p. 26
  • Phase estimation, amplitude estimation, and distance or inner-product estimation supply the main numerical subroutines for the quantum algorithms.Consistent phase estimation is simulated, and amplitude estimation supports distance and inner-product calculations through a modified Hadamard test.Source: Appendix B · pp. 26–27
  • Quantum PCA extracts top singular vectors and related values through threshold search and tomography, while q-means approximates classical k-means centroids under quantum-access assumptions.The PCA pipeline includes binary search for a singular-value threshold; q-means produces centroids δ-close in ℓ2 norm with iteration counts proportional to the classical method.Source: Appendix B · p. 27

Appendix C. Vector state tomography

The tomography experiment compares a theoretical measurement bound with simulated performance for the first principal component of CIC-MalMem-2022. Simulation reaches the target error with far fewer measurements than the bound predicts.

Appendix C. Vector state tomography

  • The theoretical and simulated curves report the number of measurements needed to obtain a specified vector-estimation error, with the target ℓ2 error set to 0.03.The theoretical bound and numerical simulation are shown as separate curves in Figure C.6.Source: Appendix C · p. 28, Figure C.6 · p. 28
  • About 10^4 measurements achieve ℓ2 error 0.03, compared with approximately 10^7 suggested by the theoretical bound.The experiment uses the first principal component of a 55-dimensional CIC-MalMem-2022 dataset.Source: Appendix C · pp. 27–28, Figure C.6 · p. 28
  • Repeating tomography 1000 times with 20.861 measurements produces an error distribution roughly centered at 0.03.The measurement count was selected as sufficient to reach the target error in the preceding simulation.Source: Appendix C · p. 28, Figure C.7 · p. 28
  • The case study also compares classical PCA70 and quantum QPCA70 principal-component classifiers using major and minor components on KDDCUP99.The supplied table caption identifies the comparison scope but does not report cell-level outcomes.Source: Table C.7 · p. 28

Appendix D. Performance analysis with minor and major components over KDDCUP99

The experiment evaluates a threshold-based intrusion classifier using both major and minor principal components, with quantum and classical models configured to extract nearly matching component counts. The quantum model matches classical performance, and including minor components improves recall over using major components alone.

Classification setup

  • The classifier labels a sample as an attack when either T1 > c1 or T2 > c2, and as normal otherwise.The experiment retains the error parameters used in Section 5.3 for estimating major and minor components.Source: Appendix D · p. 28

Performance comparison

  • The quantum model matches the classical performance when both major and minor principal components are used.QPCA70 extracts 10 major and 7 minor components, compared with 10 major and 6 minor components classically.Source: Appendix D · p. 28
  • Using both major and minor components produces higher recall than using major components alone.Source: Appendix D · p. 28

Appendix E. Clustering with PCA-based dimensionality reduction and K-means over KDDCUP99

The clustering experiment applies K-Means after PCA-based dimensionality reduction on KDDCUP99 and compares classical with quantum algorithm versions using the Calinski-Harabasz index. It projects the data into one PCA dimension and varies the number of clusters to assess clustering quality.

Clustering evaluation

  • The experiment compares classical and quantum PCA-plus-K-Means pipelines on KDDCUP99 using the Calinski-Harabasz index.The CH index is computed on the resulting clusters.Source: Appendix E · pp. 28–29
  • Figure E.8 reports CH comparisons between PCA with K-Means and q-PCA with q-Means across different numbers of clusters.Source: Figure E.8 · p. 29

Experimental setup

  • The data are projected into a one-dimensional PCA space before K-Means, with cluster counts varied from nk = 10 to 100 in steps of 10.The classical first principal component retains approximately 0.6 of the variance.Source: Appendix E · p. 29

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