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A Parameter-Efficient Quantum Anomaly Detection Method on a Superconducting Quantum Processor

Maida Wang, Jinyang Jiang, Peter V. Coveney

TL;DR

PEQAD tackles anomaly detection with quantum machine learning on NISQ devices by proposing a parameter-efficient quantum neural network that maps data into a feature space and encodes it as a hypersphere with centre $\boldsymbol c$ and radius $R$. It provides a theoretical expressivity analysis using covering numbers and analyzes robustness to depolarizing noise, showing the method can match or surpass classical baselines with far fewer parameters. Empirically, PEQAD attains around 90%+ AUC on MNIST/FashionMNIST in emulation while requiring only ~200 parameters, and achieves 80–83% accuracy on a 4-qubit superconducting processor without error mitigation, demonstrating practical viability in the NISQ era. Together, these results underscore the potential of parameter-efficient quantum anomaly detection for general image datasets, enabling scalable quantum learning with limited hardware resources.

Abstract

Quantum machine learning has gained attention for its potential to address computational challenges. However, whether those algorithms can effectively solve practical problems and outperform their classical counterparts, especially on current quantum hardware, remains a critical question. In this work, we propose a novel quantum machine learning method, called Parameter-Efficient Quantum Anomaly Detection (PEQAD), for practical image anomaly detection, which aims to achieve both parameter efficiency and superior accuracy compared to classical models. Emulation results indicate that PEQAD demonstrates favourable recognition capabilities compared to classical baselines, achieving an average accuracy of over 90% on benchmarks with significantly fewer trainable parameters. Theoretical analysis confirms that PEQAD has a comparable expressivity to classical counterparts while requiring only a fraction of the parameters. Furthermore, we demonstrate the first implementation of a quantum anomaly detection method for general image datasets on a superconducting quantum processor. Specifically, we achieve an accuracy of over 80% with only 16 parameters on the device, providing initial evidence of PEQAD's practical viability in the noisy intermediate-scale quantum era and highlighting its significant reduction in parameter requirements.

A Parameter-Efficient Quantum Anomaly Detection Method on a Superconducting Quantum Processor

TL;DR

PEQAD tackles anomaly detection with quantum machine learning on NISQ devices by proposing a parameter-efficient quantum neural network that maps data into a feature space and encodes it as a hypersphere with centre and radius . It provides a theoretical expressivity analysis using covering numbers and analyzes robustness to depolarizing noise, showing the method can match or surpass classical baselines with far fewer parameters. Empirically, PEQAD attains around 90%+ AUC on MNIST/FashionMNIST in emulation while requiring only ~200 parameters, and achieves 80–83% accuracy on a 4-qubit superconducting processor without error mitigation, demonstrating practical viability in the NISQ era. Together, these results underscore the potential of parameter-efficient quantum anomaly detection for general image datasets, enabling scalable quantum learning with limited hardware resources.

Abstract

Quantum machine learning has gained attention for its potential to address computational challenges. However, whether those algorithms can effectively solve practical problems and outperform their classical counterparts, especially on current quantum hardware, remains a critical question. In this work, we propose a novel quantum machine learning method, called Parameter-Efficient Quantum Anomaly Detection (PEQAD), for practical image anomaly detection, which aims to achieve both parameter efficiency and superior accuracy compared to classical models. Emulation results indicate that PEQAD demonstrates favourable recognition capabilities compared to classical baselines, achieving an average accuracy of over 90% on benchmarks with significantly fewer trainable parameters. Theoretical analysis confirms that PEQAD has a comparable expressivity to classical counterparts while requiring only a fraction of the parameters. Furthermore, we demonstrate the first implementation of a quantum anomaly detection method for general image datasets on a superconducting quantum processor. Specifically, we achieve an accuracy of over 80% with only 16 parameters on the device, providing initial evidence of PEQAD's practical viability in the noisy intermediate-scale quantum era and highlighting its significant reduction in parameter requirements.

Paper Structure

This paper contains 22 sections, 6 theorems, 96 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Quantum Computing
  4. Methods
  5. Modelling
  6. Data Encoding and Ansätze
  7. Training Process
  8. Characterization of PEQAD's Expressivity
  9. Implementation and Results
  10. Noiseless Emulation Results
  11. Results on a Superconducting Quantum Processor
  12. Conclusion
  13. Acknowledge
  14. Expressivity of Parameter-Efficient Quantum Anomaly Detection
  15. Expressivity of Parameter-Efficient Quantum Anomaly Detection on Noisy Devices
  16. ...and 7 more sections

Key Result

Theorem 1

For $\varepsilon\in (0,\frac{1}{10})$, the covering number of the hypothesis space of PEQAD can be represented as follows: where $\mathcal{H}$ denotes the function space represented by PEQAD, $N (\mathcal{H}, \varepsilon, \|\cdot\|)$ represents its covering number, and $\boldsymbol{c}$ is the centre of the hypersphere.

Figures (10)

  • Figure 1: Diagram of the variational quantum circuit. (a) The first set of parameter-containing gates is used to embed classical features into the quantum circuit, and the rest of them are trainable gates. (b) CNOT gates for entanglement. (c) The measurement part maps quantum states back to classical vectors.
  • Figure 2: Conceptual diagram of Parameter-Efficient Quantum Anomaly Detection (PEQAD), which is a quantum-based anomaly detection algorithm that adopts QNN to map "normal data" into the hypersphere. Data points residing within the interior of the hypersphere will be labelled as "normal data", whereas those outside the hypersphere will be considered "abnormal data".
  • Figure 3: Training process of the PEQAD algorithm. (a) The pre-training neural network of the method consists of two parts: a quantum encoding layer and a classical decoding layer, where the quantum encoding layer is consistent with the PEQAD network. After the quantum encoding layer, the centre of the hypersphere mapped by PEQAD can be obtained. (b) The PEQAD neural network is composed of an amplitude encoding part (blue part), a VQC part, a measurement part and a PEQAD post-processing part.
  • Figure 4: Expressivity of PEQAD. If $\mathcal{H}$ is of moderate size and effectively encompasses the target concepts (purple solid star), the inferred hypothesis may closely approximate the target concept.
  • Figure 5: Ablation study on the effects of VQC's depth, structure, number of parameters, and training epochs. Although the effect of the PEQAD and its conventional counterpart DSVDD varies with settings variation, PEQAD always outperforms DSVDD under the same conditions.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Definition 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Definition 2: Operator norm
  • Lemma 1: Lemma 5, barthel2018fundamental
  • Lemma 2: Lemma 2, du2022efficient