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The role of data embedding in quantum autoencoders for improved anomaly detection

Jack Y. Araz, Michael Spannowsky

TL;DR

This work investigates how data embedding methods influence the performance of Quantum Autoencoders (QAEs) for anomaly detection. By comparing standard angle embedding with data reuploading, parallel embedding, and alternate embedding, and by employing strongly entangling variational layers, the study demonstrates that embedding choices can dramatically improve the representability of data and anomaly-detection accuracy across both 2D and high-dimensional datasets. While enhanced embeddings require more qubits and deeper circuits, the gains suggest embedding strategy is a critical lever for QAE-based anomaly detection, especially as quantum hardware scales toward fault-tolerant regimes. The findings underscore the practical importance of embedding design for robust quantum machine learning in anomaly detection tasks.

Abstract

The performance of Quantum Autoencoders (QAEs) in anomaly detection tasks is critically dependent on the choice of data embedding and ansatz design. This study explores the effects of three data embedding techniques, data re-uploading, parallel embedding, and alternate embedding, on the representability and effectiveness of QAEs in detecting anomalies. Our findings reveal that even with relatively simple variational circuits, enhanced data embedding strategies can substantially improve anomaly detection accuracy and the representability of underlying data across different datasets. Starting with toy examples featuring low-dimensional data, we visually demonstrate the effect of different embedding techniques on the representability of the model. We then extend our analysis to complex, higher-dimensional datasets, highlighting the significant impact of embedding methods on QAE performance.

The role of data embedding in quantum autoencoders for improved anomaly detection

TL;DR

This work investigates how data embedding methods influence the performance of Quantum Autoencoders (QAEs) for anomaly detection. By comparing standard angle embedding with data reuploading, parallel embedding, and alternate embedding, and by employing strongly entangling variational layers, the study demonstrates that embedding choices can dramatically improve the representability of data and anomaly-detection accuracy across both 2D and high-dimensional datasets. While enhanced embeddings require more qubits and deeper circuits, the gains suggest embedding strategy is a critical lever for QAE-based anomaly detection, especially as quantum hardware scales toward fault-tolerant regimes. The findings underscore the practical importance of embedding design for robust quantum machine learning in anomaly detection tasks.

Abstract

The performance of Quantum Autoencoders (QAEs) in anomaly detection tasks is critically dependent on the choice of data embedding and ansatz design. This study explores the effects of three data embedding techniques, data re-uploading, parallel embedding, and alternate embedding, on the representability and effectiveness of QAEs in detecting anomalies. Our findings reveal that even with relatively simple variational circuits, enhanced data embedding strategies can substantially improve anomaly detection accuracy and the representability of underlying data across different datasets. Starting with toy examples featuring low-dimensional data, we visually demonstrate the effect of different embedding techniques on the representability of the model. We then extend our analysis to complex, higher-dimensional datasets, highlighting the significant impact of embedding methods on QAE performance.
Paper Structure (9 sections, 9 equations, 5 figures, 4 tables)

This paper contains 9 sections, 9 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Quantum Autoencoder
  3. Data embedding and the choice of ansatz
  4. Results
  5. Low dimensional datasets
  6. High dimensional datasets
  7. Summary & Conclusion
  8. Dataset and code availability
  9. Acknowledgement

Figures (5)

  • Figure 1: Schematic comparison between classical (top panel) and quantum (bottom panel) autoencoders. Encoder and decoder are labelled as $\mathcal{E}$ and $\mathcal{D}$, respectively.
  • Figure 2: Schematic representation of a quantum autoencoder circuit.
  • Figure 3: Schematic representation of the quantum autoencoder circuit. $\mathcal{E}(\mathbf{x}, \Theta)$ represents the encoder circuit, $H$ is the Hadamard gate, and $\mathcal{H}_i$ represents different Hilbert spaces.
  • Figure 4: Selected results from 2D datasets. From left to right, the image shows moons, s-curve, circle and doughnut datasets and from top to bottom, it shows the models $M_1$, $M_5$ and $M_9$.
  • Figure 5: The ROC curves show the results for credit card fraud data, where rows represent 1 and 3 reference states used in the model and from left to right, each plot shows 4, 6, and 8-layer models. Letters are used in the legend to represent data-reuploading (R), parallel embedding (P) and alternate embedding (A). The dashed black line represents the random choice.