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A Comparative Study of Encoding Strategies for Quantum Convolutional Neural Networks

Xingyun Feng

TL;DR

The paper addresses how input encoding choices affect QCNN performance under depolarizing noise and limited quantum resources. It develops an end-to-end differentiable PyTorch–Qiskit pipeline and performs a systematic, architecture-aware comparison of Angle, Amplitude, and Hybrid encodings on downsampled MNIST and Fashion-MNIST at $4\times 4$ and $8\times 8$. Key findings show Angle encoding is robust at aggressive compression, Hybrid encoding can surpass Angle with more feature bandwidth under moderate noise, and Amplitude encoding excels in lightweight or full-resolution settings, informing encoder selection under resolution, noise, and budget constraints. The results offer practical guidance for implementing QCNNs in near-term quantum hardware and highlight the value of an integrated, noise-aware training framework for encoding comparisons.

Abstract

Quantum convolutional neural networks (QCNNs) offer a promising architecture for near-term quantum machine learning by combining hierarchical feature extraction with modest parameter growth. However, any QCNN operating on classical data must rely on an encoding scheme to embed inputs into quantum states, and this choice can dominate both performance and resource requirements. This work presents an implementation-level comparison of three representative encodings -- Angle, Amplitude, and a Hybrid phase/angle scheme -- for QCNNs under depolarizing noise. We develop a fully differentiable PyTorch--Qiskit pipeline with a custom autograd bridge, batched parameter-shift gradients, and shot scheduling, and use it to train QCNNs on downsampled binary variants of MNIST and Fashion-MNIST at $4\times 4$ and $8\times 8$ resolutions. Our experiments reveal regime-dependent trade-offs. On aggressively downsampled $4\times 4$ inputs, Angle encoding attains higher accuracy and remains comparatively robust as noise increases, while the Hybrid encoder trails and exhibits non-monotonic trends. At $8\times 8$, the Hybrid scheme can overtake Angle under moderate noise, suggesting that mixed phase/angle encoders benefit from additional feature bandwidth. Amplitude-encoded QCNNs are sparsely represented in the downsampled grids but achieve strong performance in lightweight and full-resolution configurations, where training dynamics closely resemble classical convergence. Taken together, these results provide practical guidance for choosing QCNN encoders under joint constraints of resolution, noise strength, and simulation budget.

A Comparative Study of Encoding Strategies for Quantum Convolutional Neural Networks

TL;DR

The paper addresses how input encoding choices affect QCNN performance under depolarizing noise and limited quantum resources. It develops an end-to-end differentiable PyTorch–Qiskit pipeline and performs a systematic, architecture-aware comparison of Angle, Amplitude, and Hybrid encodings on downsampled MNIST and Fashion-MNIST at and . Key findings show Angle encoding is robust at aggressive compression, Hybrid encoding can surpass Angle with more feature bandwidth under moderate noise, and Amplitude encoding excels in lightweight or full-resolution settings, informing encoder selection under resolution, noise, and budget constraints. The results offer practical guidance for implementing QCNNs in near-term quantum hardware and highlight the value of an integrated, noise-aware training framework for encoding comparisons.

Abstract

Quantum convolutional neural networks (QCNNs) offer a promising architecture for near-term quantum machine learning by combining hierarchical feature extraction with modest parameter growth. However, any QCNN operating on classical data must rely on an encoding scheme to embed inputs into quantum states, and this choice can dominate both performance and resource requirements. This work presents an implementation-level comparison of three representative encodings -- Angle, Amplitude, and a Hybrid phase/angle scheme -- for QCNNs under depolarizing noise. We develop a fully differentiable PyTorch--Qiskit pipeline with a custom autograd bridge, batched parameter-shift gradients, and shot scheduling, and use it to train QCNNs on downsampled binary variants of MNIST and Fashion-MNIST at and resolutions. Our experiments reveal regime-dependent trade-offs. On aggressively downsampled inputs, Angle encoding attains higher accuracy and remains comparatively robust as noise increases, while the Hybrid encoder trails and exhibits non-monotonic trends. At , the Hybrid scheme can overtake Angle under moderate noise, suggesting that mixed phase/angle encoders benefit from additional feature bandwidth. Amplitude-encoded QCNNs are sparsely represented in the downsampled grids but achieve strong performance in lightweight and full-resolution configurations, where training dynamics closely resemble classical convergence. Taken together, these results provide practical guidance for choosing QCNN encoders under joint constraints of resolution, noise strength, and simulation budget.

Paper Structure

This paper contains 37 sections, 4 equations, 9 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Quantum Convolutional Neural Network (QCNN)
  4. Data Encoding Methods
  5. Angle encoding
  6. Amplitude encoding
  7. Hybrid encoding
  8. Methodology
  9. System Architecture
  10. QCNN Model and Data Encoding
  11. QCNN Architecture
  12. Data Encoding Schemes
  13. Datasets and Preprocessing
  14. Differentiable Training Framework
  15. Backward pass via batched parameter-shift
  16. ...and 22 more sections

Figures (9)

  • Figure 1: Schematic overview of the QCNN architecture used in this work.
  • Figure 2: Circuit-level schematic of the Angle, Amplitude, and Hybrid encoding schemes implemented in this study.
  • Figure 3: End-to-end parameter and data flow from classical inputs through encoding, QCNN processing, and gradient back-propagation.
  • Figure 4: Batched parameter-shift evaluation, aggregating all $\pm \pi/2$ weight shifts and all batch circuits into a single Estimator call.
  • Figure 5: Test accuracy versus depolarizing noise level for QCNN encoders on $4\times 4$ downsampled MNIST (Angle and Hybrid) and Fashion-MNIST (Hybrid).
  • ...and 4 more figures