ATP: Adaptive Threshold Pruning for Efficient Data Encoding in Quantum Neural Networks

TL;DR

The paper tackles the data encoding bottleneck in quantum neural networks by introducing Adaptive Threshold Pruning (ATP), which prunes nonessential input features before encoding to reduce entanglement and qubit requirements. It formalizes pruning with a threshold $\tau$ and optimizes $\tau$ via $L$-BFGS-B to maximize the test accuracy $Acc_{test}$ on the pruned data $\mathcal{X}_{\tau}$, using the rule $x_{\tau}(i,j)=0$ when class-averaged intensities fall below $\tau$. Across MNIST, FashionMNIST, CIFAR, and PneumoniaMNIST, ATP delivers higher accuracy with lower entanglement entropy than baseline encodings, and shows improved robustness under depolarizing noise and adversarial training. Hardware experiments on IBM Quantum hardware corroborate gains, indicating ATP enables more practical QNN deployment in resource-limited settings by reducing data-induced quantum overhead.

Abstract

Quantum Neural Networks (QNNs) offer promising capabilities for complex data tasks, but are often constrained by limited qubit resources and high entanglement, which can hinder scalability and efficiency. In this paper, we introduce Adaptive Threshold Pruning (ATP), an encoding method that reduces entanglement and optimizes data complexity for efficient computations in QNNs. ATP dynamically prunes non-essential features in the data based on adaptive thresholds, effectively reducing quantum circuit requirements while preserving high performance. Extensive experiments across multiple datasets demonstrate that ATP reduces entanglement entropy and improves adversarial robustness when combined with adversarial training methods like FGSM. Our results highlight ATPs ability to balance computational efficiency and model resilience, achieving significant performance improvements with fewer resources, which will help make QNNs more feasible in practical, resource-constrained settings.

Figures (6)

• Figure 1: Demonstration of the adaptive threshold pruning framework. The original image (top) is split into a 3x3 grid, with each section assessed for information density. The pruned image (bottom) shows filtered regions that fall below a defined intensity threshold in blue indicating areas that do not contribute significantly to the classification task, effectively freeing qubits and optimizing resources by focusing only on key areas of high relevance.
• Figure 2: Average accuracy across four datasets, comparing the performance of various encoding methods: Adaptive Threshold Pruning (ATP), Principal Component Analysis (PCA), Single Qubit Encoding (SQE), Angle, and Amplitude encoding. Horizontal error bars represent entanglement entropy (EE), with longer bars indicating higher entanglement. ATP generally achieves the highest accuracy with lower EE.
• Figure 3: Data distribution across positions in FashionMNIST for two classes (T-shirt/top and Trouser), with dashed lines marking threshold levels. Positions with lower variance are pruned to streamline training and focus on more informative regions.
• Figure 4: Test accuracy for MNIST class pairs with varying pruning thresholds. Moderate thresholds improve accuracy, while higher thresholds may exclude key information.
• Figure 5: Test accuracy for FashionMNIST class pairs with varying thresholds. Similar to MNIST, a threshold around 0.3 generally provides optimal performance.