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ATP: Adaptive Threshold Pruning for Efficient Data Encoding in Quantum Neural Networks
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Proposes Adaptive Threshold Pruning (ATP), a pre-encoding feature pruning method that tunes a per-dataset intensity threshold via L-BFGS-B to lower entanglement entropy and improve accuracy and adversarial robustness of small binary QNN classifiers.
Problem
QNNs are constrained by limited qubits and high entanglement, and redundant input features inflate circuit requirements and entanglement, hurting scalability and efficiency.
Approach
Prune low-information image grid regions before angle encoding, with the pruning threshold chosen by bi-level optimization (L-BFGS-B) that maximizes test accuracy, so that less redundant data yields lower entanglement entropy and better accuracy.
Key results
- ATP achieves the highest accuracy on (0,1) MNIST at 99.0% versus 96.0% for angle encoding, and 87.0% on PneumoniaMNIST versus 81.0% for angle encoding.
- ATP yields the lowest entanglement entropy in nearly all tasks, e.g. 0.39 vs 0.67 for angle encoding on MNIST (0,1) and 0.37 vs 0.88 on PneumoniaMNIST.
- Under FGSM (epsilon=0.3) without adversarial training, ATP reaches 67.2% on MNIST (0,1) vs 62.0% for angle encoding; ATP shows a 7% average gain over direct encoding on IBM Sherbrooke hardware for five MNIST subsets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adaptive threshold pruning before angle encoding instead of the strongest non-ATP encoding | QNN · MNIST (0,1) | accuracy: 99.0 -> 99.0 | No clear effect |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · MNIST (0,3) | accuracy: 89.0 -> 91.0 | Helped |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · MNIST (2,4) | accuracy: 85.0 -> 86.0 | Helped |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · MNIST (5,6) | accuracy: 86.0 -> 87.0 | Helped |
| Use adaptive threshold pruning before angle encoding instead of PCA | QNN · MNIST (2,8) | accuracy: 86.0 -> 83.0 | Hurt |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · FashionMNIST (0,1) | accuracy: 88.5 -> 91.5 | Helped |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · FashionMNIST (2,8) | accuracy: 86.0 -> 86.0 | No clear effect |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · FashionMNIST (3,9) | accuracy: 94.0 -> 94.0 | No clear effect |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · FashionMNIST (7,9) | accuracy: 82.0 -> 83.0 | Helped |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · CIFAR (0,1) | accuracy: 70.0 -> 74.2 | Helped |
| Use adaptive threshold pruning before angle encoding instead of angle encoding alone | QNN · PneumoniaMNIST (0,1) | accuracy: 81.0 -> 87.0 | Helped |
| Apply adaptive threshold pruning instead of angle encoding under depolarizing noise | QNN · CIFAR (0,1) | accuracy: 60.4 -> 61.0 | Helped |
Surprising findings
- Angle encoding unexpectedly achieved the highest accuracy on PneumoniaMNIST and CIFAR under FGSM attack in Table 4 for some tasks, contrary to the ATP narrative.
- ATP's accuracy on CIFAR (0,1) and other tasks was not uniformly best; for example, Angle encoding reached 94.0% on FashionMNIST (3,9), tying ATP.
Limitations
- Evaluated only on binary classification with small image datasets and a compact three-layer QNN.
- Adversarial robustness is limited; ATP alone lacks inherent robustness and relies on adversarial training.
- Threshold optimization incurs moderate computational overhead (about 15% over angle encoding).
Experimental setup
Datasets: MNIST FashionMNIST CIFAR PneumoniaMNIST
Benchmarks: MNIST FashionMNIST CIFAR PneumoniaMNIST
Metrics: accuracy entanglement entropy adversarial accuracy under FGSM
Baselines: Angle encoding Amplitude encoding PCA Single-Qubit Encoding (SQE)
Builds on: L-BFGS-B angle encoding FGSM
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