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Predictive Performance of Deep Quantum Data Re-uploading Models
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Shows theoretically and empirically that data re-uploading quantum models with deep encoding layers and limited qubits, on high-dimensional data, degrade toward random-guess predictive performance, and repetitions cannot fix this.
Problem
Predictive (unseen-data) performance of quantum data re-uploading models is poorly understood, especially when high-dimensional data must be encoded with few qubits through many encoding layers.
Approach
Bypasses the train/generalization error decomposition by analyzing the expected encoded state over the data distribution via Pauli-basis coefficient decay; shows the expected state converges exponentially to the maximally mixed state as encoding layers grow, and uses approximating circuits to show repetitions cannot undo this.
Key results
- Single-qubit classification on linearly separable data: test error rises toward 0.5 as encoding layers L increase, while training error stays low.
- Divergence between expected encoded state and maximally mixed state decays exponentially with encoding layers L (N=1, P=1 experiments).
- With N=8, P=2, MNIST (0/1) outperformed grayscale CIFAR-10, attributed to near-zero variance of MNIST pixels.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase encoding layers L (ablation) | Single-qubit data re-uploading model · Synthetic linearly separable classification | test error: to 0.5 | Hurt |
| Increase repetition count P (ablation) | Single-qubit data re-uploading model · Synthetic linearly separable classification | test error: converges to 0.5 faster | Hurt |
| Increase repetition count P (ablation) | Single-qubit data re-uploading model · Synthetic linearly separable classification | training error | Helped |
| Use more encoding layers at fixed parameter count (ablation) | Data re-uploading models · Same synthetic dataset (D=24) | test error: to 0.5 | Hurt |
| Use L=4 rather than L=1 (ablation) | Data re-uploading models with P=8 · Same synthetic dataset (D=24) | test error | Hurt |
| Use RGB rather than grayscale CIFAR-10 input (ablation) | Data re-uploading model (N=8, P=2) · CIFAR-10 airplane/automobile, 12 × 12 pixels | test accuracy | Hurt |
| Use MNIST rather than grayscale CIFAR-10 | Data re-uploading model (N=8, P=2) · MNIST digit 0/1 and CIFAR-10-Gray airplane/automobile | test accuracy | Helped |
| Increase repetition count P (ablation) | Data re-uploading models on real-world datasets · CIFAR-10-Gray, MNIST, and CIFAR-10-RGB | test accuracy | Hurt |
| Increase encoding layers L (ablation) | Data re-uploading model · Gaussian binary-classification divergence experiments | quantum divergence | Hurt |
| Train the model (ablation) | Data re-uploading model · Gaussian binary-classification divergence experiments | quantum divergence | No clear effect |
| Increase repetition count P after training (ablation) | Data re-uploading model (N=1) · Gaussian binary-classification divergence experiments | quantum divergence | No clear effect |
Surprising findings
- Increasing the number of repetitions P does not mitigate the degradation; with more repetitions the test error converges to 0.5 even faster as L grows.
- With L=1 the divergence stays near the theoretical bound regardless of repetitions, explaining why shallow-encoding models work well in practice.
Limitations
- Analysis assumes independent Gaussian data elements; strongly correlated high-dimensional data may avoid the limitation.
- Repetition analysis relies on approximating circuits used only for theory, which need many ancilla qubits.
Experimental setup
Datasets: synthetic linearly separable Gaussian data MNIST (digits 0/1, 12x12) CIFAR-10 airplane/automobile (grayscale and RGB, 12x12)
Benchmarks: MNIST CIFAR-10 airplane/automobile
Metrics: test error training error quantum divergence D2 accuracy
Baselines: Li et al. (encoding-layer bound)
Builds on: data re-uploading (Pérez-Salinas et al.) Li et al. encoding-layer analysis Petz-Rényi divergence
Closest papers by meaning
- Rethink the Role of Deep Learning towards Large-scale Quantum Systems (ICML 2025 · similarity 0.86)
- Exponential Quantum Communication Advantage in Distributed Inference and Learning (NeurIPS 2024 · similarity 0.84)
- ATP: Adaptive Threshold Pruning for Efficient Data Encoding in Quantum Neural Networks (CVPR 2025 · similarity 0.84)
- On the Relation between Trainability and Dequantization of Variational Quantum Learning Models (ICLR 2025 · similarity 0.82)
- Neural Auto-designer for Enhanced Quantum Kernels (ICLR 2024 · similarity 0.82)
- Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machine (NeurIPS 2026 · similarity 0.82)
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