深度量子数据重加载模型在高维数据上预测性能会随层数增加而急剧下降。
Predictive Performance of Deep Quantum Data Re-uploading Models
- 理论证明：层数越多，高维数据下预测性能越接近随机猜测。
- 实验验证：合成与真实数据集均显示深层结构性能恶化。
- 建议：处理高维数据应选宽架构而非深窄架构。
包含数据重加载电路的量子机器学习模型因其卓越的表达能力和可训练性受到广泛关注。然而，其对未见数据生成准确预测的能力——即预测性能——尚未得到充分研究。本研究揭示了在数据重加载模型中采用深度编码层时存在的根本性局限。具体而言，我们从理论上证明，当使用有限量子比特处理高维数据时，随着编码层数的增加，模型的预测性能会逐渐退化至接近随机猜测水平。在此情况下，重复数据加载无法缓解性能下降。该结论在合成线性可分数据集和真实世界数据集上的实验中得到验证。结果表明，处理高维数据时，应设计更宽的电路架构，而非更深更窄的结构。
原文摘要 · Abstract (English)
Quantum machine learning models incorporating data re-uploading circuits have garnered significant attention due to their exceptional expressivity and trainability. However, their ability to generate accurate predictions on unseen data, referred to as the predictive performance, remains insufficiently investigated. This study reveals a fundamental limitation in predictive performance when deep encoding layers are employed within the data re-uploading model. Concretely, we theoretically demonstrate that when processing high-dimensional data with limited-qubit data re-uploading models, their predictive performance progressively degenerates to near random-guessing levels as the number of encoding layers increases. In this context, the repeated data uploading cannot mitigate the performance degradation. These findings are validated through experiments on both synthetic linearly separable datasets and real-world datasets. Our results demonstrate that when processing high-dimensional data, the quantum data re-uploading models should be designed with wider circuit architectures rather than deeper and narrower ones.
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