Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for specific families of classification problems. However, deploying deep QFMs on real quantum hardware remains challenging due to circuit noise and hardware constraints. Additionally, variational quantum algorithms often suffer from computational bottlenecks, particularly in accurate gradient estimation, which significantly increases quantum resource demands during training. We propose Iterative Quantum Feature Maps (IQFMs), a hybrid quantum-classical framework that constructs a deep architecture by iteratively connecting shallow QFMs with classically computed augmentation weights. By incorporating contrastive learning and a layer-wise training mechanism, the IQFMs framework effectively reduces quantum runtime and mitigates noise-induced degradation. In tasks involving noisy quantum data, numerical experiments show that the IQFMs framework outperforms quantum convolutional neural networks, without requiring the optimization of variational quantum parameters. Even for a typical classical image classification benchmark, a carefully designed IQFMs framework achieves performance comparable to that of classical neural networks. This framework presents a promising path to address current limitations and harness the full potential of quantum-enhanced machine learning.

翻译：利用量子电路作为量子特征映射（QFMs）的量子机器学习模型，因其在学习任务中增强的表达能力而受到认可。此类模型已针对特定分类问题族展示了严格的端到端量子加速。然而，由于电路噪声和硬件限制，在真实量子硬件上部署深度QFMs仍然具有挑战性。此外，变分量子算法常常面临计算瓶颈，特别是在精确梯度估计方面，这显著增加了训练期间的量子资源需求。我们提出了迭代量子特征映射（IQFMs），这是一种混合量子-经典框架，通过迭代地将浅层QFMs与经典计算的增强权重相连接来构建深度架构。通过结合对比学习和分层训练机制，IQFMs框架有效减少了量子运行时间并缓解了噪声引起的性能下降。在涉及含噪量子数据的任务中，数值实验表明，IQFMs框架的性能优于量子卷积神经网络，且无需优化变分量子参数。即使对于典型的经典图像分类基准任务，精心设计的IQFMs框架也能达到与经典神经网络相当的性能。该框架为应对当前局限性和充分利用量子增强机器学习的全部潜力提供了一条有前景的路径。