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：量子机器学习模型利用量子电路作为量子特征映射(QFMs)，因其在学习任务中增强的表达能力而受到认可。这类模型已在特定分类问题族上展现出严格的端到端量子加速优势。然而，由于电路噪声和硬件限制，在真实量子硬件上部署深层QFMs仍面临挑战。此外，变分量子算法常遭遇计算瓶颈，尤其在精确梯度估计方面，这大大增加了训练期间的量子资源需求。我们提出迭代量子特征映射(IQFMs)，这是一种混合量子-经典框架，通过迭代连接浅层QFMs与经典计算的增强权重来构建深层架构。通过结合对比学习和逐层训练机制，IQFMs框架有效减少了量子运行时间并缓解了噪声导致的性能退化。在涉及噪声量子数据的任务中，数值实验表明，IQFMs框架无需优化变分量子参数，即优于量子卷积神经网络。即使对于典型的经典图像分类基准，精心设计的IQFMs框架也能达到与经典神经网络相当的性能。该框架为解决当前局限并充分发挥量子增强机器学习的潜力提供了一条有前景的路径。