Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging this gap by presenting the first fully-coherent quantum implementation of a multilayer neural network with non-linear activation functions. Our constructions mirror widely used deep learning architectures based on ResNet, and consist of residual blocks with multi-filter 2D convolutions, sigmoid activations, skip-connections, and layer normalizations. We analyse the complexity of inference for networks under three quantum data access regimes. Without any assumptions, we establish a quadratic speedup over classical methods for shallow bilinear-style networks. With efficient quantum access to the weights, we obtain a quartic speedup over classical methods. With efficient quantum access to both the inputs and the network weights, we prove that a network with an $N$-dimensional vectorized input, $k$ residual block layers, and a final residual-linear-pooling layer can be implemented with an error of $\epsilon$ with $O(\text{polylog}(N/\epsilon)^k)$ inference cost.

翻译：容错量子处理单元（QPUs）有望在特定计算任务中实现指数级加速，但其与现代深度学习流程的整合仍不明确。本研究通过提出首个具有非线性激活函数的多层神经网络的完全相干量子实现，朝着弥合这一差距迈出了一步。我们的构造模拟了基于ResNet的广泛使用的深度学习架构，包含具有多滤波器二维卷积、Sigmoid激活函数、跳跃连接和层归一化的残差块。我们分析了三种量子数据访问机制下网络的推理复杂度。在无任何假设的情况下，我们证明了浅层双线性风格网络相较于经典方法具有二次加速。在能够高效量子访问权重的条件下，我们获得了相较于经典方法的四次加速。在能够同时对输入和网络权重进行高效量子访问的条件下，我们证明了对于具有$N$维向量化输入、$k$个残差块层以及一个最终残差-线性-池化层的网络，可以以$O(\text{polylog}(N/\epsilon)^k)$的推理成本实现误差为$\epsilon$的运算。