<p>Convolutional operations are a cornerstone for extracting hierarchical spatial features and a foundational component of modern machine learning. However, implementing convolutional layers on NISQ-era hardware is hindered by significant resource hurdles. The primary challenge is the data-loading bottleneck, as qubit registers often scale with the large input image size. Furthermore, many methods require deep arithmetic circuits or numerous precision ancillas, rendering them infeasible. This paper proposes a qubit-efficient, hybrid quantum-classical algorithm that mitigates these limitations. Our key innovation is a patch-based framework that reformulates convolution as parallel inner products computed within a small, kernel-sized Hilbert space. This design makes the number of data-holding qubits scale with the small kernel size rather than the large image size, corresponding to an exponential reduction in the dimension of the data-encoding Hilbert space. The algorithm uses two controlled multiplexer oracles to prepare patch and filter states in superposition. In addition, a modified, parallel Hadamard test then directly estimates all normalized inner products. This method avoids deep quantum arithmetic and precision ancillas, instead achieving accuracy by statistically aggregating repeated measurements. Results show a successful reconstruction of the classical feature map and confirm the theoretical convergence. This work provides a pragmatic, resource-efficient blueprint for implementing core machine learning primitives on near-term quantum devices.</p>