Non-local operations play a crucial role in computer vision enabling the capture of long-range dependencies through weighted sums of features across the input, surpassing the constraints of traditional convolution operations that focus solely on local neighborhoods. Non-local operations typically require computing pairwise relationships between all elements in a set, leading to quadratic complexity in terms of time and memory. Due to the high computational and memory demands, scaling non-local neural networks to large-scale problems can be challenging. This article introduces a hybrid quantum-classical scalable non-local neural network, referred to as Quantum Non-Local Neural Network (QNL-Net), to enhance pattern recognition. The proposed QNL-Net relies on inherent quantum parallelism to allow the simultaneous processing of a large number of input features enabling more efficient computations in quantum-enhanced feature space and involving pairwise relationships through quantum entanglement. We benchmark our proposed QNL-Net with other quantum counterparts to binary classification with datasets MNIST and CIFAR-10. The simulation findings showcase our QNL-Net achieves cutting-edge accuracy levels in binary image classification among quantum classifiers while utilizing fewer qubits.

This parity illustrates the algorithm's robustness since, in expectation, the Euclidean distance conserves the sequence of resemblance among pixels. The NL-means, in addition to giving the comparison of the grey level in a single point, can compare the geometrical configuration in an entire neighborhood. A team in Carnegie Mellon University and Facebook AI Research, has been inspired by the above-mentioned classical non-local means and developed a non-local operation. It is usual to utilize CNN (Convolutional Neural Network) and RNN (Recurrent Neural Network) architectures in long-range dependency modeling for sequential data (image, time-series, signal, …), and these both process a local neighborhood. Consequently, we have to apply these local operations frequently. This repeating has some limitations; being computationally inefficient and making optimization harder.

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