A Scalable Quantum Non-local Neural Network for Image Classification

TL;DR

This work tackles the quadratic complexity of classical non-local neural networks by introducing a scalable hybrid quantum-classical non-local network (QNL-Net) that leverages quantum parallelism and entanglement to efficiently model long-range dependencies in images. It integrates a four-qubit quantum module (Encoder, VQC, measurement) into CNN- or PCA-driven pipelines (CNN-QNL-Net and PCA-QNL-Net), with three entanglement strategies (Ansatz-0/1/2) and a final Pauli-$Z$ readout to produce a binary decision. On MNIST (0 vs 1) and CIFAR-10 (birds vs ships), the CNN-QNL-Net achieves state-of-the-art-like accuracy while using only 4 qubits, outperforming several larger-qubit quantum baselines and illustrating a scalable path for quantum-assisted vision in the NISQ era. The results demonstrate that hybrid quantum-classical architectures can capture long-range structure more efficiently than purely classical NL blocks in low-qubit regimes, with potential applicability to broader image-classification tasks as quantum hardware advances.

Abstract

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.

Figures (5)

• Figure 1: The Quantum Non-local Neural Network (QNL-Net) comprises a four-qubit circuit composed of three parts: (i) Encoder: To encode classical data into quantum states. (ii) Variational Quantum Circuit (VQC): classically trainable quantum circuit. (iii) Measurement: the circuit is measured at qubit $0$ in the Pauli-$Z$ basis. The encoder and the VQC ansatz have $r$ and $D$ repetitions respectively. The Encoder has $4r$ trainable parameters and the VQC has $5D$ trainable parameters (for $n=4$ input qubits).
• Figure 2: The three ansatzes used as the Variational Quantum Circuits (VQC) in our QNL-Net mechanism. $R_x, R_y, R_z$ rotation gates represent single-qubit rotations along the $x, y, z$ axes, respectively, with trainable parameters. The strategies for performing entanglement using $C_X$ gates (CNOT) are: cyclic pattern (Ansatz-0), reverse linear chain (Ansatz-1), and a mixed pattern (Ansatz-2).
• Figure 3: The proposed hybrid Classical-quantum QNL-Net frameworks comprises the following components: (a) CNN-QNL-Net: Two convolutional layers with ReLU activation and max-grouping are used to extract features from input images. Subsequently, a dropout layer is applied, followed by flattening of the features. Two fully connected (FC) layers are utilized to preprocess the data for integration with the QNL-Net. (b) PCA-QNL-Net: Principal Component Analysis (PCA) is utilized to reduce the dimensionality of the input data to 4 components. These components are processed by a fully connected (FC) layer before being input into the proposed QNL-Net. (c) QNL-Net: This component of the pipeline conducts computations on the four features obtained from the classical models within the mechanism and generates a single measurement from qubit 0. (d) Post-QNL-Net Classical Computation: A fully connected layer is employed to fine-tune the quantum output. Subsequently, this output is transformed and concatenated as required for binary classification.
• Figure 4: Training loss convergence and test accuracy plots for the CNN-QNL-Net and PCA-QNL-Net models for the three ansatzes with one feature map repetition ($r = 1$) and one ansatz repetition ($D = 1$). (a) and (b) display the training loss convergence on MNIST and CIFAR-10, respectively. (c) and (d) show the corresponding test accuracy on these datasets.
• Figure 5: Sample images from the datasets used: MNIST lecun1998 (classes 0 and 1) and CIFAR-10 alexnet2012 (classes 2 and 8, i.e., bird and ship respectively).