The convolution operation plays a vital role in a wide range of critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. In existing implementations, particularly in quantum neural networks, convolution operations are usually approximated by the application of filters with data strides that are equal to the filter window sizes. One challenge with these implementations is preserving the spatial and temporal localities of the input features, specifically for data with higher dimensions. In addition, the deep circuits required to perform quantum convolution with a unity stride, especially for multidimensional data, increase the risk of violating decoherence constraints. In this work, we propose depth-optimized circuits for performing generalized multidimensional quantum convolution operations with unity stride targeting applications that process data with high dimensions, such as hyperspectral imagery and remote sensing. We experimentally evaluate and demonstrate the applicability of the proposed techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.
The convolution operation plays a vital role in a wide range of critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. In existing implementations, particularly in quantum neural networks, convolution operations are usually approximated by the application of filters with data strides that are equal to the filter window sizes. One challenge with these implementations is preserving the spatial and temporal localities of the input features, specifically for data with higher dimensions. In addition, the deep circuits required to perform quantum convolution with a unity stride, especially for multidimensional data, increase the risk of violating decoherence constraints. In this work, we propose depth-optimized circuits for performing generalized multidimensional quantum convolution operations with unity stride targeting applications that process data with high dimensions, such as hyperspectral imagery and remote sensing. We experimentally evaluate and demonstrate the applicability of the proposed techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.
Convolution is a fundamental operation in many critical algorithms across various domains, such as digital image processing, convolutional neural networks, and quantum machine learning. Existing implementations of the convolution operator, for example, in quantum neural networks, usually approximate the operation by applying filters with a stride equal to the filter window size. Therefore, it becomes challenging to accurately capture the spatial and temporal locality of the input features, particularly for data of higher dimensions than the commonly-investigated 1-D or 2-D data. Moreover, performing quantum convolution with a unity stride on data of higher dimensions typically requires deep quantum circuits that risk exceeding decoherence constraints. In this work, we propose depth-optimized techniques of implementing multidimensional quantum convolution operations with arbitrary filtering and unity stride. We present theoretical analysis of our techniques and provide the corresponding optimized quantum circuits. We also experimentally demonstrate the applicability of our techniques by using real-world, high-resolution, multidimensional image data on a state-of-the-art quantum simulator from IBM Quantum.
Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role for extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data, to 2-D image data, to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.
Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than a fully connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multifeatures in multidimensional data. In this paper, we present an multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multifeature quantum convolution with average and Euclidean pooling, thus adapting the CNN structure to a variational quantum algorithm (VQA). The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results show the favorable characteristics of our proposed techniques compared with existing work with respect to a number of quantitative metrics, such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count.
Algorithms such as quantum wavelet transform (QWT) can be utilized on quantum processors to gain significant speedup compared to their classical counterparts. Domains such as high-energy-physics and remote-sensing hyperspectral imagery require high compute capabilities and can benefit from applying QWT for dimension reduction of multidimensional data. However, quantum circuits for QWT include permutations that contribute to large overall circuit depth. Deep circuits pose a critical challenge for state-of-the-art quantum computers because of quantum decoherence. In this work, we propose QWT circuits, which are optimized in terms of circuit depth, to account for the effects of decoherence, and resulting in high fidelity and efficient implementation on quantum processors. We present the circuits in generalized forms and show that they can be used for multilevel decomposable, multidimensional wavelet operations. Experimental evaluation of the proposed circuits is performed through simulation using MATLAB and IBM-Q qasm, and implemented on a real 15-qubit quantum processor from IBM.
Image classification plays a vital role in large-scale data analysis, especially in object recognition tasks using advanced Deep Learning (DL) frameworks. However, the growing complexity and computational demands of modern DL models have introduced challenges related to scalability and efficiency. Quantum Computing (QC) has emerged as a promising alternative, capable of addressing these limitations by leveraging the principles of Quantum Machine Learning (QML). However, many existing QML models require a large number of qubits, which poses limitations within the current Noisy Intermediate-Scale Quantum (NISQ) era. This work introduces a novel Adaptive Quantum Convolutional Neural Network (AQCNN) designed for efficient and scalable image classification within the constraints of NISQ devices. Addressing the limitations of existing QML approaches, particularly the high qubit requirements, AQCNN incorporates a resource-efficient quantum convolutional layer that performs localized quantum filtering using parameterized quantum circuits. A classical preprocessing layer encodes input features to reduce qubit load, followed by quantum embedding and hybrid quantum-classical layers that optimize feature extraction and classification performance. The model leverages an adaptive quantum convolution strategy, minimizing quantum gate depth and circuit complexity while preserving critical spatial hierarchies in image data. Evaluated on benchmark datasets, AQCNN achieved 95.88% accuracy on MNIST and 95.68% on FMNIST, outperforming comparable QML architectures. Additionally, the model supports scalable execution through parallel quantum circuit arrays, enabling practical deployment on current quantum hardware. This architecture demonstrates a significant advance in quantum-assisted image classification, balancing performance with qubit and gate efficiency. The integration of adaptive quantum convolution and hybrid processing not only enhances classification accuracy but also provides a viable path forward for deploying QML solutions under realistic hardware constraints.
The resource need for deep learning and quantum computers' high computing power potential encourage collaboration between the two fields. Today, variational quantum circuits are used to perform the convolution operation with quantum computing. However, the results produced by variational circuits do not show a direct resemblance to the classical convolution operation. Because classical data is encoded into quantum data with their exact values in value-encoded methods, in contrast to variational quantum circuits, arithmetical operations can be applied with high accuracy. In this study, value-encoded quantum circuits for convolution and pooling operations are proposed to apply deep learning in quantum computers in a traditional and proven way. To construct the convolution and pooling operations, some modules such as addition, multiplication, division, and comparison are created. In addition, a window-based framework for quantum image processing applications is proposed. The generated convolution and pooling circuits are simulated on the IBM QISKIT simulator in parallel thanks to the proposed framework. The obtained results are verified by the expected results. Due to the limitations of quantum simulators and computers in the NISQ era, the used grayscale images are resized to 8x8 and the resolution of the images is reduced to 3 qubits. With developing the quantum technologies, the proposed approach can be applied for bigger and higher resolution images. Although the proposed method causes more qubit usage and circuit depth compared to variational convolutional circuits, the results they produce are exactly the same as the classical convolution process.