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 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 multi-features in multidimensional data. In this paper, we present a multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multi-feature quantum convolution with average and Euclidean pooling and thus adapting the CNN structure to a variational quantum algorithm (VQA). Average pooling is based on the quantum Haar transform (QHT) and Euclidean pooling is based on partial quantum measurement. 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 showed favorable characteristics of our proposed techniques compared to 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.