Exploiting Data Locality for Improving Multidimensional Variational Quantum Classification

Quantum computing presents an opportunity to accelerate machine learning (ML) tasks on quantum processors in a similar vein to existing classical accelerators, such as graphical processing units (GPUs). In the classical domain, convolutional neural networks (CNNs) effectively exploit data locality using the convolution operation to reduce the number of fully-connected operations in multi-layer perceptrons (MLPs). Preserving data locality enables the pruning of training parameters, which results in reduced memory requirements and shorter training time without compromising classification accuracy. However, contemporary quantum machine learning (QML) algorithms do not leverage the data locality of input features in classification workloads, particularly for multidimensional data. This work presents a multidimensional quantum convolutional classifier (MQCC) that adapts the CNN structure to a variational quantum algorithm (VQA). The proposed MQCC uses quantum implementations of multidimensional convolution, pooling based on the quantum Haar transform (QHT) and partial measurement, and fully-connected operations. Time-complexity analysis will be presented to demonstrate the speedup of the proposed techniques in comparison to classical convolution and pooling operations on modern CPUs and/or GPUs. Experimental work is conducted on state-of-the-art quantum simulators from IBM Quantum and Xanadu modeling noise-free and noisy quantum devices. High-resolution multidimensional images are used to demonstrate the correctness and scalability of the convolution and pooling operations. Furthermore, the proposed MQCC model is tested on a variety of common datasets against multiple configurations of related ML and QML techniques. Based on standard metrics such as log loss, classification accuracy, number of training parameters, circuit depth, and gate count, it will be shown that MQCC can deliver a faithful implementation of CNNs on quantum machines. Additionally, it will be shown that by exploiting data locality MQCC can achieve improved classification over contemporary QML methods.