Contemporary quantum computers face many critical challenges that limit their usefulness for practical applications. A primary limiting factor is classical-to-quantum (C2Q) data encoding, which requires specific circuits for quantum state initialization. The required state initialization circuits are often complex and violate decoherence constraints, particularly for I/O intensive applications. Existing Noisy Intermediate-Scale Quantum (NISQ) devices are noise-sensitive and have low quantum bit (qubit) counts, thus limiting the applicability of C2Q circuits for encoding large and realistic datasets. This has made the study of complete and realistic circuits that include data encoding challenging and has also led to a heavy dependency on costly and resource-intensive simulations on classical platforms. In this work, we propose a cost-effective, classical-hardware-accelerated framework for realistic and complete emulation of quantum algorithms. The emulation framework incorporates components for the critical C2Q data encoding process, as well as architectures for quantum algorithms such as the quantum Haar transform (QHT). The framework is used to investigate optimizations for C2Q and QHT algorithms, and the corresponding optimized quantum circuits are presented. The framework is implemented on a High-Performance Reconfigurable Computer (HPRC) which emulates the proposed QHT circuits combined with proposed C2Q data encoding methods. For performance benchmarks, CPU-based emulations and simulations on a state-of-the-art quantum computing simulator are also carried out. Results show that the proposed hardware-accelerated emulation framework is more efficient in terms of speed and scalability compared to CPU-based emulation and simulation.

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.

With the rapid advancement of quantum computing technology, there is a strong motivation to explore suitable practical applications for quantum algorithms and quantum computers. This chapter focuses on reviewing recent research on practical applications of quantum computing, specifically dimension reduction, pattern recognition, quantum sorting, and quantum communications for which optimized/modified versions of the quantum wavelet transform (QWT) and Grover’s algorithm are presented. For practical implementations of the presented algorithms, this chapter also includes methodologies for classical-to-quantum (C2Q) data encoding and quantum-to-classical (Q2C) data decoding. Additionally, the chapter presents an efficient quantum sorting technique by combining perfect-shuffle and bitonic networks. In the domain of quantum communications, the chapter reviews a technique that combines chaotic communications with quantum key distribution (QKD) to enhance both security and communication range. The effectiveness of these techniques is validated through practical results obtained from experiments conducted on IBM-Q simulators and hardware, as well as on high-performance-reconfigurable-computers (HPRCs). This chapter aims to provide readers with a comprehensive understanding of these applications, covering the necessary prerequisites by showcasing the potential of quantum computing in various domains for innovative problem-solving.

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.

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 in 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.