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 promises of advanced quantum computing technology have driven research in the simulation of quantum computers on classical hardware, where the feasibility of quantum algorithms for real-world problems can be investigated. In domains such as High Energy Physics (HEP) and Remote Sensing Hyperspectral Imagery, classical computing systems are held back by enormous readouts of high-resolution data. Due to the multi-dimensionality of the readout data, processing and performing pattern recognition operations for this enormous data are both computationally intensive and time-consuming. In this article, we propose a methodology that utilizes Quantum Haar Transform (QHT) and a modified Grover's search algorithm for time-efficient dimension reduction and dynamic pattern recognition in data sets that are characterized by high spatial resolution and high dimensionality. QHT is performed on the data to reduce its dimensionality at preserved spatial locality, while the modified Grover's search algorithm is used to search for dynamically changing multiple patterns in the reduced data set. By performing search operations on the reduced data set, processing overheads are minimized. Moreover, quantum techniques produce results in less time than classical dimension reduction and search methods. The feasibility of the proposed methodology is verified by emulating the quantum algorithms on classical hardware based on field programmable gate arrays (FPGAs). We present designs of the quantum circuits for multi-dimensional QHT and multi-pattern Grover's search. We also present two emulation techniques and the corresponding hardware architectures for this methodology. A high performance reconfigurable computer (HPRC) was used for the experimental evaluation, and high-resolution images were used as the input data set. Analysis of the methods and implications of the experimental results are discussed.