Design of quantum image processing algorithms in quantum computing

Abstract

Digital image processing deals with the use of algorithms to analyze and manipulate images. Conventional digital images are processed with classical computers, while images stored as quantum information can be processed using quantum algorithms. Quantum computing offers greater efficiency than classical computers due to features such as superposition and entanglement, which promote parallelism and reduce the number of operations required. Quantum computing represents information as quantum bits or qubits, which, unlike classical bits, are in a probabilistic state and are defined by linear algebra rather than Boolean algebra. Effective use of quantum algorithms requires proper utilization of qubit properties in storing and processing information. This thesis proposed different approaches to image processing with quantum. Firstly, in quantum image processing, images are represented in qubits; different image representations have distinct features and advantages. A quantum image filtering approach for rotation gate-based image representation is proposed. The filter is proposed as a quantum gate that combines addition and subtraction operations on the angle of rotation. Image thresholding was achieved using well-known quantum algorithms: QAOA and Grover search. The best threshold was found using an optimization approach on a QAOA circuit. Then, a Grover search circuit is used to find pixel values based on the threshold. The oracle operator is designed to take a threshold value as input and search for a range of values. Graph applications in image processing can encode image features and relationships between regions. A quantum optimization approach is employed to segment the image using the graph cut algorithm based on pixel similarity. Graphs can also be used to find similar regions by analyzing the density of a graph. The dense part of a graph usually represents nodes with similar features or statistical interrelationships.