QUANTUM ARTIFICIAL INTELLIGENCE: A SURVEY OF RECENT ADVANCES AND FUTURE CHALLENGES IN COMBINING QUANTUM COMPUTING AND MACHINE LEARNING

Abstract

Quantum Artificial Intelligence has been considered as one of transformative interdisciplinary areas that have joined quantum calculation with machine learning and optimization. The paper is a survey of the recent development in QAI and a detailed case study of the Quantum Approximate Optimization Algorithm, its mathematical formulation, operator-based modeling, and utility in practical application to combinatorial optimization. Based on the background principles of the Hilbert space theory, Hermitian operators and variational quantum circuits, the paper examines the process of encoding a classical optimization problem in a quantum Hamiltonian and the effects of circuit depth, parameterization, and graph structure on the algorithms. An example of Max-Cut case study shows how the algorithm performs on regular graph, irregular graph and weighted graph cases, showing good approximation even at small depths, and showing convergence behavior as outlined in theory. The comparative perspectives in regards to existing models of QAI further outline the advantages of QAOA with regard to interpretability and operator design, and also outline the constraints associated with noise sensitivity, measurement load, and hardware scalability. The way QAOA is related to spectral methods, variational theory, and discrete optimization are discussed as giving theoretical implications of QAOA to applied mathematics. The research finds that QAOA is a bright future of practical, yet mathematically rich, quantum computation in the near-term. The development in the future depends on the interdisciplinary cooperation, noise-resistant circuit engineering, and the development of quantum hardware to achieve the full potential of QAI in both science and engineering uses.