Abstract
In recent years, rapid developments of quantum computer are witnessed in both the hardware and the algorithm domains, making it necessary to have an updated review of some major techniques and applications in quantum algorithm design. In this survey as well as tutorial article, the authors first present an overview of the development of quantum algorithms, then investigate five important techniques: Quantum phase estimation, linear combination of unitaries, quantum linear solver, Grover search, and quantum walk, together with their applications in quantum state preparation, quantum machine learning, and quantum search. In the end, the authors collect some open problems influencing the development of future quantum algorithms.
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