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Quantum algorithms provide a recipe for efficiently solving practical problems on a quantum computer. Well-known examples include Shor's algorithm, which allows us to find the prime factors of a large integer efficiently, and Grover's algorithm, which outperforms a classical search algorithm.

Going hand in hand with computational complexity, the study of quantum algorithms allows us to understand the possibilities of quantum computation. Of particular interest are problems which are difficult to solve on a classical computer, but which can be solved efficiently on a quantum machine. Can we construct efficient algorithms for such problems?