Abstract
The power of quantum mechanics, that is too complex for conventional computers, can be solved by an innovative model of computing known as quantum computing. Quantum algorithms can provide exponential speedups for some types of problems, such as many difficult mathematical ones. In this paper, we review some of the most important quantum algorithms for hard mathematical problems. When factoring large numbers, Shor's algorithm is orders of magnitude faster than any other known classical algorithm. The Grover's algorithm, which searches unsorted databases much more quickly than conventional algorithms, is then discussed.
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