Quantum algorithms have the potential to demonstrate that for some problems quantum computation is more efficient than classical computation. A goal of quantum computing is to determine for which problems quantum computers are faster than classical computers. In our survey we present recent quantum algorithms for basic problems from graph and algebra theory. The quantum algorithms for these problems use a combination of Grovers search algorithms, quantum amplitude amplification and quantum random walks. These quantum algorithms are faster than the best known classical algorithms for the corresponding problems.
Keywords: Quantum computing, quantum algorithms, graph theory, algebra, quantum query complexity
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