Quantum Biased Oracles

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This paper reviews researches on quantum oracle computations when oracles are not perfect i.e. they may return wrong answers. We call such oracles biased oracles and discuss the formal model of them. Then we provide an intuitive explanation how quantum search with biased oracles by Hoyer et al. (2003) works. We also review the method by Buhrman et al. (2005) to obtain all the answers of a quantum biased oracle without any overhead compared to the perfect oracle case. Moreover we discuss two special cases of quantum biased oracles and their interesting properties which are not found in the classical corresponding cases. Our discussion implies that the model of quantum biased oracle adopted by the existing researches is natural.

This paper reviews researches on quantum oracle computations when oracles are not perfect,i.e., they may return wrong answers. We call such oracles biased oracles, and discuss the formal model of them. Then we provide an intuitive explanation how quantum search with biased oracles by Hoyer, et al. (2003) works. We also review the method, by Buhrman, et al. (2005), to obtain all the answers of a quantum biased oracle without any overhead compared to the perfect oracle case. Moreover, we discuss two special cases of quantum biased oracles and their interesting properties, which are not found in the classical corresponding cases. Our discussion implies that the model of quantum biased oracle adopted by the existing researches is natural.

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