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The quantum query models is one of the most important models in quantum. Several well-known quantum algorithms are captured by this model, the Deutsch-Jozsa algorithm, the Simon algorithm, the Grover and others. In this paper, we characterize the computational power of one-query quantum algorithms. It is proved that a total Boolean functionf: \\0, 1\\ⁿ \ \\0, 1\\ can be exactly computed by a one-query algorithm if and only if f (x) =x₈䃑 or x₈䃑 \ x₈䃒 (up to isomorphism). Note that unlike most work in the literature based on the method, our proof does not resort to any knowledge about the degree of f.
Chen et al. (Thu,) studied this question.