Polynomial Degree vs. Quantum Query Complexity
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چکیده
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f . This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function with polynomial degree M and quantum query complexity Ω(M). This is the first superlinear separation between polynomial degree and quantum query complexity. The lower bound is shown by a new, more general version of quantum adversary method.
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تاریخ انتشار 2003