Average-case quantum query complexity
نویسندگان
چکیده
منابع مشابه
Average-Case Quantum Query Complexity
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for averagecase complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-expo...
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In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded error using T queries in the worst case, then a deterministic classical computer can evaluate f using O(T ) queries in the average case, under a uniform distribu...
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We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associatedwith an underlying distribution. Amongst other properties, we (a) obtain speed-ups over the best known quantum algorithms for identity testing, equivalence testing and uniformity testing of probability distributions; (b) study the power of the...
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We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that computes some total boolean function depending on n variables must make Ω(n) queries to the input in total. Second, we show that, if there exists a quantum algor...
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We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function cl...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2001
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/34/35/302