On Quantum Versions of the Yao Principle
نویسندگان
چکیده
The classical Yao principle states that the complexity R (f) of an optimal randomized algorithm for a function f with success probability 1− equals the complexity maxμ D (f) of an optimal deterministic algorithm for f that is correct on a fraction 1 − of the inputs, weighed according to the hardest distribution μ over the inputs. In this paper we investigate to what extent such a principle holds for quantum algorithms. We propose two natural candidate quantum Yao principles, a “weak” and a “strong” one. For both principles, we prove that the quantum bounded-error complexity is a lower bound on the quantum analogues of maxμ D μ (f). We then prove that equality cannot be obtained for the “strong” version, by exhibiting an exponential gap. On the other hand, as a positive result we prove that the “weak” version holds up to a constant factor for the query complexity of all symmetric Boolean functions.
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