On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Randomized algorithms
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A note on quantum black-box complexity of almost all Boolean functions
Information Processing Letters
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
The Query Complexity of Order-Finding
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Quantum communication and complexity
Theoretical Computer Science - Natural computing
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Classical and quantum partition bound and detector inefficiency
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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The classical Yao principle states that the complexity R驴(f) of an optimal randomized algorithm for a function f with success probability 1 - 驴 equals the complexity max碌 D驴碌 (f) of an optimal deterministic algorithm for f that is correct on a fraction 1 - 驴 of the inputs, weighed according to the hardest distribution 碌 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 complexityis a lower bound on the quantum analogues of max碌 D驴碌 (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.