Quantum algorithms a decade after shor
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New upper and lower bounds for randomized and quantum local search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the power of Ambainis lower bounds
Theoretical Computer Science
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Separation of Local Search and Fixed Point Computation
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Quantum Queries on Permutations with a Promise
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
A new rank technique for formula size lower bounds
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Lower bounds using kolmogorov complexity
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the black-box complexity of sperner's lemma
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Adversary lower bound for the k-sum problem
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Properties and applications of boolean function composition
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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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 (M1.321...). 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.