On the distributional complexity of disjointness
Theoretical Computer Science
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
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
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Quantum Oracle Interrogation: Getting All Information for Almost Half the Price
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On rank vs. communication complexity
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic algorithms. For total Boolean functions in the query model, the biggest known gap was just a factor of 2: PARITY of N input bits requires N queries classically but can be computed with N/2 queries by an exact quantum algorithm. We present the first example of a Boolean function f(x1, ..., xN) for which exact quantum algorithms have superlinear advantage over deterministic algorithms. Any deterministic algorithm that computes our function must use N queries but an exact quantum algorithm can compute it with O(N0.8675...) queries. A modification of our function gives a similar result for communication complexity: there is a function f which can be computed by an exact quantum protocol that communicates O(N^{0.8675...}) quantum bits but requires Omega(N) bits of communication for classical protocols.