STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Quantum algorithms using the curvelet transform
Proceedings of the forty-first annual ACM symposium on Theory of computing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Symmetry-Assisted Adversaries for Quantum State Generation
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Quantum Query Complexity of State Conversion
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Span programs and quantum algorithms for st-connectivity and claw detection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We describe a method for upper bounding the quantum query complexity of certain boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method gives an upper bound on query complexity without producing an algorithm. For example, we describe an oracle problem that we prove (non-constructively) can be solved in O(1) queries, where the previous best quantum algorithm uses a polynomial number of queries. We then give an explicit O(1) query algorithm based on span programs, and show that for a special case of this problem, there exists a O(1) query algorithm that uses the quantum Haar transform. This special case is a potentially interesting problem in its own right, which we call the Haar Problem.