Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first 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
Counting by quantum eigenvalue estimation
Theoretical Computer Science
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Almost-everywhere superiority for Quantum polynomial time
Information and Computation
Quantum computing – Facts and folklore
Natural Computing: an international journal
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Computing with quanta-impacts of quantum theory on computation
Theoretical Computer Science - Natural computing
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Quantum summation with an application to integration
Journal of Complexity
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Separating Quantum and Classical Learning
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Average-Case Quantum Query Complexity
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
The Quantum Computing Challenge
Informatics - 10 Years Back. 10 Years Ahead.
On Quantum Versions of the Yao Principle
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On a problem in quantum summation
Journal of Complexity
One complexity theorist's view of quantum computing
Theoretical Computer Science - Algorithms,automata, complexity and games
From Monte Carlo to quantum computation
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Information and Computation
A Better Lower Bound for Quantum Algorithms Searching an Ordered List
FOCS '99 Proceedings of the 40th 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
Quantum zero-error algorithms cannot be composed
Information Processing Letters
Sensitivity, block sensitivity, and l-block sensitivity of boolean functions
Information and Computation
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
Graph entropy and quantum sorting problems
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
A lower bound on the quantum query complexity of read-once functions
Journal of Computer and System Sciences
The power of various real-valued quantum queries
Journal of Complexity
Average case quantum lower bounds for computing the Boolean mean
Journal of Complexity
Classical and Quantum Complexity of the Sturm--Liouville Eigenvalue Problem
Quantum Information Processing
Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
On the Complexity of Searching for a Maximum of a Function on a Quantum Computer
Quantum Information Processing
The Quantum Setting with Randomized Queries for Continuous Problems
Quantum Information Processing
A lower bound for the Sturm-Liouville eigenvalue problem on a quantum computer
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Improved algorithms for quantum identification of Boolean oracles
Theoretical Computer Science
Quantum lower bounds by entropy numbers
Journal of Complexity
On the complexity of the multivariate Sturm--Liouville eigenvalue problem
Journal of Complexity
Quantum search on bounded-error inputs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
An improved lower bound on query complexity for quantum PAC learning
Information Processing Letters
The polynomial degree of recursive Fourier sampling
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Quantum interpolation of polynomilas
Quantum Information & Computation
On quantum one-way permutations
Quantum Information & Computation
Quantum lower bound for recursive Fourier sampling
Quantum Information & Computation
Broken promises and quantum algorithms
Quantum Information & Computation
A geometric approach to quantum circuit lower bounds
Quantum Information & Computation
Quantum communication complexity of block-composed functions
Quantum Information & Computation
Improved algorithms for quantum identification of boolean oracles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Optimality proofs of quantum weight decision algorithms
Quantum Information Processing
Robust quantum algorithms with ε-biased oracles
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Bounds for error reduction with few quantum queries
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Boolean functions with a low polynomial degree and quantum query algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Superiority of exact quantum automata for promise problems
Information Processing Letters
Numerical analysis on a quantum computer
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Random oracles in a quantum world
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions (i.e. problems involving a promise on the input) by Deutsch and Jozsa and by Simon cannot be obtained for any total function: if a quantum algorithm computes some total Boolean function f with bounded-error using T black-box queries then there is a classical deterministic algorithm that computes f exactly with O(T^6) queries. We also give asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings. Finally, we give new precise bounds for AND, OR, and PARITY. Our results are a quantum extension of the so-called polynomial method, which has been successfully applied in classical complexity theory, and also a quantum extension of results by Nisan about a polynomial relationship between randomized and deterministic decision tree complexity.