Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Introduction to Recent Quantum Algorithms
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum symmetrically-private information retrieval
Information Processing Letters
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
On the power of Ambainis lower bounds
Theoretical Computer Science
Efficient discrete-time simulations of continuous-time quantum query algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Nonadaptive quantum query complexity
Information Processing Letters
Unbounded-error quantum query complexity
Theoretical Computer Science
Broken promises and quantum algorithms
Quantum Information & Computation
Reconstructing strings from substrings with quantum queries
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Superlinear advantage for exact quantum algorithms
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+sqrt(N) queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2+O(sqrt(N)) oracle queries. In the second part of the article `approximate interrogation' is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio.