A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Quantum Algorithms for Element Distinctness
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Quantum Search of Spatial Regions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A Lower Bound for the Bounded Round Quantum Communication Complexity of Set Disjointness
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Quantum algorithms for subset finding
Quantum Information & Computation
Claw finding algorithms using quantum walk
Theoretical Computer Science
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
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This paper gives a quantum algorithm to search in an set S for a k-tuple satisfying some predefined relation, with the promise that some components of a desired k-tuple are in some subsets of S. In particular when k=2, we show a tight bound of the quantum query complexity for the Claw Finding problem, improving previous upper and lower bounds by Buhrman, Durr, Heiligman, Hoyer, Magniez, Santha and de Wolf [7]. We also consider the distributed scenario, where two parties each holds an n-element set, and they want to decide whether the two sets share a common element. We show a family of protocols s.t.q(P)3/2 . c(P)= O(n2log n), where q(P) and c(P) are the number of quantum queries and the number of communication qubits that the protocol P makes, respectively. This implies that we can pay more for quantum queries to save on quantum communication, and vice versa. To our knowledge, it is the first result about the tradeoff between the two resources.