Quantum Algorithms for Element Distinctness

We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Høyer, and Tapp, and imply an Ç´Æ¿ ÐÓ Æµ quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with ¢´Æ ÐÓ Æµ classical complexity. We also prove a lower bound of ª´ Ô Æµ comparisons for this problem and derive bounds for a number of related problems.

• Type: Conference
• Year: 2001
• Where: COCO
• Authors: Harry Buhrman, Christoph Dürr, Mark Heiligman, Peter Høyer, Frédéric Magniez, Miklos Santha, Ronald de Wolf
• Keywords: Algorithms, COCO 2001, Comparison Complexity Model, Quantum Amplitude Amplification, Quantum Upper Bound