Encyclopedia of Algorithms

Editors: Ming-Yang Kao

Quantum Algorithm for Element Distinctness

Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_306

Years and Authors of Summarized Original Work

  • 2004; Ambainis

Problem Definition

In the element distinctness problem, one is given a list of N elements x1, , xN ∈ {1, , m} and one must determine if the list contains two equal elements. Access to the list is granted by submitting queries to a black box, and there are two possible types of query.

Value Queries. In this type of query, the input to the black box is an index i. The black box outputs xi as the answer. In the quantum version of this model, the input is a quantum state that may be entangled with the workspace of the algorithm. The joint state of the query, the answer register, and the workspace may be represented as \(\sum_{i,y,z} a_{i,y,z}|i,y,z \rangle\)

Keywords

Element distinctness Quantum algorithms Quantum search Quantum walks 
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Recommended Reading

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculty of Computing, University of LatviaRigaLatvia