A Quantum Circuit to Construct All Maximal Cliques Using Grover Search Algorithm
Quantum Physics
2019-07-23 v2
Abstract
A quantum circuit to construct all maximal cliques using Grover search algorithm is presented. This oracle circuit takes as input an n-qubit state |x> and the adjacency matrix data A of an n-node network, and outputs the state (-1)^f(x) |x> where f(x)=1 if |x> is a maximal clique, and f(x)=0, otherwise. The oracle workspace requires 2n^2 qubits. Each oracle call makes about 10n^2 calls to the Toffoli gates. The overall Grover search algorithm takes as input a uniform superposition n-qubit state and the adjacency matrix data, and outputs a uniform superposition of all maximal clique states.
Cite
@article{arxiv.1711.06146,
title = {A Quantum Circuit to Construct All Maximal Cliques Using Grover Search Algorithm},
author = {Chu Ryang Wie},
journal= {arXiv preprint arXiv:1711.06146},
year = {2019}
}
Comments
13 pages, 3 figures