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arXiv · 1711.06146

A Quantum Circuit to Construct All Maximal Cliques Using Grover Search Algorithm

Chu Ryang Wie
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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.

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Chu Ryang Wie. 2017-11-16. A Quantum Circuit to Construct All Maximal Cliques Using Grover Search Algorithm. https://arxiv.org/abs/1711.06146

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