Quantum walk for community clique detection

A method of detecting cliques in a graph, comprising:

• determining, based on a number of nodes in said graph, a number of qubits to be included in a quantum processor;
• assigning to each node in said graph, a qubit of said quantum processor having said determined number of qubits;
• operating on said qubits of said quantum processor with a preparation circuit to create a quantum state in said qubits that corresponds to said graph;
• operating on said quantum state in said qubits with a random walk circuit;
• and
• measuring said qubits of said quantum processor to detect cliques in said graph based on said operating with said random walk circuit,
• wherein said preparation circuit comprises a plurality of single- and two-qubit operators, wherein, for each pair of adjacent nodes in said graph, an operator of said plurality of two-qubit operators acts on a pair of qubits corresponding to said pair of adjacent nodes to create said quantum state.