  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.
