A Quantum Algorithm for the Sub-graph Isomorphism Problem

We propose a novel variational method for solving the sub-graph isomorphism problem on gate-based quantum computer. The relies (1) new representation of adjacency matrices underlying graphs, which requires number qubits that scales logarithmically with vertices graphs; and (2) ansatz can efficiently probe permutation space. Simulations are then presented to showcase approach graphs up 16 vertices, whereas, given logarithmic scaling, could be applied realistic instances in medium term.