A Quantum Algorithm for the Sub-Graph Isomorphism Problem

• URL: http://arxiv.org/abs/2111.09732v2
• Date: Fri, 2 Sep 2022 08:51:50 GMT
• Title: A Quantum Algorithm for the Sub-Graph Isomorphism Problem
• Authors: Nicola Mariella and Andrea Simonetto
• Abstract summary: We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. We show that the method can be applied to realistic sub-graph isomorphism problem instances in the medium term.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number of qubits that scales logarithmically with the number of vertices of the graphs; and (2) on a new Ansatz that can efficiently probe the permutation space. Simulations are then presented to showcase the approach on graphs up to 16 vertices, whereas, given the logarithmic scaling, the approach could be applied to realistic sub-graph isomorphism problem instances in the medium term.

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