Quantum Local Search with the Quantum Alternating Operator Ansatz

Teague Tomesh1, Zain H. Saleem2, and Martin Suchara2

1Department of Computer Science, Princeton University, Princeton, NJ 08540, USA.
2Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 60439, USA.

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We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. This hybrid algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We study the performance of this algorithm on 3-regular, Community, and Erdős-Rényi graphs with up to 100 nodes.

Current quantum computers are limited in terms of both their size and quality. This is an issue if our goal is to solve problems on typical, real-world data sets which may contain many thousands or millions of points. To help circumvent this restriction we investigate algorithms which combine the efforts of both classical and quantum computers to help extend the reach of current quantum systems. Specifically, we consider a local search algorithm which allows a hybrid quantum-classical system to solve very large problems by iteratively solving many smaller subproblems. We hope that such methods will be useful in extending the capabilities of quantum-classical systems now and in the future.

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Cited by

[1] Zain H. Saleem, Teague Tomesh, Michael A. Perlin, Pranav Gokhale, and Martin Suchara, "Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation", arXiv:2107.07532.

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