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Approaches to Constrained Quantum Approximate Optimization

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Abstract

We study the costs and benefits of different quantum approaches to finding approximate solutions of constrained combinatorial optimization problems with a focus on the maximum independent set. Using the Lagrange multiplier approach, we analyze the dependence of the output on graph density and circuit depth. The Quantum Alternating Operator Ansatz approach is then analyzed, and we examine the dependence on different choices of initial states. This approach, although powerful, is expensive in terms of quantum resources. We also introduce a new algorithm, the dynamic quantum variational ansatz (DQVA), that dynamically adapts to ensure the maximum utilization of a fixed allocation of quantum resources. Our analysis and the new proposed algorithm can also be generalized to other related constrained combinatorial optimization problems.

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Acknowledgements

We thank Kaiwen Gui, Brajesh Gupt, Ruslan Shaydulin, Stuart Hadfield, and James Stokes for the helpful discussions. This material is based on work partly supported by the National Science Foundation under Award No. 2037984 and partly by Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. T.T. is supported in part by EPiQC, an NSF Expedition in Computing, under Grant No. CCF-1730082.

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Authors and Affiliations

  1. Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL, 60439, USA

    Zain H. Saleem, Bilal Tariq & Martin Suchara

  2. Department of Computer Science, Princeton University, Princeton, NJ, 08540, USA

    Teague Tomesh

  3. Department of Physics, University at Buffalo, SUNY, Buffalo, NY, 14260, USA

    Bilal Tariq

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  1. Zain H. Saleem
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Correspondence to Zain H. Saleem.

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Saleem, Z.H., Tomesh, T., Tariq, B. et al. Approaches to Constrained Quantum Approximate Optimization. SN COMPUT. SCI. 4, 183 (2023). https://doi.org/10.1007/s42979-022-01638-4

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