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Least-squares solutions to polynomial systems of equations with quantum annealing

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Abstract

This work proposes and analyzes a methodology for finding least-squares solutions to the systems of polynomial equations. Systems of polynomial equations are ubiquitous in computational science, with major applications in machine learning and computer security (i.e., model fitting and integer factorization). The proposed methodology maps the squared-error function for a polynomial equation onto the Ising–Hamiltonian model, ensuring that the approximate solutions (by least squares) to real-world problems can be computed on a quantum annealer even when the exact solutions do not exist. Hamiltonians for integer factorization and polynomial systems of equations are implemented and analyzed for both logical optimality and physical practicality on modern quantum annealing hardware.

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Acknowledgements

The authors would like to thank Wu-chun Feng and Mohamed W. Hassan for their council and feedback. Also, the authors would like to acknowledge the anonymous reviewers for their helpful comments, which greatly improved this paper.

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Author notes

  1. Tyler H. Chang, Thomas C. H. Lux, and Sai Sindhura Tipirneni have contributed equally to this work.

Authors and Affiliations

  1. Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Tyler H. Chang, Thomas C. H. Lux & Sai Sindhura Tipirneni

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  1. Tyler H. Chang
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  2. Thomas C. H. Lux
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  3. Sai Sindhura Tipirneni
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Correspondence to Tyler H. Chang.

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Chang, T.H., Lux, T.C.H. & Tipirneni, S.S. Least-squares solutions to polynomial systems of equations with quantum annealing. Quantum Inf Process 18, 374 (2019). https://doi.org/10.1007/s11128-019-2489-x

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