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Quantum IPMs for Linear Optimization

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Encyclopedia of Optimization

Introduction

Building efficient quantum computing algorithms is an active, emerging area of research. The Deutsch-Jozsa algorithm [8] was the first instance of a quantum algorithm outperforming the best classical algorithm. After this algorithm, many quantum algorithms are proposed with speed-up compared to algorithms on conventional computers to solve challenging mathematical problems, such as integer factorization [20] and unstructured search [10]. Due to various applications of mathematical optimization and the computational challenges on classical computers, several quantum computing optimization algorithms were developed such as the quantum approximation optimization algorithm (QAOA) for quadratic unconstrained binary optimization (QUBO) [9] and quantum interior point methods (QIPMs) for linear optimization problems (LOPs) [17].

QIPMs are analogous to classical interior point methods(IPMs) that use quantum linear system algorithms (QLSAs) to solve the Newton system at each...

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Acknowledgements

This work is supported by Defense Advanced Research Projects Agency as part of the project W911NF2010022: The Quantum Computing Revolution and Optimization: Challenges and Opportunities.

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Authors and Affiliations

  1. Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA

    Mohammadhossein Mohammadisiahroudi & Tamás Terlaky

Authors
  1. Mohammadhossein Mohammadisiahroudi
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  2. Tamás Terlaky
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Corresponding author

Correspondence to Mohammadhossein Mohammadisiahroudi .

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Editors and Affiliations

  1. Department of Industrial & Systems Engin, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Departmentl of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Oleg A. Prokopyev

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Mohammadisiahroudi, M., Terlaky, T. (2023). Quantum IPMs for Linear Optimization. In: Pardalos, P.M., Prokopyev, O.A. (eds) Encyclopedia of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-54621-2_851-1

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  • DOI: https://doi.org/10.1007/978-3-030-54621-2_851-1

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