Variational Quantum Algorithms for Semidefinite Programming

• URL: http://arxiv.org/abs/2112.08859v3
• Date: Wed, 12 Jun 2024 02:26:50 GMT
• Title: Variational Quantum Algorithms for Semidefinite Programming
• Authors: Dhrumil Patel, Patrick J. Coles, Mark M. Wilde,
• Abstract summary: A semidefinite program (SDP) is a convex optimization problem with applications in operations research, optimization, quantum information science, and beyond. We propose variational quantum algorithms for approximately solving SDPs.
• Score: 3.481985817302898
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., $N\gg M$, where $N$ is the dimension of the input matrices and $M$ is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

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