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Trapped Ion Quantum Computing Quantum Simulation

Variational Quantum Algorithms for Semidefinite Programming

arXiv

Authors: Dhrumil Patel, Patrick J. Coles, Mark M. Wilde

Year

2021

Paper ID

40575

Status

Preprint

Abstract Read

~2 min

Abstract Words

125

Citations

N/A

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., $Ngg M$, 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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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2112.08859 [2] arXiv https://arxiv.org/abs/2112.08859 [3] Publisher https://arxiv.org/abs/2112.08859

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