Variational Quantum Algorithms for Semidefinite Programming

Patel, Dhrumil; Coles, Patrick J.; Wilde, Mark M.

doi:10.22331/q-2024-06-17-1374

Variational Quantum Algorithms for Semidefinite Programming

Journal Article · Mon Jun 17 00:00:00 EDT 2024 · Quantum

DOI:https://doi.org/10.22331/q-2024-06-17-1374· OSTI ID:2426830

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Cornell Univ., Ithaca, NY (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Louisiana State Univ., Baton Rouge, LA (United States); Cornell Univ., Ithaca, NY (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2426830

Report Number(s):: LA-UR--21-32169

Journal Information:: Quantum, Journal Name: Quantum Vol. 8; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

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