Variational Quantum Algorithms for Semidefinite Programming

Technical Report · Mon Dec 13 04:00:00 EST 2021

DOI:https://doi.org/10.2172/2377985· OSTI ID:2377985

Patel, Dhrumil ^[1]; Coles, Patrick Joseph ^[2]; Wilde, Mark M. ^[3]

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1. Cornell Univ., Ithaca, NY (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
3. 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 " 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: 89233218CNA000001
• OSTI ID: 2377985
• Report Number(s): LA-UR--21-32169
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING