A study of the performance of classical minimizers in the Quantum Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm (QAOA) was proposed as a way of finding good, approximate solutions to hard combinatorial optimization problems. QAOA uses a hybrid approach. A parametrized quantum state is repeatedly prepared and measured on a quantum computer to estimate its average...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 404; p. 113388
Main Authors: Fernández-Pendás, Mario, Combarro, Elías F., Vallecorsa, Sofia, Ranilla, José, Rúa, Ignacio F.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2022
Subjects:
Combinatorial optimization
Function minimization
Max-Cut
Quantum Approximate Optimization Algorithm
Combinatorial optimization
Quantum Approximate Optimization Algorithm
Function minimization
Max-Cut
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The Quantum Approximate Optimization Algorithm (QAOA) was proposed as a way of finding good, approximate solutions to hard combinatorial optimization problems. QAOA uses a hybrid approach. A parametrized quantum state is repeatedly prepared and measured on a quantum computer to estimate its average energy. Then, a classical optimizer, running in a classical computer, uses such information to decide on the new parameters that are then provided to the quantum computer. This process is iterated until some convergence criteria are met. Theoretically, almost all classical minimizers can be used in the hybrid scheme. However, their behaviour can vary greatly in both the quality of the final solution and the time they take to find it. In this work, we study the performance of twelve different classical optimizers when used with QAOA to solve the maximum cut problem in graphs. We conduct a thorough set of tests on a quantum simulator both, with and without noise, and present results that show that some optimizers can be hundreds of times more efficient than others in some cases.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113388