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Deep-Circuit QAOA

Research output: Working paper/Preprint › Preprint

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Original languageEnglish
Publication statusE-pub ahead of print - 22 Oct 2022

Abstract

Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. So far, those findings mostly account for a regime of few qubits and shallow circuits. We find clear evidence for a `no free lunch'-behavior of QAOA on a general optimization task with no further structure; individual cases have, however, to be analyzed more carefully. We propose and justify a performance indicator for the deep-circuit QAOA that can be accessed by solely evaluating statistical properties of the classical objective function. We further discuss the various favorable properties a generic QAOA instance has in the asymptotic regime of infinitely many gates, and elaborate on the immanent drawbacks of finite circuits. We provide several numerical examples of a deep-circuit QAOA method based on local search strategies and find that - in alignment with our performance indicator - some special function classes, like QUBO, admit a favorable optimization landscape.

Keywords

    quant-ph, math-ph, math.MP

Cite this

Deep-Circuit QAOA. / Koßmann, Gereon; Binkowski, Lennart; van Luijk, Lauritz et al.
2022.

Research output: Working paper/Preprint › Preprint

Koßmann, G., Binkowski, L., van Luijk, L., Ziegler, T., & Schwonnek, R. (2022). Deep-Circuit QAOA. Advance online publication.
Koßmann G, Binkowski L, van Luijk L, Ziegler T, Schwonnek R. Deep-Circuit QAOA. 2022 Oct 22. Epub 2022 Oct 22.
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AU - Koßmann, Gereon

AU - Binkowski, Lennart

AU - van Luijk, Lauritz

AU - Ziegler, Timo

AU - Schwonnek, René

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