Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 22 Oct 2022 |
Abstract
Keywords
- quant-ph, math-ph, math.MP
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2022.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Deep-Circuit QAOA
AU - Koßmann, Gereon
AU - Binkowski, Lennart
AU - van Luijk, Lauritz
AU - Ziegler, Timo
AU - Schwonnek, René
N1 - 19 pages, 13 figures
PY - 2022/10/22
Y1 - 2022/10/22
N2 - 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.
AB - 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.
KW - quant-ph
KW - math-ph
KW - math.MP
M3 - Preprint
BT - Deep-Circuit QAOA
ER -