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In contrast to the classical optimization process required by the quantum approximate optimization algorithm, FALQON, a feedback-based algorithm for quantum optimization A. B. Magann et al. , bluePhys. Rev. Lett. {129, 250502 (2022) }, enables one to obtain approximate solutions to combinatorial optimization problems without any classical optimization effort. In this study, we leverage the specifications of a recent experimental platform for the neutral atom system Z. Fu et al. , bluePhys. Rev. A {105, 042430 (2022) } and present a scheme to implement an optimally tuned small-angle controlled-phase gate. By examining the 2- to 4-qubit FALQON algorithms in the Max-Cut problem and considering the spontaneous emission of the neutral atomic system, we have observed that the performance of FALQON implemented with small-angle controlled-phase gates exceeds that of FALQON utilizing CZ gates. This approach has the potential to significantly simplify the logic circuit required to simulate FALQON and effectively address the Max-Cut problem, which may pave a way for the experimental implementation of near-term noisy intermediate-scale quantum algorithms with neutral-atom systems.
Li et al. (Thu,) studied this question.