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Quantum computation shows promise for addressing numerous classically intractable problems, such as optimization tasks. Many optimization problems are NP-hard, meaning that they scale exponentially with problem size and thus cannot be addressed at scale by traditional computing paradigms. The recently proposed quantum algorithm arXiv:2206.14999 addresses this challenge for some NP-hard problems, and is based on classical semidefinite programming (SDP). In this manuscript, we generalize the SDP-inspired quantum algorithm to sum-of-squares programming, which targets a broader problem set. Our proposed algorithm addresses degree- polynomial optimization problems with variables (which are representative of many NP-hard problems) using qubits, quantum measurements, and classical calculations. We apply the proposed algorithm to the prototypical Max-SAT problem and compare its performance against classical sum-of-squares, state-of-the-art heuristic solvers, and random guessing. Simulations show that the performance of our algorithm surpasses that of classical sum-of-squares after rounding. Our results further demonstrate that our algorithm is suitable for large problems and approximates the best known classical heuristics, while also providing a more generalizable approach compared to problem-specific heuristics. 

Summary Effective insect pollination requires appropriate responses to internal and external environmental cues in both the plant and the pollinator.Helianthus annuus, a highly outcrossing species, is marked for its uniform eastward orientation of mature pseudanthia, or capitula. Here we investigate how this orientation affects floral microclimate and the consequent effects on plant and pollinator interactions and reproductive fitness.We artificially manipulated sunflower capitulum orientation and temperature in both field and controlled conditions and assessed flower physiology, pollinator visits, seed traits and siring success.East‐facing capitula were found to have earlier style elongation, pollen presentation and pollinator visits compared with capitula manipulated to face west. East‐facing capitula also sired more offspring than west‐facing capitula and under some conditions produced heavier and better‐filled seeds. Local ambient temperature change on the capitulum was found to be a key factor regulating the timing of style elongation, pollen emergence and pollinator visits.These results indicate that eastward capitulum orientation helps to control daily rhythms in floral temperature, with direct consequences on the timing of style elongation and pollen emergence, pollinator visitation, and plant fitness.