Platforms of Rydberg atoms have been proposed as promising candidates to solve some combinatorial optimization problems. Here we compute quantitative requirements on the system sizes and noise levels that these platforms must fulfill to reach quantum advantage in approximately solving the Unit-Disk Maximum Independent Set problem. Using noisy simulations of Rydberg platforms of up to 26 atoms interacting through realistic van der Waals interactions, we compute the average approximation ratio that can be attained with a simple quantum annealing-based heuristic within a fixed temporal computational budget. Based on estimates of the correlation lengths measured in the engineered quantum state, we extrapolate the results to large atom numbers and compare them to a simple classical approximation heuristic. We find that approximation ratios of at least $\approx 0.84$ are within reach for near-future noise levels. Not taking into account further classical and quantum algorithmic improvements, we estimate that quantum advantage could be reached by attaining a number of controlled atoms of $\sim 8000$ for a time budget of 2 s, and $\sim 1000–1200$ for a time budget of 0.2 s, provided the coherence levels of the system can be improved by a factor 10 while maintaining a constant repetition rate.

中文翻译：

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用里德伯格模拟量子计算机解决优化问题：使用噪声模拟和经典基准测试对量子优势的现实要求

里德伯格原子的平台已经被提出来解决一些组合优化问题。在这里，我们计算这些平台必须满足的系统大小和噪声级别的定量要求，才能在近似解决单位磁盘最大独立集问题时获得量子优势。使用通过现实范德华相互作用进行相互作用的最多26个原子的Rydberg平台的噪声模拟，我们计算了在固定的时间计算预算内，可以通过基于量子退火的简单启发式算法获得的平均近似率。基于在工程量子态下测量的相关长度的估计，我们将结果外推到大原子数，并将其与简单的经典近似启发式算法进行比较。我们发现近似比至少为$\approx 0.84$接近未来的噪音水平。不考虑经典和量子算法的进一步改进，我们估计可以通过获得一定数量的可控原子来达到量子优势。$〜8000$ 时间预算为2秒，并且 $〜1000–1200$ 如果时间预算为0.2 s，则系统的相干性水平可以提高10倍，同时保持恒定的重复率。