中性原子量子优化中 shots 到近似解的缩放规律
Shots-to-Approximate-Solution Scaling in Neutral-Atom Quantum Optimization
浏览论文内容
中文总结 AI 辅助
本研究针对中性原子量子优化的 shots 缩放问题，提出 STS(r) 度量，通过实验证明量子退火对低能解的集中效应优于随机基线，明确了其在近精确与松弛目标下的不同性能表现及适用范围。
中文摘要 AI 辅助
中性原子量子优化协议是否表现出对低能解结构的真正集中效应仍是一个开放问题。本文引入 shots-to-approximate-solution 度量 STS(r)，其中 r 表示近似比，通过由单一有效参数 β 控制的简并加权壳层分布建模的后处理输出来评估该度量，β 量化了对近最优独立集的集中程度。为提取量子数据中的真正集中效应，本文对实验比特串和激发密度匹配的随机生成比特串应用相同的后处理，从而构建了激发匹配的随机基线。对系统规模达 125 个位点的可编程里德伯原子阵列的实验表明，量子退火始终优于随机基线，证明其对低能解结构的增强集中效应超出了仅由激发密度可解释的范围。结果进一步揭示了两种不同的目标依赖 regime：对于 r≈1 的近精确目标，所需的 shot 数随系统规模呈指数增长，而在壳层模型描述内，量子退火可将该指数级降低；相比之下，对于松弛目标，shot 成本变为有效常数，对应的量子增强消失，仅经典后处理启发式方法就能在单位数量的尝试内达到目标。这些结果共同建立了一种量化量子优化性能的可操作方法，并阐明了量子方法可产生实际益处的 regime。
英文摘要
Whether neutral-atom quantum optimization protocols exhibit genuine concentration toward low-energy solution structure remains an open question. Here, we introduce a shots-to-approximate-solution metric, STS(r), where r denotes the approximation ratio, and evaluate it using postprocessed outputs modeled by a degeneracy-weighted shell distribution governed by a single effective parameter, $β$, that quantifies concentration toward near-optimal independent sets. To extract the genuine concentration effect in the quantum data, we apply identical postprocessing to both experimental bitstrings and randomly generated bitstrings with matched excitation density, thereby constructing an excitation-matched random baseline. Experiments on programmable Rydberg-atom arrays with system sizes up to 125 sites show that quantum annealing consistently exceeds the random baseline, demonstrating enhanced concentration toward low-energy solution structure beyond what can be attributed solely to excitation density. The results further reveal two distinct target-dependent regimes. For near-exact targets with $r \approx 1$, the required shot count grows exponentially with system size and is reduced at the same exponential level by quantum annealing within the shell-model description. By contrast, for relaxed targets, the shot cost becomes effectively constant, and the corresponding quantum enhancement diminishes, with the classical postprocessing heuristic alone reaching the target in order-unity attempts. Together, these results establish an operational method for quantifying quantum optimization performance and clarify the regimes under which quantum approaches can yield practical benefits.
