AI 中文总结
该研究针对里德堡梯系统真空态的比特串概率分布开展有限尺寸标度分析，发现低概率态的累积分布可近似坍缩为类费米函数形式，且测量次数随原子数指数增长，为真空可观测量计算提供参考。
AI 中文摘要
我们计算了含$N_q$个原子的里德堡梯系统真空态下被测比特串$\u0026#123;n\u0026#125;$的概率$p_{\u0026#123;n\u0026#125;}$。随着$N_q$增大，$p_{\u0026#123;n\u0026#125;}$数值降低，但在低概率区域分布更密集，这意味着低概率态的数量优势可能弥补其单态概率小的不足。低概率态的重要性可通过累积概率分布$\u03a3(p_\u039b,N_q)$估算，该分布表示观测到概率$p\u2264p_\u039b$的任意态的总概率。当$p_\u039b$不太大时，将不同$N_q$对应的$\u03a3(p_\u039b,N_q)$以$-\u2212\rn(p_\u039b)$为横坐标作图，可近似坍缩为类似费米函数的形式。我们证明，将$\u03a3(p_\u039b,N_q)$降至足够低的数值所需的测量次数随$N_q$呈指数增长。我们还讨论了这一结果对计算真空态相关可观测量的启示。
英文摘要
We calculate the probabilities $p_{\{n\}}$ of the measured bitstrings $\{n\}$ for the vacuum of Rydberg ladders with $N_q$ atoms. As $N_q$ increases, the $p_{\{n\}}$ decrease but become more dense in the low $p$ region raising the possibility that their smallness could be compensated by their large number. The importance of the low probability states can be estimated from the cumulative probability distribution $Σ(p_Λ,N_q)$, which is the probability to observe any state having a probability $p\leq p_Λ$. For not too large values of $p_Λ$, it is possible to approximately collapse the $Σ(p_Λ,N_q)$ for successive $N_q$ into a function resembling the Fermi function when plotted as a function of $-\ln(p_Λ)$. We show that the number of shots necessary to reduce $Σ(p_Λ,N_q)$ to some low enough value grows exponentially with $N_q$. We discuss the implications for calculating observables associated with the vacuum.
Comments9 pages, 9 figures
