Finite size scaling of bitstring probability distributions for Rydberg arrays

• URL: http://arxiv.org/abs/2607.27013v1
• Date: Wed, 29 Jul 2026 15:13:40 GMT
• Title: Finite size scaling of bitstring probability distributions for Rydberg arrays
• Abstract summary: We calculate the probabilities $p_n$ of the measured bitstrings $n$ for the vacuum of Rydberg ladders with $N_q$ atoms.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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