Programmable quantum devices are now able to probe wave functions at unprecedented levels. This is based on the ability to project the many-body state of atom and qubit arrays onto a measurement basis which produces snapshots of the system wave function. Extracting and processing information from such observations remains, however, an open quest. One often resorts to analyzing low-order correlation functions—that is, discarding most of the available information content. Here, we introduce wave-function networks—a mathematical framework to describe wave-function snapshots based on network theory. For many-body systems, these networks can become scale-free—a mathematical structure that has found tremendous success and applications in a broad set of fields, ranging from biology to epidemics to Internet science. We demonstrate the potential of applying these techniques to quantum science by introducing protocols to extract the Kolmogorov complexity corresponding to the output of a quantum simulator and implementing tools for fully scalable cross-platform certification based on similarity tests between networks. We demonstrate the emergence of scale-free networks analyzing experimental data obtained with a Rydberg quantum simulator manipulating up to 100 atoms. Our approach illustrates how, upon crossing a phase transition, the simulator complexity decreases while correlation length increases—a direct signature of buildup of universal behavior in data space. Comparing experiments with numerical simulations, we achieve cross-certification at the wave-function level up to timescales of $4\mathrm{\mu }\mathrm{s}$ with a confidence level of 90% and determine experimental calibration intervals with unprecedented accuracy. Our framework is generically applicable to the output of quantum computers and simulators with in situ access to the system wave function and requires probing accuracy and repetition rates accessible to most currently available platforms.

中文翻译：

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量子多体系统的波函​​数网络描述和柯尔莫哥洛夫复杂度


可编程量子设备现在能够以前所未有的水平探测波函数。这是基于将原子和量子位阵列的多体状态投影到测量基础上的能力，从而产生系统波函数的快照。然而，从这些观察中提取和处理信息仍然是一个悬而未决的任务。人们经常诉诸于分析低阶相关函数，即丢弃大部分可用的信息内容。在这里，我们介绍波函数网络——一种基于网络理论描述波函数快照的数学框架。对于多体系统来说，这些网络可以变得无标度——这种数学结构在从生物学到流行病再到互联网科学的广泛领域中取得了巨大的成功和应用。我们通过引入协议来提取与量子模拟器的输出相对应的柯尔莫哥洛夫复杂度，并基于网络之间的相似性测试实现完全可扩展的跨平台认证工具，展示了将这些技术应用于量子科学的潜力。我们展示了无标度网络的出现，分析了通过操纵多达 100 个原子的里德堡量子模拟器获得的实验数据。我们的方法说明了在跨越相变时，模拟器的复杂性如何降低，而相关长度却增加——这是数据空间中普遍行为累积的直接特征。通过将实验与数值模拟进行比较，我们在时间尺度为 $4\mathrm{\mu }\mathrm{s}$ 的波函数水平上实现了交叉认证，置信度为 90%，并以前所未有的精度确定了实验校准间隔。 我们的框架通常适用于可原位访问系统波函数的量子计算机和模拟器的输出，并且需要当前大多数可用平台都可以访问的探测精度和重复率。