Complex Networks on Quantum States in AMO Platforms

复杂性科学是21世纪深刻的突出问题之一。一般来说，复杂性的起源是什么？它会出现在量子层面吗？如果是，如何量化它，它究竟意味着什么？这项工作将在量子模拟器平台的三个具体实验背景下解决这些问题，通过科学的进步促进国家利益。这项工作将原子、分子、光学物理和量子信息科学进一步扩展到复杂性科学，提供了量化量子态复杂性的具体方法。它将为统计物理学和复杂网络科学提供一个跨学科的联系，到目前为止主要应用于经典层面。半导体技术革命在很大程度上基于单粒子量子力学，从能带理论到量子隧道；量子技术的下一步肯定会涉及到纠缠。该提案将通过确定纠缠的复杂性来探索复杂性科学，将其作为下一次革命的关键组成部分。该团队将通过将复杂网络测量应用于量子互信息来探索量子临界现象的复杂性，量子互信息由所有两点相关器从下而上限定。有限温度和无序在复杂性中的作用是什么？复杂度如何依赖于不同的通用性类？其次，该团队将研究量子元胞自动机中复杂性的出现，特别是在金发姑娘规则中，它表现出鲁棒的动态特征和持续的熵波动。复杂性的动态特性是什么？它容易去相干吗？它对量子运算中的门保真度有多敏感，或者在量子模拟器中实现哈密顿量的精度有多敏感？第三，本团队将把复杂的网络测量应用于原子干涉测量中的高阶相位相关器。复杂度取决于相关器的顺序吗？从复杂性的角度来看，在这种相关器的高维空间中，可能会解锁哪些新功能？此外，该基金还支持本科生和研究生在科学问题解决的批判性分析和高性能并行计算的严格数值技术方面的培训，这是在社会许多领域取得成功的关键，从材料基因组计划到空间计划，再到量子计算和量子技术的下一阶段。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Complexity science is one of the deep outstanding problems of the 21st century. What are the origins of complexity generally? Does it appear at the quantum level? If so, how can it be quantified and what exactly does it imply? This work will address these questions in three concrete experimental contexts in quantum simulator platforms, promoting national interests through the progress of science. This work will expand atomic, molecular, and optical physics and quantum information science further into complexity science, providing a concrete way to quantify complexity of quantum states. It will provide an interdisciplinary connection to statistical physics and complex network science, applied up till now mainly at the classical level. The semiconductor technological revolution is based heavily on single-particle quantum mechanics, from band theory to quantum tunneling; the next step in quantum technology will certainly involve entanglement. This proposal will explore complexity science as a key component of that next revolution, by determining the complexity of entanglement.This team will explore the complexity of quantum critical phenomena by applying complex network measures to quantum mutual information, bounded from below by all two-point correlators. What is the role of finite temperature and disorder in complexity? How does complexity depend on different universality classes? Second, this team will study the emergence of complexity in quantum cellular automata, in particular in Goldilocks rules, which exhibit robust dynamical features and persistent entropy fluctuations. What are the dynamical properties of complexity? Does it decohere easily? How sensitive is it to gate fidelity in quantum operations, or precision of a Hamiltonian realized in a quantum simulator? Third, this team will apply complex network measures to higher order phase correlators in atom interferometry. Does complexity depend on the order of the correlator? What new features might be unlocked in the high-dimensional spaces of such correlators with a complexity perspective? Moreover, this grant supports the training of undergraduate and graduate students in critical analysis for scientific problem solving and rigorous numerical techniques for high-performance parallel computing, which are key to success in a number of arenas in society, from the materials genome initiative to the space program to quantum computing and the next stage of quantum technology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.