Quantum Cellular Automata Dynamics: Integrability, Many-Body Decoherence, and Complex Entanglement

量子元胞自动机动力学：可积性、多体退相干和复杂纠缠

• 批准号: 2210566
• 负责人: Lincoln Carr
• 金额: $ 40万
• 依托单位: Colorado School of Mines
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210566&HistoricalAwards=false
• 关键词: Quantum; Cellular; Automata; Dynamics; Integrability

Complexity science is one of the deep outstanding problems of the 21st century, tapping into such profound questions as the biological origin of consciousness. What are the origins of complexity generally? Does it appear already in quantum mechanics? Do we require a new physical theory, or is complexity an outgrowth of what we know? Noisy intermediate scale quantum (NISQ) computers involve an increasing number of interacting quantum subsystems giving rise to complexity. One way to study such emergent complexity in NISQ computers is with Goldilocks quantum cellular automata (QCA). Goldilocks QCA are dynamic computational rules written into a quantum circuit which involve a trade-off or balance between not too many and not too few in a local neighborhood -- thus the term "Goldilocks". Enhancing the progress of science, this project will connect formerly disparate foundational mathematical and scientific concepts, such as integrability and complexity; point the way to possible beyond-classical computing demonstrations with 2D QCA; and develop new quantum computing paradigms for open quantum systems via irreversible elementary QCA making use of the environment instead of avoiding it, just as living systems do. Additionally, the team proposes a multi-faceted approach to meet broader impact goals. First, they will mentor 2-3 undergraduates per year in research from one of the largest undergraduate physics programs in the US. Second, they will engage internationally by serving on the executive editorial board of the Journal of Physics: Complexity; and by supporting science diplomacy via the U.S. Department of State as a Jefferson Science Fellow alumni. Third, they will engage in educational development in the quantitative study of student collaboration networks in hybrid and virtual class environments; and by creation of a science diplomacy course in the Mines honors program accessible to all STEM students and publicly disseminated. Fourth, they will increase diversity, equity, and inclusion in physics via a supportive, diverse group environment with a track record of success in this area. Finally, at present the quantum workforce is insufficient to meet our national quantum initiative requirements. This program will train a sizeable cadre of students at BS, MS, and PhD levels with practical hands-on experience modeling near-term analog and digital quantum computers, crossing over into quantum networks, to help fill this pressing need. In this project on new insight into entanglement dynamics enabled by NISQ devices, the team will pursue the connections between (i) complex entanglement, (ii) many-body decoherence, and (iii) integrability. QCA provide a practical quantum test-bed, proven in recent work to be realizable on digital quantum computers. (i) They will systematically study the full set of quasi-1D (extended 5-site) and 2D QCA, their complexity properties, and their prospective efficient implementation in digital quantum circuits on the Sycamore chip. Is complex entanglement a result of integrability? Or, are integrable systems, which happen to provably encompass 1D (3-site) Goldilocks QCA, a red herring for complexity? This remains to be resolved. (ii) They will systematically treat the decoherence properties of quasi-1D and 2D Goldilocks and non-Goldilocks QCA under quantum trajectories evolution with realistic conditions for both digital quantum circuits and analog quantum simulators. They will then build on prior studies of the 16 reversible elementary 1D QCA to a representative selection of the remaining 240 irreversible elementary 1D QCA in small quantum systems to see if many-body decoherence properties hold up. This study will include Rule 110, which is classically Turing complete; and point the way to the long-term goal of realizing a quantum version of Conway's game of life. (iii) They will provide a complete proof that 1D 3-site QCA under quite general conditions are integrable, and strong evidence for a conjecture that the proof extends to arbitrary sized neighborhoods. To this end they will study thermalization via a truncated generalized Gibbs ensemble based on newly discovered conserved charges; scrambling via the dynamics of the out-of-time-order correlator; and Page curves and spectral characteristics including many-body scars.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.

复杂性科学是21世纪世纪的重大问题之一，它深入探讨了诸如意识的生物学起源等深刻问题。 一般来说，复杂性的起源是什么？ 它已经出现在量子力学中了吗？ 我们需要一个新的物理理论，还是复杂性是我们所知道的产物？ 噪声中尺度量子计算机（NISQ）涉及越来越多的相互作用的量子子系统，从而增加了复杂性。 在NISQ计算机中研究这种紧急复杂性的一种方法是使用Goldilocks量子细胞自动机（QCA）。 Goldilocks QCA是写入量子电路的动态计算规则，涉及局部邻域中不太多和不太少之间的权衡或平衡-因此术语“Goldilocks”。 该项目将连接以前不同的基础数学和科学概念，如可积性和复杂性;为2D QCA的可能超越经典计算演示指明方向;并通过不可逆的基本QCA为开放量子系统开发新的量子计算范例，利用环境而不是避免环境，就像生命系统一样。 此外，该团队还提出了一种多方面的方法来实现更广泛的影响目标。 首先，他们每年将指导2-3名本科生从事美国最大的本科物理课程之一的研究。 其次，他们将通过担任《物理学杂志：复杂性》的执行编辑委员会来参与国际事务;并通过美国国务院作为杰斐逊科学研究员校友来支持科学外交。第三，他们将在混合和虚拟课堂环境中参与学生合作网络定量研究的教育发展;并通过在所有STEM学生均可访问的矿山荣誉计划中创建科学外交课程并公开传播。 第四，他们将通过一个支持性的、多样化的群体环境来增加物理学的多样性、公平性和包容性，并在这一领域取得成功。 最后，目前量子劳动力不足以满足我们的国家量子倡议要求。 该计划将培养相当数量的BS，MS和PhD级别的学生，他们具有模拟近期模拟和数字量子计算机的实际动手经验，跨越到量子网络，以帮助满足这一迫切需求。在这个关于NISQ设备实现的纠缠动力学的新见解的项目中，该团队将追求（i）复杂纠缠，（ii）多体退相干和（iii）可积性之间的联系。 QCA提供了一个实用的量子测试平台，在最近的工作中被证明可以在数字量子计算机上实现。 (i)他们将系统地研究全套准1D（扩展的5-site）和2D QCA，它们的复杂性特性，以及它们在西卡莫尔芯片上的数字量子电路中的预期有效实现。 复杂纠缠是可积性的结果吗？ 或者，可积系统，恰好可证明包含1D（3-site）Goldilocks QCA，是复杂性的一个红鲱鱼？ 这个问题有待解决。 (ii)他们将系统地处理准一维和二维Goldilocks和非Goldilocks QCA在量子轨道演化下的退相干特性，具有数字量子电路和模拟量子模拟器的现实条件。 然后，他们将在先前对16个可逆基本1D QCA的研究基础上，对小量子系统中剩余的240个不可逆基本1D QCA进行代表性选择，以确定多体退相干特性是否成立。 这项研究将包括规则110，这是经典的图灵完成;并指出了实现康威生命游戏的量子版本的长期目标。 (iii)他们将提供一个完整的证明，1D 3-网站QCA在相当一般的条件下是可积的，和一个猜想，证明扩展到任意大小的邻居强有力的证据。 为此，他们将通过基于新发现的守恒电荷的截断广义吉布斯系综来研究热化;通过非时间顺序相关器的动力学来扰乱;以及佩奇曲线和光谱特征，包括多体疤痕。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

项目成果

Integrable fractional modified Korteweg–deVries, sine-Gordon, and sinh-Gordon equations

• DOI: 10.1088/1751-8121/ac8844
• 发表时间: 2022-03
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: M. Ablowitz;Joel B. Been;L. Carr

Correlations between student connectivity and academic performance: A pandemic follow-up

学生连通性与学业成绩之间的相关性：大流行的后续行动

• DOI: 10.1103/physrevphyseducres.19.010106
• 发表时间: 2023
• 期刊: Physical Review Physics Education Research
• 影响因子: 3.1
• 作者: Crossette, Nathan;Carr, Lincoln D.;Wilcox, Bethany R.
• 通讯作者: Wilcox, Bethany R.

Emergent complex quantum networks in continuous-variables non-Gaussian states

• DOI: 10.1088/2058-9565/accdfd
• 发表时间: 2020-12
• 期刊: Quantum Science and Technology
• 影响因子: 6.7
• 作者: M. Walschaers;Bhuvanesh Sundar;N. Treps;L. Carr;V. Parigi