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

复杂性科学是21世纪深层次的突出问题之一，它涉及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？我们是否需要一种新的物理理论，或者复杂性是我们所知的产物？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，这导致了复杂性。研究NISQ计算机中这种新出现的复杂性的一种方法是用金发姑娘量子细胞自动机(QCA)。金发姑娘QCA是写入量子电路的动态计算规则，它涉及到在局部邻域内不太多和不太少之间的权衡--因此有了术语“金发姑娘”。促进科学进步，这个项目将连接以前截然不同的基本数学和科学概念，如可积性和复杂性；指出使用2D QCA进行可能的超经典计算演示的方法；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式，利用环境而不是像生命系统那样避开环境。此外，该团队提出了一种多方面的方法来满足更广泛的影响目标。首先，他们将每年指导2-3名来自美国最大的本科物理项目之一的本科生的研究。其次，他们将参与国际事务，在《物理杂志：复杂性》的执行编辑委员会任职；并作为杰斐逊科学学院的校友，通过美国国务院支持科学外交。第三，他们将致力于在混合和虚拟课堂环境中对学生合作网络进行量化研究方面的教育发展；并在Mines荣誉计划中创建一门科学外交课程，供所有STEM学生使用并公开传播。第四，他们将通过在这一领域取得成功的支持性、多样化的团队环境来增加物理学领域的多样性、公平性和包容性。最后，目前量子劳动力不足以满足我们国家量子倡议的要求。该计划将培训相当数量的BS、MS和博士水平的学生，他们具有对近期模拟和数字量子计算机进行建模的实际动手经验，并跨越到量子网络，以帮助满足这一紧迫需求。在这个由NISQ设备实现的关于纠缠动力学的新洞察项目中，该团队将探索(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试验台，最近的工作证明可以在数字量子计算机上实现。(I)他们将系统地研究准1D(扩展的5位点)和2D QCA的全集，它们的复杂性，以及它们在Sycamore芯片上的数字量子电路中的预期有效实现。复杂的纠缠是可积性的结果吗？或者，碰巧包含一维(3站点)金发姑娘QCA的可积系统是在转移复杂性吗？这个问题还有待解决。(Ii)他们将在数字量子电路和模拟量子模拟器的现实条件下，系统地处理准一维、二维金发姑娘和非金发姑娘QCA在量子轨迹演化下的退相干性质。然后，他们将在先前对16个可逆的基本1D QCA的研究的基础上，在小量子系统中选择剩余的240个具有代表性的不可逆的基本1D QCA，以查看多体消相干特性是否成立。这项研究将包括经典的图灵完成的规则110；并为实现康威生命游戏的量子版本的长期目标指明了方向。(Iii)他们将提供一个完整的证明，证明在相当一般的条件下一维三点QCA是可积的，并为一个猜想提供强有力的证据，该证明推广到任意大小的邻域。为此，他们将研究基于新发现的守恒电荷的截断广义吉布斯系综的热化；通过无序相关器的动力学；以及包括多体疤痕在内的佩奇曲线和光谱特征的混乱。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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, 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.