Complex Networks on Quantum States in AMO Platforms

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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.