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Bounds on quantum evolution complexity via lattice cryptography

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I will present some results from arXiv:2202.13924, where we addressed the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. The notion of complexity of interest to us will be Nielsen’s complexity applied to the time-dependent evolution operator of the quantum systems. I will review Nielsen’s complexity, discuss the difficulties associated with this definition and introduce a simplified approach which appears to retain essential information about the integrable properties of the dynamical systems.

This talk is part of the Quantum Fields and Strings Seminars series.

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