标题： 关于复杂性和对偶性 显示英文标题

标题： On Complexity and Duality

摘要： 我们探讨量子系统中复杂性和对偶性之间的关系，重点研究局部和非局部算符在时间演化下的行为。 我们发现，在特定映射下与局部算符对偶的非局部算符表现出类似于其局部对应物增长的行为，特别是在考虑状态复杂性时。 对于开放的横向伊辛模型，这导致了对偶两侧算符动力学的整洁组织，均与二次费米子模型（如基塔耶夫链）中预期的增长一致。 然而，在检查周期性链时，边界项的映射提供了访问高度复杂算符多个分支的途径。 这些算符导致了奇偶混合算符的更大饱和复杂度值，并与二次哈密顿量所预期的结果形成对比。 我们的结果揭示了量子系统中非局域性、复杂度增长和对偶性之间错综复杂的关系。 显示英文摘要

摘要： We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local operators under specific mappings, exhibit behavior that mimics the growth of their local counterparts, particularly when considering state complexity. For the open transverse Ising model this leads to a neat organisation of the operator dynamics on either side of the duality, both consistent with growth expected in a quadratic fermion model like the Kitaev chain. When examing periodic chains, however, the mapping of boundary terms provides access to multiple branches of highly complex operators. These give rise to much larger saturation values of complexity for parity-mixing operators and are in contrast to what one would expect for a quadratic Hamiltonian. Our results shed light on the intricate relationship between non-locality, complexity growth, and duality in quantum systems.