[2605.28681] Krylov complexity has all of it

View a PDF of the paper titled Krylov complexity has all of it, by Wolfgang M”uck

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Summary:This paper establishes that Krylov complexity comprises your complete details about the dynamics of a quantum operator, extending the checklist of equal portions that may serve this goal, such because the Lanczos coefficients, the return amplitude, and the spectral density. To display this equivalence, an express recursive algorithm is constructed to calculate Lanczos coefficients from the Taylor growth of the Krylov complexity round $t=0$. Moreover, the paper discusses the excellence between Krylov and unfold complexity, clarifying why an identical recursive algorithm can not exist for the latter with out further dynamical enter. These outcomes present a “proof of precept” for utilizing Krylov complexity as a whole characterization of operator evolution in quantum methods.