Multiseed Krylov complexity
arXiv:2409.15666 · doi:10.1103/PhysRevLett.134.050402
Abstract
Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and chaotic dynamics, but its ability to do so depends precariously on the choice of the initial seed. We propose to apply such considerations not to a single operator, but simultaneously to a collection of initial seeds in the manner of the block-Lanczos algorithm. We furthermore suggest that this collection should comprise all simple (few-body) operators in the theory, which echoes the applications of Nielsen complexity to dynamical evolution. The resulting construction, unlike the conventional Krylov complexity, reliably distinguishes integrable and chaotic Hamiltonians without any need for fine-tuning.
v2: comments and references added, published version
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- From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
- Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory
- Probing the localization effects in Krylov basis