Krylov construction and complexity for driven quantum systems

Abstract

Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos, and has recently been much studied for various time-independent systems. We initiate the study of K-complexity in time-dependent (driven) quantum systems. For periodic time-dependent (Floquet) systems, we develop a natural method for doing the Krylov construction and then define (state and operator) K-complexity for such systems. Focusing on kicked systems, in particular the quantum kicked rotor on a torus, we provide a detailed numerical study of the time dependence of Arnoldi coefficients as well as of the K-complexity with the system coupling constant interpolating between the weak and strong coupling regime. We also study the growth of the Krylov subspace dimension as a function of the system coupling constant.

version 3: 19 pages, minor changes, more references added, 2 new plots on spectral statistics, published in Phys. Rev. E

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Cited by in corpus (18)

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• Integrability and complexity in quantum spin chains
• Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
• Spread complexity and quantum chaos for periodically driven spin chains
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Measurable Krylov Spaces and Eigenenergy Count in Quantum State Dynamics
• Streamlined Krylov construction and classification of ergodic Floquet systems
• Properties of Krylov state complexity in qubit dynamics
• Exploring quantum ergodicity of unitary evolution through the Krylov approach
• Inflationary power spectrum from the Lanczos algorithm
• Dependence of Krylov complexity on the initial operator and state
• Engineering Quantum Reservoirs through Krylov Complexity, Expressivity and Observability
• From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
• Probing the localization effects in Krylov basis
• Spread complexity and localization in $\mathcal{P}\mathcal{T}$-symmetric systems
• Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures