The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
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An analytical method is presented to calculate Lanczos coefficients governing Krylov complexity in the reduced pulsating fuzzy sphere version of the BMN matrix model for large and small deformations.
In the BMN matrix model and its holographic duals, Krylov basis states and Lanczos coefficients are uniquely fixed by the model's mass parameter.
Spread complexity is recovered as the infinitesimal-time limit of a circuit complexity defined by minimal-cost synthesis with time-evolution and beam-splitting operations.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.
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Krylov Dynamics and Operator Growth in Time-Dependent Systems via Lie Algebras
The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
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Krylov state complexity for BMN matrix model
An analytical method is presented to calculate Lanczos coefficients governing Krylov complexity in the reduced pulsating fuzzy sphere version of the BMN matrix model for large and small deformations.
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Krylov complexity for Lin-Maldacena geometries and their holographic duals
In the BMN matrix model and its holographic duals, Krylov basis states and Lanczos coefficients are uniquely fixed by the model's mass parameter.
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A Quantum Computational Perspective on Spread Complexity
Spread complexity is recovered as the infinitesimal-time limit of a circuit complexity defined by minimal-cost synthesis with time-evolution and beam-splitting operations.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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Quantum Dynamics in Krylov Space: Methods and Applications
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.