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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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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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.