Krylov winding emerges as a generic feature of quantum chaotic systems from the universal operator growth bound, producing size winding when a low-rank Krylov-to-size mapping exists and the chaos bound saturates.
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Entropy injection from an environment enlarges the effective Hilbert space and enhances many-body chaos, demonstrated via analytical computation of relaxation and Lyapunov exponent in a solvable complex Brownian SYK model.
The Levy SYK model is solved exactly at large N, with mu tuning the system from free theory at mu=0 to the standard maximally chaotic SYK at mu=2.
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for consistency.
Lyapunov exponents act as order parameters for first-order phase transitions in Horava-Lifshitz black holes with mean-field critical exponent 1/2, while chaos bounds are violated below a horizon-radius threshold even in stable phases.
Double-scaled fermionic and bosonic embedded ensembles are equivalent to double-scaled complex SYK and solvable via the Wick product of non-commuting Gaussian random variables, yielding a duality to the chord Hilbert space.
Mixing time of Lindblad-governed open quantum systems is determined by the Liouvillian gap plus trace-norm factors of eigenmodes, yielding rapid mixing conditions via sparsity constraints on the Hamiltonian and local Lindblad operators.
In the fully chaotic regime of the kicked top, long-time freeness is reached exponentially fast, accompanied by a hierarchy of time scales indicating a multifractal approach.
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.
TETRIS-ADAPT-VQE achieves fidelities above 99.3% for SYK (N=20) and 99.9998% for SK (L=18) but requires large resources for SYK models.
Perspective review comparing variational and feedback quantum algorithms for simulating phase transitions in quantum many-body systems, highlighting barren plateaus and advocating physics-informed hybridization.
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 Winding and Emergent Coherence in Operator Growth Dynamics
Krylov winding emerges as a generic feature of quantum chaotic systems from the universal operator growth bound, producing size winding when a low-rank Krylov-to-size mapping exists and the chaos bound saturates.