Quantum

On Information Propagation in Krylov Subspaces

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Briefings

A 2026 arXiv preprint establishes a speed limit for information propagation in Krylov subspaces, identifying super-ballistic lightcones for power-law growing Lanczos coefficients. The study confirms causality constraints limiting these coefficients to linear growth, validated against $SL(2,R)$, Heisenberg Weyl algebras, and the Ising model. Results extend to $Q$-complexity families, offering a Lieb-Robinson bound analogue for condensed matter physics.

Key points

• Krylov subspace methods model quantum initial value problems as one-dimensional chains using time-ordered path formulations.
• Power-law growing Lanczos coefficients ($b_n \sim n^\delta$) yield super-ballistic lightcones with exponential spreading for maximal growth $\Δ = 1$.

Context and limitations

The findings are limited to specific algebraic structures ($SL(2,R)$, Heisenberg Weyl, Ising model) and $Q$-complexity families. Results are based on theoretical analysis and illustrative examples rather than experimental verification. The preprint status indicates uncertainty regarding the general applicability of the bounds.

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