Krylov complexity as a proxy for circuit or holographic complexity (especially for subsystems)

Determine whether Krylov complexity provides a reliable proxy for circuit complexity and for holographic complexity in quantum field theories, particularly for subsystem complexity, given that Krylov complexity’s behavior depends sensitively on its ultraviolet definition.

Background

Beyond circuit complexity, other measures such as Krylov complexity have been widely investigated as potential diagnostics of operator/state growth. However, rigorous connections between such measures and circuit or holographic complexity are not established.

The authors note that in QFT the behavior of Krylov complexity depends on UV regularization choices, and they highlight uncertainty about whether it tracks circuit or holographic complexity—especially in the context of subsystems—thereby posing a clear open question for future work.