Entangling Power and Quantum Circuit Complexity

Notions of circuit complexity and cost play a key role in quantum computing simulation where they capture the (weighted) minimal number gates that is required to implement unitary. Similar notions also become increasingly prominent high energy physics study holography. While entanglement have general little implications for unitary, this note, we discuss simple such relationship when both state unitary take small values, building on ideas how values entangling power add up. This bound implies if entropies grow linearly time, so does cost. The are two-fold: It provides insights into growth short times. In context simulation, it allows compare digital analog simulators. main technical contribution continuous-variable incremental bound.