アイテム詳細

要旨

We study circuit and state complexity in the universal setting of
(1+1)-dimensional conformal field theory and unitary transformations generated
by the stress-energy tensor. We provide a unified view of assigning a cost to
circuits based on the Fubini-Study metric and via direct counting of the
stress-energy tensor insertions. In the former case, we iteratively solve the
emerging integro-differential equation for sample optimal circuits and discuss
the sectional curvature of the underlying geometry. In the latter case, we
recognize that optimal circuits are governed by Euler-Arnold type equations and
discuss relevant results for three well-known equations of this type in the
context of complexity.