Spacetime as a quantum circuit

A bstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits map between boundary states at different times and Wilsonian cutoffs, the complexity those is given by gravitational action. The optimal circuit minimizes This a generalization both “complexity equals volume” conjecture to unoptimized circuits, path integral optimization cutoffs. Using tools from $$ T\overline{T} T ¯ , we find surfaces constant scalar curvature play special role in optimizing circuits. also an interesting connection our proposal kinematic space, discuss possible representations gate counting interpretations