  We investigate the proposed connection between de Sitter spacetime and the
MERA (Multiscale Entanglement Renormalization Ansatz) tensor network, and ask
what can be learned via such a construction. We show that the quantum state
obeys a cosmic no-hair theorem: the reduced density operator describing a
causal patch of the MERA asymptotes to a fixed point of a quantum channel, just
as spacetimes with a positive cosmological constant asymptote to de Sitter. The
MERA is potentially compatible with a weak form of complementarity (local
physics only describes single patches at a time, but the overall Hilbert space
is infinite-dimensional) or, with certain specific modifications to the tensor
structure, a strong form (the entire theory describes only a single patch plus
its horizon, in a finite-dimensional Hilbert space). We also suggest that de
Sitter evolution has an interpretation in terms of circuit complexity, as has
been conjectured for anti-de Sitter space.
