De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity

TL;DR

This paper explores how de Sitter spacetime can be modeled using tensor networks, revealing insights into cosmic no-hair, complementarity, and the potential link between spacetime evolution and quantum circuit complexity.

Contribution

It demonstrates that MERA tensor networks can model de Sitter space, showing fixed points of quantum channels and proposing a complexity-based interpretation of de Sitter evolution.

Findings

Reduced density operators approach a fixed point, illustrating cosmic no-hair.

MERA can be adapted to represent different forms of complementarity.

De Sitter evolution may be understood through circuit complexity concepts.

Abstract

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.