  Topological phases of matter are often described using auxiliary systems in
one extra dimension. I review the one-dimensional cluster state--the simplest
quantum state with Symmetry-Protected Topological (SPT) order--as a toy model
of holographic duality, and inspect it for clues about defining holographic
complexity. Group cohomology, which classifies SPT orders, is a viable
candidate for a robust definition of complexity in gauge/gravity duality.
