  We propose measurement-based quantum computation (MBQC) as a quantum
mechanical toy model for spacetime. Within this framework, we discuss the
constraints on possible temporal orders enforced by certain symmetries present
in every MBQC. We provide a classification for all MBQC temporal relations
compatible with a given initial quantum state and measurement setting, in terms
of a matroid. Further, we find a symmetry transformation related to local
complementation that leaves the temporal relations invariant. After light cones
and closed time-like curves have previously been found to have MBQC
counterparts, we identify event horizons as a third piece of the phenomenology
of General Relativity that has an analogue in MBQC.
