  Quantum teleportation can be used to define a notion of parallel transport
which characterizes the entanglement structure of a quantum state
\cite{Czech:2018kvg}. This suggests one can formulate a gauge theory of
entanglement. In \cite{Wong:2022mnv}, it was explained that measurement based
quantum computation in one dimension can be understood in term of such a gauge
theory (MBQC). In this work, we give an alternative formulation of this
"entanglement gauge theory" as an extended topological field theory. This
formulation gives a alternative perspective on the relation between the circuit
model and MBQC. In addition, it provides an interpretation of MBQC in terms of
the extended Hilbert space construction in gauge theories, in which the
entanglement edge modes play the role of the logical qubit.
