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

Edge modes, extended TQFT, and measurement based quantum computation