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We present the idea of emergent qubits by an exact model construction on atrestle, also generalized to arbitrary graphs. The corresponding eigenstatesare quantum paramagnetic, with free multipolar moments. We rigorously transformthe toric code model on a torus, cylinder and sheet into emergent qubits,writing all the eigenstates exactly. We devise exact quantum circuits for thetoric code and other eigenstates described here. The depth of the circuit fortoric code eigenstates on torus grows linearly with the total number of qubits,as compared to the sublinear growth on cylinder or sheet.

Unfolding the Toric Code Model with Emergent Qubits