  Recently it has been shown that projected entangled-pair states can be
considered as a (physically motivated) resource state for measurement-based
quantum computation. Here we elaborate on how to construct a deterministic
measurement-based quantum computation model on projected entangled-pair states.
In particular, we use this scheme to build a 4-level many-body model for
universal quantum computation on qubits. We also derive a 3-local parent
Hamiltonian for this model, whose ground state is non-degenerate.
