Quantum measurements and gates by code deformation

The usual scenario in the fault-tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We propose to complement these techniques with code deformation, in which a given code is progressively changed in such a way that encoded qubits can be created, manipulated and non-destructively measured. We apply this approach to surface codes, where the computation is performed in a single code layer which is deformed using 'cut and paste' operations. All the interactions between qubits remain purely local in a two-dimensional setting.