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Formally a parallel execution looks feasible also if thed network can be implemented with physical couplings between arbitrary pair of bits, in particular between the ancillas and each encoding qubit. Note, however, that in such schemes there is typically only one channel that mediates the coupling between the various qubits [11,8]. Consequently, simultaneous execution of several two-qubit operations would result in N-qubit dynamics (N > 2) which is to be excluded. Therefore, in certain cases application of nearest-neighbor coupling appears to be even more powerful than coupling between arbitrary pairs of qubits.
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