  We consider the problem of selectively controlling couplings in a practical
quantum processor with always-on interactions that are diagonal in the
computational basis, using sequences of local NOT gates. This methodology is
well-known in NMR implementations, but previous approaches do not scale
efficiently for the general fully-connected Hamiltonian, where the complexity
of finding time-optimal solutions makes them only practical up to a few tens of
qubits. Given the rapid growth in the number of qubits in cutting-edge quantum
processors, it is of interest to investigate the applicability of this control
scheme to much larger scale systems with realistic restrictions on
connectivity. Here we present an efficient scheme to find near time-optimal
solutions that can be applied to engineered qubit arrays with local
connectivity for any number of qubits, indicating the potential for practical
quantum computing in such systems.
