  The ability to implement any desired quantum logic gate on a quantum
processing unit is equivalent to evolution-operator controllability of the
qubits. Conversely, controllability analysis can be used to minimize the
resources, i.e., the number of external controls and qubit-qubit couplings,
required for universal quantum computing. Standard controllability analysis,
consisting in the construction of the dynamical Lie algebra, is, however,
impractical already for a comparatively small number of qubits. Here, we show
how to leverage an alternative approach, based on a graph representation of the
Hamiltonian, to determine controllability of arrays of coupled qubits. We
provide a complete computational framework and exemplify it for arrays of five
qubits, inspired by the ibmq_quito architecture. We find that the number of
controls can be reduced from five to one for complex qubit-qubit couplings and
to two for standard qubit-qubit couplings.
