Graph test of controllability in qubit arrays: A systematic way to determine the minimum 
number of external controls.

Abstract

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 ibmqquito 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.