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.