Determining the ability for universal quantum computing: 
Testing controllability via dimensional expressivity

Abstract

Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and 
is a prerequisite for universal quantum computing. Controllability tests can be used in the
design of quantum devices to reduce the number of external controls. Their practical use 
is hampered, however, by the exponential scaling of their numerical effort with the 
number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a 
parametrized quantum circuit. We show that controllability is linked to the number of 
independent parameters, which can be obtained by dimensional expressivity analysis. 
We exemplify the application of the algorithm to qubit arrays with nearest-neighbour 
couplings and local controls. Our work provides a systematic approach to the resource-
efficient design of quantum chips.