  The quality of controlling a system of optical cavities in the
Tavis-Cummings-Hubbard (TCH) model is estimated with the examples of quantum
gates, quantum walks on graphs, and of the detection of singlet states. This
type of control of complex systems is important for quantum computing, for the
optical interpretation of mechanical movements, and for quantum cryptography,
where singlet states of photons and charges play an essential role. It has been
found that the main reason for the decrease of the control quality in the THC
model is due to the finite width of the atomic spectral lines, which is itself
related to the time energy uncertainty relation. This paper evaluates the
quality of a CSign-type quantum gate based on asynchronous atomic excitations
and on the optical interpretation of the motion of a free particle.
