  We propose efficient algorithms with logarithmic step complexities for the
generation of entangled $GHZ_N$ and $W_N$ states useful for quantum networks,
and we demonstrate an implementation on the IBM quantum computer up to $N=16$.
Improved quality is then investigated using full quantum tomography for low-$N$
GHZ and W states. This is completed by parity oscillations and histogram
distance for large $N$ GHZ and W states respectively. We are capable to
robustly build states with about twice the number of quantum bits which were
previously achieved. Finally we attempt quantum error correction on GHZ using
recent schemes proposed in the literature, but with the present amount of
decoherence they prove detrimental.
