Efficient quantum algorithms for $GHZ$ and $W$ states, and implementation on the IBM quantum computer

Efficient deterministic algorithms are proposed with logarithmic step complexities for the generation of entangled GHZ(N) and W-N states useful for quantum networks, and an implementation on the IBM quantum computer up to N = 16 is demonstrated. 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. Robust states are built with about twice the number of quantum bits which were previously achieved.