  We will call a pure qubit state real if all its amplitudes are real numbers.
We show that any real 3-qubit state can be prepared using $R_y(\theta)$ gates
and at most four controlled-$Z$ gates, and we conjecture that four is optimal.
We also present an algorithm -- different from the 2008 algorithm given by
Znidaric, Giraud and Georgeot -- that prepares any 3-qubit state using local
gates and at most three controlled-$Z$ gates. Videos showing how our method
works for two- and three-qubit states can be found at
https://youtu.be/LIdYSs-rE-o and https://youtu.be/Kne0Vq7gyzQ
