You may have heard the story about a scientist who wanted to bring the dead back to life, right? His name was Dr. Robert E. Cornish. He is best known for resurrection experiments as well as his use of electricity to force human and dog parts of a dead person to move. As you may know, humans have electricity of sorts inside them even after they die.
If you hit in just the right places with electricity, any part of the body can move pretty much. Now imagine seeing this before knowing that and a person with various electroshock components stands up in front of you, possibly moving. That could come off as a zombie for obvious reasons. While a real zombie apocalypse using this formula may be hard to do, it is at least possible to consider. The right inventor or scientist could make this possible.