The Japanese knew how to make an edged weapon. This is a naginata in action against rolled bamboo mats, a practice known as Tameshigiri.
You've probably seen something similar with the familiar katana, or samurai sword. The Naginata was a polearm that essentially mated the cutting edge of the samurai sword with the leverage of a spear.
Traditional tales speak of warriors whirling the naginata around their bodies like windmills, sweeping flights of arrows out of the air with a swipe, and even beheading charging horses with one well-timed cut.
True? Maybe. The cutting potential of such a weapon is obvious. I'm not entirely sure I'd recommend a naginata as a zombie defense tool for the uninitiated, but it's worth looking into.