Should the initiators get enough signatures, parliament would still have to give approval before a referendum could be held. A "Yes" vote would in turn require an absolute majority of the popular vote plus a majority of cantons (states).
It looks unlikely to happen, but we'll see. Switzerland has done some surprisingly backward things recently. In 2009, citizens voted to ban the construction of new minarets, the spires on mosques. If there's lots of popular support for this referendum, opportunistic politicians might get on board.
Only one other European country, Belarus, still has the death penalty these days. It's been fading away in developed countries over the last century. If Switzerland reintroduces it, it will be joining such human rights leaders as China, Iran, and Saudi Arabia. And here in the United States we still have the death penalty, of course.
The referendum would require the death penalty for murders involving sexual assault. The group argues that the death penalty is "fair and logical" for such "unimaginably cruel actions" and that "mourning is only possible after the killer has been executed."
There are endless problems with the death penalty. Too many to get into here. But this Swiss group seems to be arguing that the death penalty is better for victims' emotional and mental health. That's just wrong. There's a wealth of scientific research showing that cultivating forgiveness instead of feelings of revenge has a wide range of emotional and physiological benefits. It can reduce blood pressure and the risk of heart disease. There's a legitimate public health argument to be made for embracing criminal justice policies that reduce a sentiment of vindictiveness.