Initiative Q is a new currently and a payment system which is yet to be implemented. It is currently unknown whether the project is legit or not.
We tried to investigate whether the scheme is legit or not. Initiative Q is asking people to sign up to their network. By signing up, users provide their name and email address. However, there is currently no network or Q currency to speak of. By having people sign up now, Initiative Q hopes to build a huge network of potential users. According to Forbes, they are targetting between 30 million to 40 million signups. The incentive for people to sign up provided by them is that it doesn't cost anything to sign up, but there is an indirect promise that there might be some big future value of that Q currency.
However, there is no guarantee that the project will ever be implemented in the future. There are also no details about the project's funding. Further, there are no recent updates provided on the website about the project. We do not know whether the introductory offer is sustainable for the company. The token being distributed right now is not tradable, and hence worthless. On the other hand, they have built a network of more than four million adopters. There is no financial risk to join as they do not ask anyone to invest any money.
To sum up, it is too early to say whether the scheme is legitimate or not.