You must make the decision on what parts and how much of the C++ project you need in C#.
If you only need some functions than my
C# Interoperability article may interest you which is more like wrapping some funtionality. I wrote another article about
C++/Cli interoperability but it was for Windows phone. But the technique should be the same.
The usage of some Qt makes only sense, when it is already in code. Adding another framework makes your code more complex and opaque.