How could I make a C++ compiler for a game engine like how QT does it?

[AI_Messiah]

I am not making a replacement for QT. I just want to make a game engine with C++ scripting. I have looked for C++ compilers and not found much that makes sense. If QT is open source, then why can't I us a compiler like Visual Studio like QT does?

[Chris Kawa]

I just want to make a game engine with C++ scripting

C++ is not a typical scripting language like lua or python. It needs to be compiled into a binary first. You either compile it along with your engine or make a plugin system - compile the code into a shared library and load/unload it at runtime.

I have looked for C++ compilers and not found much that makes sense

There are couple of major C++ compilers out there - MSVC, GCC and Clang. There are bunch of others, like the Intel's ICC, but these three are the most common ones. What do you want to know about them exactly?

If QT is open source, then why can't I us a compiler like Visual Studio like QT does?

Sorry, what you said here makes no sense. Qt is a C++ library. You can compile it with any C++ compiler you want. Visual Studio is not a compiler. It's an IDE (Integrated Development Environment). It comes with the MSVC compiler, but you can use others with it too. I've no idea what Qt being open source has anything to do with it. Visual Studio and MSVC are Microsoft's products. Qt is a Qt Company's product.
You can use MSVC however you want and it doesn't have to do anything with Qt.

[AI_Messiah]

I mean MSVC as the compiler.

[Chris Kawa]

I mean MSVC as the compiler

Ok, so you asked why you can't use it.
Well, you can.