Qt developers have made it possible to run Qt-based in the browser via Google's NaCl (Native Client) feature, and they intend to have this available as an option in the upcoming Qt 5.
NaCL is a project that allows native code to run in the browser under restricted conditions. For computation intensive bits of web applications, using NaCl to include native code can boost the performance of web applications. Applications that deal with editing multimedia, for example, can benefit a lot from this, as JavaScript often does not provide the kind of performance that native code can.
However, NaCl is not a standard, and not available on any browser other than Google Chrome. It is open source, but in many ways it isn't a clearly defined part of the web. Web applications using Native Client can be published to the Google Chrome Web Store.
Qt applications are already widely portable, and can run on Linux, Mac OSX, Windows, Android, and many other systems. GTK+, a UI framework that is used by Gnome, has another approach to enabling apps to run in the browser via an HTML5 backend. Since that uses standard canvas elements, it is perhaps a better approach that will work on more browsers.
