Native Client (NaCl) is Google's technology for allowing a sub-set of Intel x86 and ARM code to be executed natively within a web-browser for use as browser plug-ins, web applications, or even games. Google Native Client does support 3D hardware acceleration along with local file storage, dynamic loading, and other features not usually offered to web applications. The performance is said to be roughly on par with native execution. Right now Native Client is supported by Google's Chrome / Chromium web-browser, but NaCl is considered an open-source project.
There's been code to support the Qt4 tool-kit within NaCl, but now Morten Sorvig of Nokia has been working on Native Client support for Qt5. Morten shares in his mailing list message, "Qt 5 for NaCl is now roughly on par with the Qt 4 port and I would like to start the process of integrating it with the goal of continuing development upstream in Qt 5."
The Qt core, GUI, widgets, and network are among the components that are working for Qt5 right now within Google Native Client.
More information on Qt for Google Native Client can be found from the Nokia Qt developer Wiki.
Qt 5.0 is set to be release in 2012.