Digia has been experimenting with porting Google's open-source Chromium web-browser in the Qt world.
Zeno Albisser of Digia has publicly shared work they did to prototype the integration of Chromium into QtQuick 2 and Qt Widgets.
This experimental prototype of Chromium in the Qt world is still very primitive and for now only works on Linux/X11 and gyp/ninja is used as the build system wrapped around qmake. Right now the Chromium support can be toyed with by building Chromium from Google's sources and then applying separate patches from Digia atop the QtWebEngine code-base.
More details on this experiment can be found via the Digia Blog