As of June 2019 and Qt 5.13, Qt Quick 2 supports the following backends:
- OpenGL 2.0
- OpenGL ES 2.0
- Direct3D 12 (support is still experimental)
- OpenVG
- Software rendering
However, only OpenGL and OpenGL ES are fully functional. For instance some effects (like particles) do not work with the other banckends.
For more information about how to select a backend and what are the limitations of each backend I suggest to read the documentation: https://doc.qt.io/qt-5/qtquick-visualcanvas-adaptations.html
Regarding Vulkan specifically, Qt has added support to it since Qt 5.10.
However, the support is still very limited and does not cover Qt Quick.
Change will come in the future; quoting an email from Qt development mailing list:
A very early preview of Qt Quick for Vulkan, Metal, and D3D11 may come already in Qt 5.14, then evolve in 5.15 and beyond, with 6.0 as its final destination.
So rendering Qt Quick with Vulkan should be possible when Qt 6 will be out. The planned release date for Qt 6 is currently November 2020. In the mean time technical previews might be available starting with Qt 5.14.
I would not be too optimistic for anything before Qt 6 as (1) it will just be technical previews and (2) as far as I know, current official Qt binaries are not linked with Vulkan at all and you need to build Qt from source if you want to use Vulkan.