Going back nearly one year there has been Vulkan work around Qt while with Qt 5.10 it's becoming a reality. However, with Qt 5.9 not even being released until the end of May, Qt 5.10 isn't going to officially debut until either the very end of 2017 or early 2018.
Qt Vulkan support had been staged in this repository but that's been shutdown as the work has now landed in the "dev" code-base for Qt 5.10.
Introduced is a QVulkanWindow to provide a Vulkan-capable window with a double-buffered FIFO swap-chain. This is good for starting out with a Qt Vulkan application while making a custom QWindow sub-class can offer up more Vulkan possibilities.
There is also a QPA-based Vulkan library loader, core function resolver, and instance creation support for Vulkan. More details on that here. There will likely be additional Vulkan work landing in the months ahead until the Qt 5.10 feature freeze down the road.
So while we'll still need to wait another 9+ months at least, Vulkan support is coming to Qt 5.10.