I am sending the HCL report.
I am not sure what model number to use, because the commonly used 15-5578 refers to various configuration. But when I use TN-5578-N2-711S, it seems to refer to very specific piece of hardware (with different CPUs, HDDs/SSDs etc.), the number may also include they key labels (Czech and Slovak in this case), which is too specific for HCL. This one has 16GiB RAM, 512GiB SSD and i7-7500U CPU.
The hardware is quite a new for Qubes 3.2. For this reason, I had to use a newer kernel. With the original one, I had issues with suspend (always froze) and GPU support. With the new one (probably the same you can install from unstable), it is much better. See https://groups.google.com/forum/#!searchin/qubes-users/5578|sort:relevance/qubes-users/v6_B7FHnNUE/NR-yv6OHBQAJ
for more details. I hope this will require no tuning with Qubes 4.0.
With the new kernel, it still sometimes hangs on restore, but not always.
Despite the laptop has both USB2 and USB3 ports, it contains just a single USB controller that also handles touchscreen, bluetooth and camera.
A similar model (5578 but with rather lower configuration) has TPM in the spec,  so this one might also have one. I believe I have seen some TPM-related config in BIOS setup. But Qubes does not detect the TPM, not sure why.
Wi-Fi requires putting "iwlmvm iwlwifi" to /rw/config/suspend-module-blacklist. Without this, you WiFi stops working after suspend/resume.
HDMI sound just does not work. I haven't elaborated on it (it is rather nice to have for me), but it works with Fedora 25 out of box, so there is a hope it will work well with Qubes 4.
Jack works with 4-pin headset with microphone. I am currently not sure if the button(s) on the headset do work. Well, there is a slight noise that is perceivable when there is no sound output.
Touchscreen does not work, but this is a general issue with Qubes. When implemented to qubes-input-proxy, it should work well.
I am unsure if there are some sensors like accelerometer, ambient light sensor etc. If thy are there, they don't work with Qubes out of box. This also means that tent mode does not rotate the screen automatically. However, when I switch it to tablet mode (i.e., rotate the screen by 360 degrees), it turns keyboard and touchpad off automatically.
There are few features I haven't tested: Bluetooth, Camera, card reader.
Few Qubes-unrelated notes:
* It does not have numpad, even the Fn does not allow pressing numbers on numpad. You have to rely on number row (or external keyboard).
* When running without X11, the PC speaker is very loud. The first time I header it, I got frightened a bit.
My reasons for the model: Good specs (16GiB RAM, reasonably large SSD, good CPU), good size (15"-17.3") and looks good for Qubes (no dedicated GPU, VT-d support).
Vít Šesták 'v6ak'