This worked for me and might not work for you. It's a seriuos change to your system, you need to be familiar with apt and with fixing missing or invalid dependencies.
Try it at your own risk!
apt purge kubuntu-desktop plasma-desktop kde-baseapps kde-runtime kubuntu-driver-manager
apt autoremove
If you have any KDE PPA, delete it. I had kubuntu backports, so:
rm /etc/apt/sources.list.d/kubuntu-ppa-ubuntu-backports-xenial.list
$ wget -qO - 'http://archive.neon.kde.org/public.key' | sudo apt-key add -
$ sudo apt-add-repository http://archive.neon.kde.org/user/lts
$ sudo apt-get update
$ sudo apt-get install neon-desktop
dpkg-reconfigure sddm
apt install kde-config-gtk-style kde-config-gtk-style-preview plymouth-theme-breeze grub-theme-breeze
Upgrade everything. Repeat if necessary, until everything is really up to date and you have no held-back packages.
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get dist-upgrade