To check the ownership of /dev/kvm use
ls -al /dev/kvm
The user was root, the group kvm. To check which users are in the kvm group, use
grep kvm /etc/group
This returned
kvm:x:some_number:
on my system: as there is nothing rightwards of the final :, there are no users in the kvm group.
To add your user to the kvm group, you could use
sudo adduser $USER kvm