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