Might be late to the party - also, this answer is for LAMP users who got to this thread from google, like me.
Basically, the problem is PMA is trying to connect to SQL with a user that doesn't exist.
At /etc/phpmyadmin/config-db.php, you will find 2 variables: $dbuser, and $dbpass. Those specify the MySQL user and Password that PMA is trying to connect with.
Now, connect with some username/password that work (or just "root" if you are connecting from localhost), create a new user with global priviliges (e.g - %PMA User% with password %Some Random Password%), then in the above mentioned file set:
$dbuser = %PMA User% ;
$dbpass = %Some Random Password%;
You might also change other stuff there, like the server address ($dbserver), the port ($dbport, which might not be the default one on your machine), and more.