I think you want to install your second site on the same database but with a different table prefix, e.g. $table_prefix = "qa_"; in wp-config.php
You are then able to define a custom user and/or user_meta table by adding the following lines to wp-config.php
define('CUSTOM_USER_TABLE', [orig_table_prefix].'my_users');
define('CUSTOM_USER_META_TABLE', [orig_table_prefix].'my_usermeta');
Source: http://codex.wordpress.org/Editing_wp-config.php#Custom_User_and_Usermeta_Tables
I have read somewhere before that you may have to sort out a couple of issues of admin users on the second site, can’t find the link at the moment.