I had the same issue when i was setting up Q2A as in sub directory.
This is mod rewrite rule issue and can be done very easily in a second.
Go to your QA site root and find .htaccess file
Open in to notepade or any text editor ( DO NOT USE WORD OR SIMILAR )
If your q2a site directory name is qa than copy and pase same code as below
DirectoryIndex index.php
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /qa/
RewriteCond %{REQUEST_URI} ^(.*)//(.*)$
RewriteRule . %1/%2 [R=301,L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^.*$ /qa/index.php?qa-rewrite=$0&%{QUERY_STRING} [L]
</IfModule>
If your q2a site directory name is different than change /qa/ with your directory name. Make sure this is the same code I have used for my own SSO site and it works perfect and I share this to other and works perfect too. So I believe this should work for you as well :)