How to get good performances when using symfony 2 ACL system with a large number of object?

How to get good performances when using symfony 2 ACL system with a large
number of object?

In our project we are using symfony 2 ACL system to control access to the
entities stored in a database (Postgresql).
Everything works fine until we want to check permission on large quantity
of object (a few hundreds). Then the performance are getting bad. On some
pages the number of query to the database is above 4000. This number is in
fact in direct relation with the number of entities in our database. The
more it grows the more query on this page need to be done.
Is there a way to check the user's authorization on many object while
conserving descent performance (keeping the number of query to the db
low)?