So I have this headcanon for Persocom!Q.
Q is the highest quality out of the greatest Persocoms there is and his data needs to be back up constantly, otherwise there is no possible way that the collecting can catch up with his processing power. He spends 98% of his time in a vast room with other super powerful computers, but in the actual form of box contained computers with screens, and he is plugged in to all of them, they help him process and back his data up. This room is also called Q branch.
James visits him when he has time and Q shoos him away because he's busy.