Ok Lets go through this one by one
The value here is not a map at all. If it had been
then it is Map of map.
Next,
Does the structure of building map of maps is correct?
Sure, it is correct, if your program needs it. For example, a telephone directory is an example of map<Name and Number>. In case you are tourist agency and you have a number of telphone directories(of different cities) and you put them in shelves by alphabetic order, then you are using a Map pf maps.
Next,
How to lookup these map of maps to locate a particular qd instance, whose states(allocation and quotastate) matches those of my method parameters(allocation and quotastate) in which I use these map of maps.
I really dont understand the question, sorry!
Next,
Why they employ map of maps here by saving one of the qd's state in one TreeMap & other state with the qd instance in the other TreeMap?
That depends upon some requirement in the project and is a matter to be discussed with designer/developer who put that code/logic. I guess there should be some other part of the project that might require such a construct.