  We propose a way to solve BCS-type pairing model by to exactly solve its
spin-analogy in the subspace. The advantages of our method are to avoid to
directly deal with the approximate procedure and to transfer an exponentially
complicated problem to a polynomial problem. Moreover, it builds the
theoretical foundation of quantum simulation of pairing model and can be used
to check the precision of quantum simulation. It is also helpful to understand
the many-body quantum theory.
