Exact closed-form expression for unitary spin-adapted fermionic singlet double excitation operators

We derive exact closed-form expressions for the matrix exponential of the anti-Hermitian spin-adapted singlet double excitation fermionic operators. These expressions enable the efficient implementation of such operators within unitary product state frameworks targeting conventional hardware, and allow for the implementation of ansatze that guarantee convergence to specific spin symmetries. Moreover, these exact closed-form expressions might also lay the groundwork for constructing spin-adapted circuits for quantum devices.