Closed-Form Expressions for Unitaries of Spin-Adapted Fermionic Operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while na\"ive Trotterization schemes break spin symmetry. In this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalized single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.