We introduce a simple algorithm for projecting on J=0 states of a many-body system by performing a series of rotations to remove states with angular momentum projections greater than zero. Existing methods rely on unitary evolution with the two-body operator J2, which when expressed in the computational basis contains many complicated Pauli strings requiring Trotterization and leading to very deep quantum circuits. Our approach performs the necessary projections using the one-body operators Jx and Jz. By leveraging the method of Cartan decomposition, the unitary transformations that perform the projection can be parametrized as a product of a small number of two-qubit rotations, with angles determined by an efficient classical optimization. Given the reduced complexity in terms of gates, this approach can be used to prepare approximate ground states of even-even nuclei by projecting onto the J=0 component of deformed Hartree-Fock states. We estimate the resource requirements in terms of the universal gate set {H,S,CNOT,T} and briefly discuss a variant of the algorithm that projects onto J=1/2 states of a system with an odd number of fermions.
