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The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, its usual implementation in the projected form becomes nonvariational when the excitations are truncated and therefore fails to describe quantum states characterized by strong electronic correlations. Thanks to its exponential form, CC can be naturally adapted to quantum algorithms. In particular, the quantum unitary CC (q-UCC) is a popular wavefunction Ansatz for the Variational Quantum Eigensolver (VQE). The variational nature of this approach can lead to significant advantages compared to its classical equivalent (in the projected form), in particular for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCC, approximations need to be introduced in order to make this approach implementable in a stateof-the-art quantum computer. In this work, we propose several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems such as H 4 , H 2 O and N 2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. The results, which are in good agreement with the exact solutions, promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.