  The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has
recently attracted interest due to its use in Variation Quantum Eigensolver
(VQE) molecular simulations on quantum computers. However, when the size of
molecules increases, UCCSD becomes less interesting as it cannot achieve
sufficient accuracy. Including higher-order excitations is therefore mandatory
to recover the UCC's missing correlation effects. In this Letter, we extend the
Trotterized UCC approach via the addition of (true) Triple T excitations
introducing UCCSDT. We also include both spin and orbital symmetries. Indeed,
in practice, these later help to reduce unnecessarily circuit excitations and
thus accelerate the optimization process enabling to tackle larger molecules.
Our initial numerical tests (12-14 qubits) show that UCCSDT improves the
overall accuracy by at least two-orders of magnitudes with respect to standard
UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be
competitive with the CCSD(T) gold-standard classical method of quantum
chemistry.
