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Current quantum computing hardware is restricted by the availability of onlyfew, noisy qubits which limits the investigation of larger, more complexmolecules in quantum chemistry calculations on quantum computers in thenear-term. In this work, we investigate the limits of their classical andnear-classical treatment while staying within the framework of quantum circuitsand the variational quantum eigensolver. To this end, we consider naive andphysically motivated, classically efficient product ansatz for the parametrizedwavefunction adapting the separable pair ansatz form. We combine it withpost-treatment to account for interactions between subsystems originating fromthis ansatz. The classical treatment is given by another quantum circuit thathas support between the enforced subsystems and is folded into the Hamiltonian.To avoid an exponential increase in the number of Hamiltonian terms, theentangling operations are constructed from purely Clifford or near-Cliffordcircuits. While Clifford circuits can be simulated efficiently classically,they are not universal. In order to account for missing expressibility,near-Clifford circuits with only few, selected non-Clifford gates are employed.The exact circuit structure to achieve this objective is molecule-dependent andis constructed using simulated annealing and genetic algorithms. We demonstrateour approach on a set of molecules of interest and investigate the extent ofour methodology's reach. Empirical validation of our approach using numericalsimulations shows a reduction of the qubit count of up to a 50\% at a similaraccuracy as compared to the separable-pair ansatz.

Partitioning Quantum Chemistry Simulations with Clifford Circuits