Quantum Chemistry with Near-Clifford Circuits*

The variational quantum eigensolver is a near-term quantum algorithm for solving molecular electronic structure problems on quantum devices. However, current hardware is restricted by the availability of only few, noisy qubits. This limits the investigation of larger, more complex molecules. In this work, we investigate how far we can go with classical or close-to-classical treatment while staying within the framework of quantum circuits. To this end, we consider both a naive and a physically motivated product ansatz for the parametrized wavefunction in form of the separable pair ansatz, which is classically efficient; this is combined with classical post-treatment to account for interactions between subsystems originating from this ansatz. The classical treatment is given by another quantum circuit that has support between the enforced subsystems and is folded into the Hamiltonian. To avoid an exponential increase in the number of Hamiltonian terms, the entangling operations are constructed from purely Clifford or near-Clifford circuits. While purely Clifford circuits can be simulated efficiently classically, they are not universal; in order to account for the thus missing expressibility, near-Clifford circuits with only few, selected non-Clifford gates are employed. The exact circuit structure to do so is molecule-dependent and is constructed using simulated annealing and genetic algorithms. We demonstrate our approach on a set of molecules of interest and explore how far the methodology reaches. Empirical validation of our approach using numerical simulations shows up to a 50% qubit reduction for some molecules.