Shallow Electronic State Preparation for Quantum Chemistry with Quantum Monte Carlo Pre-Selection

Quantum computers hold great promise for molecular simulation, but noise remains a fundamental obstacle. We introduce a Quantum Monte Carlo (QMC) pre-screening procedure that constructs compact, physically motivated Givens rotation ans\"atze tailored to realistic quantum hardware. By identifying the most important wavefunction contributions early in a QMC simulation, we build circuits that are shallower that conventional alternatives while preserving number symmetry. Benchmarked on Quantinuum System Model H1, QMC-prescreened circuits outperform more complex ans\"atze under realistic noise conditions. The method offers a practical path toward chemical accuracy on quantum devices, by providing an adjustable trade-off between expressivity and circuit depth to generate shallow circuits suited to current high-noise devices, as well as deeper, more expressive circuits that can be deployed on future lower-noise devices.