Improving qubit reduction for molecular simulations with randomized orbital sampling

Near-term quantum devices offer promising avenues for addressing the electronic structure problem in quantum chemistry, yet their limited qubits and susceptibility to noise constrain algorithmic scalability. Although the variational quantum eigensolver (VQE) has shown potential for small-scale systems, further improvements are necessary to handle large basis sets and large many-electron molecules efficiently. In this work, we introduce RO-VQE, an improved approach derived from the earlier optimized orbital algorithm that employs a randomized procedure for selecting and optimizing orbitals. We evaluate RO-VQE on hydrogen chains systems (H₂ and H₄)—a well-established benchmark for quantum chemistry methods—using minimal, split-valence, and correlation-consistent basis sets. For these systems, RO-VQE improves ground-state energy estimations compared to conventional VQE methods, matching the accuracy of systematic strategies in these test cases. These proof-of-concept results suggest that randomized active-space selection may offer a practical compromise in NISQ-era quantum computations, offering a flexible alternative to more deterministic methods, particularly for systems constrained by limited quantum resources.