A Quantum Multi-Programming Framework to Maximize Quantum Resources for the LUCJ Ansatz

In the context of quantum computing, efficient resource management is crucial for optimizing throughput on cloud-based platforms and maximizing hardware utilization. In the present work, we propose an approach to tackle quantum chemistry problems via quantum multi-programming of the Local Unitary Cluster Jastrow (LUCJ) ans\"atze. The ground-state energy of the molecular system is obtained via Sample-based quantum diagonalization (SQD), further refined by its extended version (ext-SQD). Building upon the Qiskit Experiments package, which already supports parallel execution functionality for general tasks, we developed a novel parallel experiment class tailored for quantum chemistry problems. Cross-talk is a known issue in the multi-programming frameworks and can corrupt the ground-energy estimation of the simulated systems. To assess its impact within our approach, we simulated two conformations of the ethanol molecule: one at the equilibrium state (EtOH$_{Eq}$), and one with the O-H bond stretched to 1.2 ${{\AA}}$ (EtOH$_{1.2}$). We defined three different layouts that we executed in a randomized fashion, alternating serial and parallel execution within 10 independent replicates. The single modality of each circuit was kept as a baseline to evaluate the effect of cross-talk induced by quantum multi-programming. The energies obtained at the first-, last- and ext-SQD iteration were compared to the classical Heat-bath Configuration Interaction (HCI) reference. Our findings highlight the viability of a quantum multi-programming workflow for quantum chemistry as the robust post-processing protocol effectively mitigates possible cross-talk induced noise. At the final step of the configuration recovery process, the energy difference relative to the HCI reference is negligible, within 0.001 kcal/mol.