Obtaining Accurate Ground-State Properties on Near-term Quantum Devices

Accurate ground-state calculations on noisy quantum computers are fundamentally limited by restricted ansatz expressivity and unavoidable hardware errors. We introduce a hybrid-quantum classical framework that simultaneously addresses these challenges. Our method systematically purifies noisy two electron reduced density matrices from quantum devices by enforcing N-representability conditions through efficient semidefinite programming, guided by a norm-based distance constraint to the experimental data. To implement this constraint, we develop a hardware efficient calibration protocol based on Clifford circuits. We demonstrate near full configuration interaction accuracy for ground-state energies of H2, LiH, and H4, and compute precise scattering intensities for C6H8 on noisy hardware. This approach surpasses conventional methods by simultaneously overcoming both ansatz limitations and hardware noise, establishing a scalable route to quantum advantage and marking a critical step toward reliable simulations of complex molecularnsystems on noisy devices.