Efficient Quantum Chemistry Calculations on Noisy Quantum Hardware

Abstract A hardware‐efficient optimization scheme is presented for quantum chemistry calculations, utilizing the Sampled Quantum Diagonalization (SQD) method. This algorithm, optimized SQD (SQDOpt), combines the classical Davidson method technique with added multi‐basis measurements to optimize a quantum Ansatz on hardware using a fixed number of measurements per optimization step. This addresses the key challenge associated with other quantum chemistry optimization protocols, namely Variational Quantum Eigensolver (VQE), which must measure in hundreds to thousands of noncommuting Pauli terms to estimate energy on hardware, even for molecules with less than 20 qubits. Numerical results for various molecules, including hydrogen chains, water, and methane, demonstrate the efficacy of this method compared to classical and quantum variational approaches, and the performance on the ibm‐cleveland quantum hardware is confirmed, where instances are found where SQDOpt either matches or exceeds the solution quality of practical implementations of noiseless VQE. A runtime scaling indicates that SQDOpt on quantum hardware is competitive with classical state‐of‐the‐art methods, with a crossover point of 1.5 seconds/iteration for the SQDOpt on quantum hardware and classically simulated VQE with the 20‐qubit molecule. These findings suggest that the proposed SQDOpt framework offers a scalable and robust pathway for quantum chemistry simulations on noisy intermediate‐scale quantum (NISQ) devices.