Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography

Abstract: We introduce QC-CBT-AFQMC, a hybrid algorithm that incorporates computational basis tomography (CBT) into the quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) method proposed by Huggins et al. [Nature 603, 416-420 (2022)], replacing the use of classical shadows. While the original QC-AFQMC showed high accuracy for quantum chemistry calculations, it required exponentially costly post-processing. Subsequent work using Matchgate shadows [Commun. Math. Phys. 404, 629 (2023)] improved scalability, but still suffers from prohibitive computational requirements that limit practical applications. Our QC-CBT-AFQMC approach uses shallow Clifford circuits with a quadratic reduction of two-qubit gates over the original algorithm, significantly reducing computational requirements and enabling accurate calculations under limited measurement budgets. We demonstrate its effectiveness on the hydroxyl radical, ethylene, and nitrogen molecule, producing potential energy curves that closely match established benchmarks. We also examine the influence of CBT measurement counts on accuracy, showing that subtracting the active space AFQMC energy mitigates measurement-induced errors. Furthermore, we apply QC-CBT-AFQMC to estimate reaction barriers in [3+2]-cycloaddition reactions, achieving agreement with high-level references and successfully incorporating complete basis set extrapolation techniques. These results highlight QC-CBT-AFQMC as a practical quantum-classical hybrid method that bridges the capabilities of quantum devices and accurate chemical simulations.