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Using a photonic quantum computer for boson sampling has been demonstrated atremendous advantage over classical supercomputers. It is highly desirable todevelop boson sampling algorithms for realistic scientific problems. In thiswork, we propose a hybrid quantum-classical sampling (HQCS) algorithm tocalculate the optical spectrum for complex molecules considering anharmonicityand Duschinsky rotation (DR) effects. The classical sum-over-state method forthis problem has a computational complexity that exponentially increases withsystem size. In the HQCS algorithm, an intermediate harmonic potential energysurface (PES) is created, bridging the initial and final PESs. The magnitudeand sign (-1 or +1) of the overlap between the initial state and theintermediate state are estimated by quantum boson sampling and by classicalalgorithms respectively, achieving an exponential speed-up. Additionally, theoverlap between the intermediate state and the final state is efficientlyevaluated by classical algorithms. The feasibility of HQCS is demonstrated incalculations of the emission spectrum of a Morse model as well as pyridinemolecule by comparison with the nearly exact time-dependent density matrixrenormalization group solutions. A near-term quantum advantage for realisticmolecular spectroscopy simulation is proposed.

the journal of physical chemistry letters

Hybrid Quantum-Classical Boson Sampling Algorithm for Molecular  Vibrationally Resolved Electronic Spectroscopy with Duschinsky Rotation and  Anharmonicity