Quantum algorithms for astrochemistry and atmospheric science: Calculating vibrational spectra.

Though electronic structure is the most popular chemical application of the quantum information community, there are many substances for which it is the quantum vibrational (not electronic) behavior that is classically intractable. Here we outline the previously unaddressed ways in which solving the vibrational spectroscopy problem is mathematically distinct from the electronic problem. We discuss the calculation of high-lying excited states, low-depth methods for calculating transition amplitudes, and boson-to-qubit mappings. We study Suzuki-Trotter error for vibrational Hamiltonians relevant to astrochemistry, atmospheric science, and combustion. Most notably, we make resource comparisons with electronic structure, concluding with strong evidence that a vibrational problem instance will achieve quantum supremacy before an electronic one.