We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific lightharvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
TOC GraphicCalculating the absorption spectrum of molecules is a common and important problem in theoretical chemistry, as it aids both the interpretation of experimental spectra and the a priori design of molecules with particular optical properties prior to performing a costly laboratory synthesis. Further, in many molecular clusters and systems, absorption and emission spectra of molecules are required for calculating energy transfer rates [1]. The widespread use of mature software that solves the vibronic problem is one indication of its relevance to chemistry [2][3][4][5].Many quantum algorithms have been proposed for practical problems in chemistry, chiefly for solving the fermionic problem of determining the lowest-energy configuration of N e electrons, given the presence of a set of clamped atomic nuclei [6][7][8][9][10][11][12][13][14]. However, for many chemical problems of practical interest, solving the groundstate electronic structure problem is insufficient. To calculate exact vibronic spectra, for instance, an often combinatorially scaling classical algorithm must be imple-