RETURN TO ISSUE In this work, we present a linear optical implementation foranalog quantum simulation of molecular vibronic spectra, incorporating thenon-Condon scattering operation with a quadratically small truncation error. Todate, analog and digital quantum algorithms for achieving quantum speedup havebeen suggested only in the Condon regime, which refers to a transition dipolemoment that is independent of nuclear coordinates. For analog quantum opticalsimulation beyond the Condon regime (i.e., non-Condon transitions), theresulting nonunitary scattering operations must be handled appropriately in alinear optical network. In this paper, we consider the first- and second-orderHerzberg–Teller expansions of the transition dipole moment operator for thenon-Condon effect for implementation on linear optical quantum hardware. Webelieve that the method opens a new way to approximate arbitrary nonunitaryoperations in analog and digital quantum simulations. We report in silicosimulations of the vibronic spectra for naphthalene, phenanthrene, and benzeneto support our findings.