  In this work, we present a linear optical implementation for analog quantum
simulation of molecular vibronic spectra, incorporating the non-Condon
scattering operation with a quadratically small truncation error. Thus far,
analog and digital quantum algorithms for achieving quantum speedup have been
suggested only in the Condon regime, which refers to a transition dipole moment
that is independent of nuclear coordinates. For analog quantum optical
simulation beyond the Condon regime (i.e., non-Condon transitions) the
resulting non-unitary scattering operations must be handled appropriately in a
linear optical network. In this paper, we consider the first and second-order
Herzberg-Teller expansions of the transition dipole moment operator for the
non-Condon effect, for implementation on linear optical quantum hardware. We
believe the method opens a new way to approximate arbitrary non-unitary
operations in analog and digital quantum simulations. We report in-silico
simulations of the vibronic spectra for naphthalene, phenanthrene, and benzene
to support our findings.
