  In recent years, numerical simulations with Gaussian initial states have
demonstrated the existence of a quantum bounce in loop quantum cosmology in
various models. A key issue pertaining to the robustness of the bounce and the
associated physics is to understand the quantum evolution for more general
initial states which may depart significantly from Gaussianity and may have no
well defined peakedness properties. The analysis of such states, including
squeezed and highly non-Gaussian states, has been computationally challenging
until now. In this manuscript, we overcome these challenges by using the
Chimera scheme for the spatially flat, homogeneous and isotropic model sourced
with a massless scalar field. We demonstrate that the quantum bounce in this
model occurs even for states which are highly squeezed or are non-Gaussian with
multiple peaks and with little resemblance to semi-classical states. The
existence of the bounce is found to be robust, being independent of the
properties of the states. The evolution of squeezed and non-Gaussian states
turns out to be qualitatively similar to that of Gaussian states, and satisfies
strong constraints on the growth of the relative fluctuations across the
bounce. We also compare the results from the effective dynamics and find that,
although it captures the qualitative aspects of the evolution for squeezed and
highly non-Gaussian states, it always underestimates the bounce volume. We show
that various properties of the evolution, such as the energy density at the
bounce, are in excellent agreement with the predictions from an exactly
solvable loop quantum cosmological model for arbitrary states.
