  Non-Gaussian states are essential for many optical quantum technologies. The
so-called optical quantum state synthesizer (OQSS), consisting of Gaussian
input states, linear optics, and photon-number resolving detectors, is a
promising method for non-Gaussian state preparation. However, an inevitable and
crucial problem is the complexity of the numerical simulation of the state
preparation on a classical computer. This problem makes it very challenging to
generate important non-Gaussian states required for advanced quantum
information processing. Thus, an efficient method to design OQSS circuits is
highly desirable. To circumvent the problem, we offer a scheme employing a
backcasting approach, where the circuit of OQSS is divided into some sublayers,
and we simulate the OQSS backwards from final to first layers. Moreover, our
results show that the detected photon number by each detector is at most 2,
which can significantly reduce the requirements for the photon-number resolving
detector. By virtue of the potential for the preparation of a wide variety of
non-Gaussian states, the proposed OQSS can be a key ingredient in general
optical quantum information processing.
