Efficient backcasting search for optical quantum state synthesis

Non-Gaussian states are essential for many quantum technologies with continuous variables. 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. To remedy this, we offer an efficient scheme employing a backcasting approach, where the circuit of OQSS is devided into some sublayers, and we simulate the OQSS backwards from final to first layers. As an important example and application, we numerically show that the proposed OQSS allows us to simulate the generation of the Gottesman-Kitaev-Preskill qubit with a fidelity sufficient for universality and fault tolerance in optical quantum computation. 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. Further, 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.