Efficient Backcasting Search for Optical Quantum State Synthesis

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.

Figure 1

Schematic diagram for the OQSS consisting of linear optics and PNR detectors. The output state ${|\psi ⟩}_{\mathrm{out}}$ is generated so as to be close to the target non-Gaussian state.

Figure 2

Concept of our scheme. (a) Proposed OQSS using a backcasting approach, where the circuit is divided into sublayers. (b) Divided circuits are simulated backwards from final to first layers.

Figure 3

Proposed OQSS. (a) The proposed OQSS for a specific case with a single intermediate layer and 3 inputs for each of the circuits in the first layer. (b) The description of the whole procedure to determine the circuit parameters. (i) Step 1. (ii) Step 2. (iii) Step 3. (iv) Step 4.

Figure 4

The numerical results to prepare an approximated GKP qubit with the truncated photon number $n_{\max }=32$. The fidelities $F_{\mathrm{out}}$ are plotted as a function of the squeezing level of the target.