Measurement-induced cubic phase state generation

Abstract

The cubic phase state constitutes a nonlinear resource that is essential for universal quantum computing protocols. However, constructing such non-classical states faces many challenges. In this work, we present a protocol for generating a cubic phase state with high fidelity. The protocol is based on a set of Gaussian operations assisted by a detection operation. To find the proper set of parameters that results in both high fidelity and high detection probability, we provide a numerical multiparameter optimization. We investigate a broad range of target states and study how parameter imperfections influence fidelity.

Figures (7)

• Figure 1: Optical circuit for the measurement-induced cubic-phase-state generation. $\hat{B}$: a beam splitter with an angle $\phi_{b}$; $\hat{R}$: a phase shifter with an angle $\theta$; $\hat{S}$: two-mode squeezing with a squeezing parameter $\xi$; $\hat{D}$: displacement with an amplitude $\beta$. The input state is a two-photon Fock state $\left| 2 \right\rangle$ and a coherent state $\left| \alpha \right\rangle$. A projection $\hat{\Pi}=\left| 2 \middle\rangle \middle\langle 2 \right|$ in the first output arm gives the cubic phase state in the second arm.
• Figure 2: Wigner functions for (a) the ideal cubic phase state $\left| \psi_{T} \right\rangle$ with $r = 0.15$ and $\xi_{dB}=5$ dB and (b,c) the states $\left| \psi_{out} \right\rangle$ generated in the considered protocol. In (b) all protocol parameters are optimized (see Target 1 in TABLE \ref{['table_1']}), while in (c) the beam splitter angle is fixed as $\phi_b = \frac{\pi}{4}$, all other protocol parameters are optimized (see Target 1 in TABLE \ref{['table_2']}). The Wigner functions were calculated with the use of QuTiP software QuTiP_2024.
• Figure 3: Optimized fidelity for different combinations of $r$ and $\xi_{dB}$ values (target states), $T = 0.5$.
• Figure 4: For different target states, (a) detection probability in the upper channel and (b) optimized $\alpha$ values. $T = 0.5$ is fixed.
• Figure 5: Stability of the method used. The orange line indicates the fidelity values obtained using the continuation method when $T = 0.5$. The violin plots at different $r$ values illustrate the distribution of fidelity when an error of up to $2\%$ is introduced in the parameters.