Figure 1

Schematic view of the experiment. (a) Experimental setup to create a four-qubit hybrid entangled state. During the write process, we select two detection modes (${\mathcal{S}}_l$ or ${\mathcal{S}}_r$) for the Stokes photon to create photon spin-wave entanglement in the spatial degree. All the photonic modes are guided by single-mode fibers (SMFs) to the extended setup. (b) Level scheme utilized. The write beam is 10 MHz red-detuned from the transition $|a\rangle \leftrightarrow |e\rangle$. Double-pathway Raman scattering (to either $|b_0\rangle$ or $|b_{+2}\rangle$) is utilized to create photon spin-wave entanglement in the polarization degree. (c) Extended setup of (a) to realize active one-way quantum computing. Measurement of the polarization degree of the Stokes photon is carried out by using a combination of a quarter-wave plate (QWP), a half-wave plate (HWP), and a polarizing beam splitter (PBS), while the spatial degree is measured with BS1 and the mirror M2 with piezoelectric ceramics. The spin-wave state is measured through conversion to an anti-Stokes photon and making similar measurements as for the Stokes photon. Pumping vapor cells (PVCs) are used to filter out leakage of the write and read beams. Two electro-optic modulators (EOMs) performing Pauli error corrections are essential for deterministic one-way quantum computation. The overall detection efficiency for the Stokes (anti-Stokes) photon is $\sim$$0.25$ ($\sim$$0.20$), including propagation efficiency, coupling efficiency, detector efficiency, etc.Reuse & Permissions

Figure 2

Measured fidelity of the cluster state as a function of storage time. The fidelity values shown in the figure are the lower-bound values obtained from the witness measurements, which indicate a lifetime of the cluster state of about 14.27 $\mu$s. Error bars represent statistical errors.Reuse & Permissions

Figure 3

Demonstration of arbitrary single-qubit rotations. (a) The one-way quantum circuit configuration of single-qubit rotations. (b),(c) Experimental results for the fidelities, which are represented by distances to the circle center. In (b), $\alpha =\pi /2$ and $\beta$ is set from 0 to $2\pi$ in steps of $\pi /8$. In (c), $\alpha$ is set from 0 to $2\pi$ in steps of $\pi /8$ and $\beta =0$. The blue open dots show the ideal states with fidelity of 1, and each of the red dots with error bars shows the experimental result for the corresponding ideal state located in the same dashed line. The four concentric circles mark fidelities of 0.25, 0.5, 0.75, and 1 sequentially from the center. (d) Bloch sphere representation of the tomography results for the rotation operation $R_x(-\pi /4)R_z(-\pi /4)$ on logical qubit $|+\rangle$. The blue arrow describes the ideal state, while the red dashed arrow describes the measured state obtained from the reconstructed density matrix. The fidelity is calculated as $0.93\pm 0.02$.Reuse & Permissions