Time-Domain-Multiplexed Measurement-Based Quantum Operations with 25-MHz Clock Frequency

Continuous-variable optical quantum computation has seen much progress in recent years. In particular, cluster states—the universal resource for measurement-based quantum computation—have been realized in a scalable fashion using the time-domain multiplexing method. To utilize the cluster states in actual quantum computation, the measurement bases need to be programmed according to the desired computation. In addition, as the information is encoded in time in the time-domain multiplexing method, the measurement bases must be dynamically changed in time to fully utilize the large-scale cluster states. Here we report demonstrations of quantum operations using time-domain-multiplexed cluster states with a clock frequency of 25 MHz. This is achieved by our combining the cluster-state-generation setup with the setup to change the measurement basis in the time domain. We also formulate a method to evaluate and verify continuous-variable operations where the quantum entanglements in the cluster states are utilized. Therefore, we demonstrate the implementation of quantum operations on scalable continuous-variable cluster-state architectures. The results in this work are compatible with the developing nonlinear feedforward and non-Gaussian state generation technology, which brings the realization of the large-scale fault-tolerant universal optical quantum computer closer to reality.

Figure 1

Conceptual diagram of measurement-based quantum computation. (a) The original approach using half-teleportation. (b) The equivalent approach based on sequential teleportation that is used in the time-domain multiplexing method. 1D, one dimensional; TMS, two-mode-squeezed state.

Figure 2

The experimental setup. (a) Optical and electrical parts of the experimental setup. (b) An example of the generated signals used in the experiment. The phases of each local oscillator (LO; ${\theta }^A$ and ${\theta }^B$) are proportional to $V^A(t)$ and $V^B(t)$, respectively. BS, beam splitter; 2-CH, two-channel; EOM, electro-optic modulator; HD, homodyne detector; LO, local oscillator; ODL, optical delay line; OPO, optical parametric oscillator; TMS, two-mode-squeezed state; $\mathrm{\Delta }t$, time width of the wave packet.

Figure 3

Evaluation of quantum operations using quantum entanglements. Measurement bases are determined by the values of ${\theta }^A$ and ${\theta }^B$ at homodyne detectors A and B. The blue detectors show the measurements of the reference mode and the output mode at bases ${\theta }_{\mathrm{ref}}$ and ${\theta }_{\mathrm{out}}$. TMS, two-mode-squeezed state.

Figure 4

Verification of single-step quantum operations for phase rotation $\mathbf{R}(\varphi )$ (a), shear $\mathbf{P}(\varphi )$ (b), and squeezing with ${90}^{\circ }$ rotation $\mathbf{R}(\pi /2)\mathbf{S}(\varphi )$ (c). Each point is obtained using 38 600 correlation measurements. The error bars are also plotted. The dashed lines are theoretical plots.

Figure 5

Sequential quantum teleportation in the time domain. (a) Elements $S_{ij}$ of the symplectic matrix. (b) Variances of the nullifiers. The vacuum variance is 0 dB. Each point in both figures is calculated using 38 600 events. Dashed lines correspond to theoretical predictions. Predictions of the variances are based on the results of the single-step identity operation. Errors of the elements of the $\mathbf{S}$ matrix are plotted and the errors of the variances are about $\pm 0.03$ dB for all points.