Multiplexed quantum repeaters based on dual-species trapped-ion systems

Trapped ions form an advanced technology platform for quantum information processing with long qubit coherence times, high-fidelity quantum logic gates, optically active qubits, and a potential to scale up in size while preserving a high level of connectivity between qubits. These traits make them attractive not only for quantum computing, but also for quantum networking. Dedicated, special-purpose trapped-ion processors in conjunction with suitable interconnecting hardware can be used to form quantum repeaters that enable high-rate quantum communications between distant trapped-ion quantum computers in a network. In this regard, hybrid traps with two distinct species of ions, where one ion species can generate ion-photon entanglement that is useful for optically interfacing with the network and the other has long memory lifetimes, useful for qubit storage, have been proposed for entanglement distribution. We consider an architecture for a repeater based on such dual-species trapped-ion systems. We propose and analyze a protocol based on spatial and temporal mode multiplexing for entanglement distribution across a line network of such repeaters. Our protocol offers enhanced rates compared to rates previously reported for such repeaters. We determine the ion resources required at the repeaters to attain the enhanced rates, and the best rates attainable when constraints are placed on the number of repeaters and the number of ions per repeater. Our results bolster the case for near-term trapped-ion systems as quantum repeaters for long distance quantum communications.

Figure 1

General architecture of a repeater node based on DSTI modules to support entanglement distribution protocols based on mode multiplexing. The lines denote optical fibers.

Figure 2

Entanglement distribution rate as a function of total distance optimized over the number of repeater nodes and the degree of time multiplexing, for different values of spatial multiplexing $M$, noise parameter ${\epsilon }_g$, and ${\tau }_g=\tau =1\mu \mathrm{s}$. These rates are compared against the direct transmission benchmark, namely, the corresponding PLOB bounds (dot-dashed lines) given by $-\frac{M}{\tau }{log}_2(1-\eta ).$

Figure 3

Optimal degree of time multiplexing as a function of total distance for different values of spatial multiplexing $M$, noise parameter ${\epsilon }_g, {\tau }_g=\tau =1\mu \mathrm{s}$, and optimal number of repeaters.

Figure 4

Optimal number of repeater nodes as a function of total distance for different values of spatial multiplexing $M$, noise parameter ${\epsilon }_g, {\tau }_g=\tau =1\mu \mathrm{s}$, and optimal time multiplexing.

Figure 5

Required number of communication ions as a function of total distance for different values of spatial multiplexing $M$, noise parameter ${\epsilon }_g, {\tau }_g=\tau =1\mu \mathrm{s}$, and optimal number of repeaters and time multiplexing.

Figure 6

Required number of memory ions as a function of total distance for different values of spatial multiplexing $M$, noise parameter ${\epsilon }_g, {\tau }_g=\tau =1\mu \mathrm{s}$, and optimal number of repeaters and time multiplexing.

Figure 7

Entanglement distribution rate as a function of total distance optimized over the number of repeater nodes and the degree of time multiplexing, for different values of spatial multiplexing $M$, with realistic noisy gate operations of infidelity ${\epsilon }_g={10}^{-4},\tau =1\mu \mathrm{s}$, and ${\tau }_g=10\tau =10\mu \mathrm{s}$. These rates are compared against the direct transmission benchmark, namely, the corresponding PLOB bounds (dot-dashed lines) given by $-\frac{M}{\tau }{log}_2(1-\eta ).$

Figure 8

Entanglement distribution rate as a function of total distance optimized over the degree of time multiplexing, for spatial multiplexing degree $M=10$, noise parameter ${\epsilon }_g={10}^{-4}, {\tau }_g=\tau =1\mu \mathrm{s}$, and different values of inter-repeater spacing $L_0$. These rates are compared against the direct transmission benchmark, namely, the corresponding PLOB bound given by $-\frac{M}{\tau }{log}_2(1-\eta ).$

Figure 9

Entanglement distribution rate as a function of total distance under constrained resource availability, $N_o^{max}=125$. The values of $M$ are specified with realistic noisy gate operations of infidelity ${\epsilon }_g={10}^{-4}$ and ${\tau }_g=1\mu \mathrm{s}$, and $j={\tau }_g/\tau$. The operational clock-cycle duration $\tau$ is different for the solid $(\tau =1\mu s)$ and dotted $(\tau =10\mu s)$ lines.

Figure 10

Entanglement distribution rate as a function of total distance under constrained resource availability, $N_m^{max}$. For spatial multiplexing $M=5$, realistic noisy gate operations of infidelity ${\epsilon }_g={10}^{-4}$ and ${\tau }_g=\tau =1\mu \mathrm{s}$, the rates corresponding to different values of $N_m^{max}$ are plotted.

Figure 11

Timing diagram for Table 1, type A, when $k-j+1\ge m$.

Figure 12

Timing diagram for Table 1, type A, when $k-j+1<m$.

Figure 13

Timing diagram for Table 1, type B.

Figure 14

Timing diagram for Table 1, type C.

Figure 15

Decision tree to determine relative timing parameter ordering and associated rate equations.