Quantum Switches for Gottesman-Kitaev-Preskill Qubit-based All-Photonic Quantum Networks

TL;DR

This work introduces a GKP-qubit based quantum switch for all-photonic quantum networks, enabling multiplexed entanglement distribution among multiple clients with all-photonic storage via a concatenated Steane code. It generalizes the entanglement-ranking-based link matching (GERM) protocol to multi-client settings and derives end-to-end entanglement rates for a simple two-client case, along with optimal resource allocation and switch placement. Extending to a data-center style multi-client network, the paper defines throughput and fairness metrics, showing that symmetric resource distribution and central switch placement maximize overall switch rate while maintaining fairness under realistic topologies. The results provide design guidelines for scalable quantum networks with arbitrary topology, combining GKP-based resources, all-photonic memories, and compatible repeater architectures.

Abstract

The Gottesman-Kitaev-Preskill (GKP) code, being information theoretically near optimal for quantum communication over Gaussian thermal-loss optical channels, is likely to be the encoding of choice for advanced quantum networks of the future. Quantum repeaters based on GKP-encoded light have been shown to support high end-to-end entanglement rates across large distances despite realistic finite squeezing in GKP code preparation and homodyne detection inefficiencies. Here, we introduce a quantum switch for GKP-qubit-based quantum networks, whose architecture involves multiplexed GKP-qubit-based entanglement link generation with clients, and their all-photonic storage, together enabled by GKP-qubit graph state resources. For bipartite entanglement distribution between clients via entanglement swapping, the switch uses a multi-client generalization of a recently introduced $\textit{entanglement-ranking-based link matching}$ protocol heuristic. Since generating the GKP-qubit graph state resource is hardware intensive, given a total resource budget and an arbitrary layout of clients, we address the question of their optimal allocation towards the different client-pair connections served by the switch such that the sum throughput of the switch is maximized while also being fair in terms of the individual entanglement rates. We illustrate our results for an exemplary data center network, where the data center is a client of a switch and all of its other clients aim to connect to the data center alone -- a scenario that also captures the general case of a gateway router connecting a local area network to a global network. Together with compatible quantum repeaters, our quantum switch provides a way to realize quantum networks of arbitrary topology.

Figures (8)

• Figure 1: A generic quantum switch with $n$ clients at different distances $l_i$ and with different number $k_i$ of multiplexed elementary entanglement links with the switch, where $i\in\{1,\ldots,n\}$.
• Figure 2: The proposed multiplexed all-photonic quantum switch based on GKP-encoded qubits and the [[7,1,3]] Steane code in its simplest form consisting of just two clients. The clients are located at distances $(l_1,l_2)$ from the switch. The switch prepares $k_{\textrm{total}} = k_{1} (\textrm{left}) + k_{2} (\textrm{right})$ entangled resource states that correspond on the logical level to a Bell pair between a concatenated-coded qubit and a bare GKP qubit and on the physical level to a cube graph state of eight GKP-qubits, with the clients matching the respective preparations from their end. Remote entanglement generation is performed between the switch and each client by sending the bare physical GKP-qubits(white/empty circle) toward each other for Bell State Measurement (BSM). The elementary entanglement links thus generated are ranked according to their reliability estimated from the GKP syndromes obtained from the continuous BSM outcomes. This ranking information, as well as logical BSM outcomes, are sent to the switch. The switch chooses the best $k_{\textrm{main}} = \min(k_{1},k_{2})$ links from each channel (left and right) to perform entanglement swapping on the concatenated-coded qubits(blue/filled circle) based on that ranking information.
• Figure 3: Rate saturation with the increase in total number of resource states while optimally shared between two clients, i.e., $l_1 = l_2 = {l_{\textrm{total}}/2}$ ($l_i \in \{0.5, 1, 2, 2.5, 5\} \textrm{km}$). For every setting ($l_\textrm{total}, k_{\textrm{total}}$), the maximum rate per mode $2R_{\textrm{e2e}}/ k_{\textrm{total}}$ corresponding to the optimum setting ($k_1, k_2$) is plotted on the X-axis. The optimum allocation, regardless of the distance, is found to be $k_1 = k_2 = {k_{\textrm{total}}/2}$, i.e., ${k_1/k_{\textrm{total}}}=0.5$.
• Figure 4: The general case of a two-client switch ($\textrm{client}$-1, $\textrm{client}$-2), where $l_1 + l_2 = l_{\textrm{total}}$ ($l_i \in \{0.5, 1, 2, 2.5, 5\} \textrm{km}$). For every setting ($l_1, l_2, k_{\textrm{total}}$), the optimum resource allocation $(k_1,k_2)$, tracked by the number of entangled resource states assigned to $\textrm{client}$-1 over the total number of entangled resource states, i.e., $k_1/k_{\textrm{total}}$ is plotted on the Y-axis, while the distance of $\textrm{client}$-1 over the total distance of the setting ($l_1/l_{\textrm{total}}$) is plotted on the X-axis. The optimum allocation is found to be $k_1 = k_2 = {k_{\textrm{total}}}/2$, i.e., ${k_1/k_{\textrm{total}}}=0.5$ with small deviations at large total distances. The red diamond also shows that the maximum total rate $R_{\textrm{e2e}}$ belongs to $l_1=l_2={l_{\textrm{total}}/2}, k_1=k_2={k_{\textrm{total}}/2}$.
• Figure 5: Architecture of the proposed multiplexed all-photonic quantum switch in a multi-client data-center network scenario. The data center-switch elementary entanglement links are ranked separately from the elementary links between the switch and the rest of the clients put together. Links from these two rank lists are matched and connected via entanglement swapping at the switch to generate end-to-end entanglement links.