Universal Nested Quantum Switch

TL;DR

This work provides a nested construction with logarithmically many qubits per node and a total of $O(n\log n)$ Bell pairs, in contrast to other distributed approaches based on pre-shared entanglement that scale as $O(n^2)$.

Abstract

The quantum switch is a basic network primitive that allows one to connect multiple nodes in a quantum network via a central node. We show that the same functionality can be achieved with a different geometry that does not rely on a powerful and large central unit, but instead utilizes evenly distributed resources. This approach is resilient against node failures. We provide a nested construction with logarithmically many qubits per node and a total of $O(n\log n)$ Bell pairs, in contrast to other distributed approaches based on pre-shared entanglement that scale as $O(n^2)$. The construction achieves fully flexible pairwise connectivity, where the shared resource state can be locally transformed into $n/2$ arbitrarily distributed Bell states. We also present a graph state variant with just one qubit per node, which allows one to generate $O(n/\log^2 n)$ Bell pairs.

Figures (8)

• Figure 1: Quantum switch. General idea. A device or network architecture that enables nodes in a quantum network to establish end-to-end entanglement in different connectivity patterns, potentially simultaneously and in parallel.
• Figure 2: Different proposals for quantum switches. (a) Centralized approach: a distinguished central node shares Bell pairs with all network nodes and performs entanglement swapping to establish end-to-end connections. (b) Distributed Bell-pair approach: all-to-all direct connectivity based on Bell pairs between every node pair. (c) Decreasing size GHZ approach: multipartite GHZ entangled states of varying sizes are used to enable pairwise connections via local measurements. All these strategies can realize universal pairwise connectivity.
• Figure 3: Nested quantum switch. Each node is connected via Bell pairs to neighbors at distances $2^k$ ($k=0,\dots,d-1$) in a highly symmetric and distributed entanglement pattern. Universal pairwise connectivity is guaranteed with total resource scaling of just $O(n\log n)$.
• Figure 4: Resource scaling. Average number of Bell pairs consumed per delivered connection in a simultaneous target configuration as a function of the number of failed nodes for a network of $128$ nodes. Each data point is averaged over $M$ independent Monte Carlo trials, where each trial samples a random failure pattern and a random perfect matching on the surviving nodes. Error bars denote the standard error deviation.
• Figure 5: Robustness of the nested quantum switch against node failures. The mean fraction of served requests $S_R$ is shown for a network of $n=128$ nodes as a function of the number of failed nodes $x$. Routing is performed using a greedy $k$-shortest path algorithm with $k=20$, for edge capacities of $R=1$ (blue) and $R=2$ (orange) Bell pairs. We remark that the $R=2$ case corresponds to the actual behavior of the nested construction. Each data point is averaged over $M=500$ independent Monte Carlo trials. Error bars represent the standard error deviation. Since the served fraction is strictly bounded in $[0,1]$, concentration inequalities, e.g., Hoeffding's inequality, imply that the estimation error scales as $O(1/\sqrt{M})$. For $M=500$, the resulting statistical uncertainty is approximately $2\%$.

Theorems & Definitions (4)

• Definition 1
• Definition 2
• Theorem 1: Universality of the nested quantum switch
• proof : Proof sketch