Flexible quantum data bus for quantum networks

TL;DR

This paper introduces a flexible quantum data bus built on pre-shared $2$D cluster states to route Bell states on demand. At its core is the zipper scheme, which uses diagonal Pauli $X$ measurements to create a Bell pair between two endpoints while preserving the cluster’s remaining entanglement, enabling crossings and turns that support parallel Bell-state routing. By composing building blocks like $L$-turns, $V$-turns, and crossings, the authors construct a modular data bus capable of transporting $\mathcal{O}(n)$ Bell pairs on an $n\times n$ cluster with potential applications from long-distance networks to integrated quantum devices, all while potentially reducing latency. The approach also points to extensions to multiparty states such as GHZ and raises questions about noise robustness and fidelity in realistic networks.

Abstract

We consider multi-path routing of entanglement in quantum networks, where a pre-prepared multipartite entangled 2D cluster state serves as a resource to perform different tasks on demand. We show how to achieve parallel connections between multiple, freely chosen groups of parties by performing appropriate local measurements among diagonal paths, which preserves the entanglement structure of the remaining state. We demonstrate how to route multiple Bell-states along parallel lines via crossings, turns and fade-in/-outs, analogously to a data bus. The results apply to networks at any scale.

Figures (10)

• Figure 1: Zipper scheme (inset): The orange qubits are measured in the Pauli $X$ basis such that the purple qubit is routed along the diagonal measurement path while the obtained edges between the red qubits restore the underlying cluster state. The qubits in the neighborhood of the purple qubit need to be removed by Pauli $Z$ measurements leading to holes. Simultaneous Bell state routing (main figure): We extract three Bell states, purple, blue and turquoise, by applying the zipper scheme along diagonals of orange qubits. Merely on turning and endpoints holes appear due to the yellow Pauli $Z$ measurements to disconnect the Bell state qubits from the remaining cluster state. The zipper scheme enables crossing of paths except in the vicinity of end and turning points, and note that the paths are adjusted such that the measurement sequence is taken into account (first purple, then turquoise and blue).
• Figure 2: Quantum data bus and its building blocks: The red lines represent parallel transport along diagonal lines, including crossings orthogonal to the diagonals. The black lines show a parallel transport, both vertical and horizontal. The blue and pink lines depict parallel ' L' - and ' V' -turns, whereas the green lines demonstrate a merging or splitting of data lines. Finally, the yellow qubits depict qubits on which we need to perform Pauli $Z$ measurements.
• Figure 3: The figure shows a step-by-step guide for the measurement pattern to perform a perpendicular turn from vertical to horizontal in a 2D cluster state with four parallel data lines. The zipper scheme is applied from the left- to right-most qubits, where each application of the zipper scheme enables the next measurement. Note that the red arrows are only visual elements to better see the turn of data lines, and the arrows can be also reversed.
• Figure 4: In the center is a graph state depicted, whereas vertices correspond to qubits, which are initialized in the $\ket{+}$ state and edges represent maximally entanglement between two qubits. In the corners the resulting graph states are shown, which are caused by local single-qubit Pauli measurements or local complementation as indicated by the labeled arrows.
• Figure 5: Core of zipper scheme: The aim is to establish the Bell-pair $(b_1,b_2)$ with the zipper scheme on the diagonal $v_1$ to $v_6$, the initial setting is shown in first step. The second step shows the result of a local complementation on the qubit $b1$, which enlarges the neighborhood of $v_1$. The next step shows the Pauli $Y$ measurement on $v_1$, which establishes the edge $(b_1,v_2)$, necessary for the next measurement, as well as the edge $(r_1,r_2)$, necessary for restoring the cluster state, and it removes the qubit $r_1$ from the measurement collective, which removes the necessity to measure it in Pauli $Z$ basis. The last step shows the final local complementation on $b_1$, which restores a similar configuration as in the initial step, merely $r_1$ is replaced by $r_2$ and the exclusive neighbors switch from $b_1$ to $v_2$ and from $v_1$ to $b_1$.