Architecture and protocols for all-photonic quantum repeaters

TL;DR

This work advances all-photonic quantum repeaters by introducing a half-RGS building block that anchors photonic graph states to emitter memories at end nodes, enabling seamless integration with memory-based repeaters and reducing end-node memory requirements. It presents a Pauli-frame-aware protocol that tracks side-effects and propagates corrections through a measurement-tree framework, validated with a stabilizer-simulation toolkit to produce correct end-to-end Bell pairs. The key contributions are (i) the half-RGS construction and its generation sequence, (ii) a resource-optimized architecture that preserves rapid trial rates, and (iii) a concrete protocol for Pauli-frame calculations and correction propagation that bridges all-photonic and memory-based repeater networks. Together, these advances push toward practical, scalable quantum networks capable of distributed computation and teleportation, not just quantum key distribution, by enabling corrected Bell pairs across heterogeneous repeater architectures.

Abstract

The all-photonic quantum repeater scheme, utilizing a type of graph state called the repeater graph state (RGS), promises resilience to photon losses and operational errors, offering a fast Bell pair generation rate limited only by the RGS creation time (rather than enforced round-trip waits). While existing research has predominantly focused on RGS generation and secret key sharing rate analysis, there is a need to extend investigations to encompass broader applications, such as distributed computation and teleportation, the main tasks envisioned for the Quantum Internet. Here we propose a new emitter-photonic qubit building block and an RGS protocol that addresses several key considerations: end node involvement in connection establishment, decoding of logical qubits within the RGS, and computing the Pauli frame corrections at each participating node to ensure the desired correct end-to-end Bell pair state. Our proposed building block significantly reduces the total number of emissive quantum memories required for end nodes and seamlessly integrates all-photonic and memory-based repeaters under the same communication protocol. We also present an algorithm for decoding logical measurement results, employing graphical reasoning based on graph state manipulation rules.

Figures (7)

• Figure 1: Two graph state representations of the same quantum state are depicted at the top. Here, vertices represent qubits in the quantum circuit, and the application of a controlled-phase gate between two qubits corresponds to an edge between the corresponding vertices. An example of such an edge is highlighted in green in the top left. The graph state on the top right is obtained by altering the description through local complementation on vertex 3. This process deletes any existing edges between neighboring vertices of vertex 3, such as the edge $(1,4)$ in this case, and introduces new edges that were previously absent, highlighted in red as $(1,5)$ and $(4,5)$. The application of the depicted Clifford operations ensures that despite the differing graph representations, the quantum states remain identical in both cases. Visualization of a Z measurement with side effects is presented in the bottom left, while the impact of two X measurements (XX measurement) on a different graph is illustrated in the lower right. The Clifford side effects ($I/Z$) of qubits 3, 4, and 5 depend on the measurement outcome of qubit 2, while those of qubits 6 and 7 hinge on the outcome of qubit 1, as indicated by the blue and green arrows.
• Figure 2: An overview of the RGS scheme. The three steps shown here have corresponding actions to the memory-based repeater scheme, where inner encoded qubits correspond to the memories while outer qubits correspond to the emitted photons. RGS generation in step 1 (at RGSS) mirrors the entanglement swapping of quantum memories but without actually choosing which inner qubits will be paired up. Step 2 (at ABSA) illustrates the link-level generation process through the BSM between each pair of outer qubits. The Z measurement on inner qubits in step 2 and the X measurements in step 3 signify the choosing of which pairs are swapped. Logical measurement of inner qubits in the Z basis is depicted at the bottom. The $Z$ and $X$ labels inside the blue physical qubits indicate the actual physical measurement bases. For logical X measurement, the Z and X measurement bases of physical qubits are swapped. The indirect Z basis measurement of a physical qubit in the tree encoding is shown in the bottom right. If a direct Z measurement on a qubit fails due to photon loss, the result can still be inferred from the eigenvalue parity of qubits within any of the dotted triangles.
• Figure 3: An example of half-RGS and the transformation of two half-RGSs into a biclique RGS. The anchor emitter qubits of the two half-RGSs are joined via an application of a CZ gate follwed by the XX measurement resulting in a biclique RGS.
• Figure 4: Architectures supporting the RGS scheme where the photonic states generated at end nodes are different. (a) The architecture proposed in zhan-graph-based-repeater-analysis, where end nodes require $m$ emissive memories for each trial, along with $rm$ idle memories that have already been utilized in prior trials and are awaiting messages from all ABSAs. (b) Proposed architecture, featuring end nodes equipped with half-RGS building blocks. In this setup, end nodes require $|\vec{b}|+1$ quantum emitters (where $|\vec{b}|$ represents the depth of the tree encoding plus one), while reserving $r$ memories awaiting notification messages from prior trials. Purple circles with black borders represent the quantum emitters utilized in the current trial. Purple circles with colored borders in both (a) and (b) indicate idle memories awaiting messages from ABSAs, with the same colors denoting memories participating in the same trials.
• Figure 5: Segments constituting RGSS (repeater graph state source, in light blue) and ABSA (advanced Bell state analyzer, omitted) nodes are treated as virtual links to memory-equipped repeaters (orange). The RGS scheme link is invisible at the connection level protocol, reducing the cost of connection setup and management.