Distributing Graph States Across Quantum Networks

TL;DR

The paper tackles distributing graph states across quantum networks by introducing Graph State Transfer (GST), which builds a local copy of the desired graph state at a root node and then transfers connections to destination nodes along network paths. GST can be implemented via graphical operations or teleportation, enabling substantial parallelization and yielding provable bounds on EPR consumption and completion time, with a polynomial-time method to minimize completion time using network flow. It shows GST never consumes more EPR pairs than the prior EDCG approach and, in some topologies such as full binary trees, achieves significant reductions in both resources and time; it also introduces a resource graph state that pre-distributes a flexible entangled structure to enable rapid future graph-state requests. Overall, the approach advances scalable, low-memory distribution of entangled graph states across general quantum networks, with practical implications for distributed one-way quantum computing and multi-party quantum protocols.

Abstract

Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which local operations are free-and EPR pairs shared between nodes that can continually be generated. We prove upper bounds for our approach on the number of EPR pairs consumed, number of timesteps taken, and amount of classical communication required, all of which are equal to or better than that of prior work. We also reduce the problem of minimizing the number of timesteps taken to distribute a graph state using our approach to a network flow problem having polynomial time complexity.

Figures (9)

• Figure 1: An example quantum network. Red circles represent nodes; blue edges represent connections between nodes, which can be regenerated after being consumed by quantum operations within nodes.
• Figure 2: A 4 node example of a resource graph state. (a) A 4-node network such that the network graph state is the complete graph among 4 qubits, each qubit in a different node. (b) A 4-node network such that the network graph state is the edge-decorated complete graph: a complete graph with additional vertices added to split each edge into two. The additional vertices added can exist in either of the nodes of the edge which that vertex split in two. $Z$ or $Y$ measuring a decoration vertex deletes or preserves the original edge, respectively. By $Z$ or $Y$ measuring each decoration vertex (along with associated local correction operations), any 4-qubit graph state can be prepared among the 4 nodes.
• Figure 3: The setup and end result of the connection transfer process. We transfer the edges connected to $a$ to qubit $c$, by consuming the EPR pair between $b$ and $c$.
• Figure 4: Connection transfer via graphical operations.
• Figure 5: Example setup and end result of our GST algorithm. A local copy of the final graph state (green) is prepared within a node and distributed throughout the network.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof