Flexible Qubit Allocation of Network Resource States

TL;DR

This work introduces a modeling framework for overlaying entanglement topologies on physical networks and demonstrates how optimized and even random qubit assignment, creates shortcuts and improves robustness and memory savings, while substantially reducing the average hop distance between remote network nodes, when compared to conventional approaches.

Abstract

The Quantum Internet is still in its infancy, yet identifying scalable and resilient quantum network resource states is an essential task for realizing it. We explore the use of graph states with flexible, non-trivial qubit-to-node assignments. This flexibility enables adaptable engineering of the entanglement topology of an arbitrary quantum network. In particular, we focus on cluster states with arbitrary allocation as network resource states and as a promising candidate for a network core-level entangled resource, due to its intrinsic flexible connectivity properties and resilience to particle losses. We introduce a modeling framework for overlaying entanglement topologies on physical networks and demonstrate how optimized and even random qubit assignment, creates shortcuts and improves robustness and memory savings, while substantially reducing the average hop distance between remote network nodes, when compared to conventional approaches.

Figures (8)

• Figure 1: Schematic representation of our research problem with (\ref{['fig:1a']})--the general allocation problem considered, and (\ref{['fig:1b']})--the network core application that serves as a representative scenario to illustrate the benefits of flexible resource qubit allocation.
• Figure 2: Schematic representation of our proposed framework for the description of resource state allocation and the entanglement topology of an arbitrary quantum network.
• Figure 3: Example of 1D Entanglement topology with a given assignment $f$ and featuring a resource state $\ket{R} = \bigotimes_{m = 1}^{3} \ket{L}^{(m)}_\text{4}$ with $\text{N}=4$ and $\mu = 3$. The figure also shows some relevant internal structures of the logical systems, enabled by local operations at the nodes.
• Figure 4: Node failures in a Snake entanglement topology $\mathcal{S_N}$ and -- decorated -- 2D entanglement topology $\mathcal{\hat{T}_{M,N}}$. In particular, Fig (a) highlights how qubit decorations allow for more remaining entangled link after a node failure. Fig (b) highlights how (costless) local qubit operations can be used to restore connectivity between separate connectivity graph components after a sequence of node failures.
• Figure 5: Static analysis of different 1D and 2D entanglement topologies with $20$ nodes. The plots show (a) the average worst-case inter-node distances ($\max_{c \in \mathcal{C}} \mathcal{D}_c$) and (b) the average number of vertex-disjoint inter-node paths ($\bar{\kappa}$), both computed over 100 independent executions for each lattice configuration and different qubit allocation strategy. The number of allowed qubits per node $\square_c = \mu |S_c|$ is indicated by dotted red vertical lines, while the histograms average the results for every allowed 1D and 2D lattices with increasing number occurrences $|S_c|$.

Theorems & Definitions (23)

• Definition 1: Path
• Definition 2: Shortest path distance
• Definition 3: Vertex-Disjoint Paths
• Definition 4: Connected Component
• Definition 5: Colored Graph
• Definition 6: Graph State
• Definition 7: Pauli Measurement on Graph States
• Definition 8: Number of nodes of the network
• Definition 9: Qubits per network node
• Definition 10: Resource state