Fidelity-Guarantee Entanglement Routing in Quantum Networks

Abstract

As one of the most important function in quantum networks, entanglement routing, i.e., how to efficiently establish remote entanglement connection between two arbitrary quantum nodes, becomes a critical problem that is worth to be studied. However, the entanglement fidelity, which can be regarded as the most important metric to evaluate the quality of connection, is rarely considered in existing works. Thus, in this paper, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (S-D) pairs in quantum networks. To find the routing path with minimum entangled pair cost, we first design an iterative routing algorithm for single S-D pair, called Q-PATH, to find the optimal solution. After that, due to the relatively high computational complexity, we also design a low-complexity routing algorithm by using an extended dijkstra algorithm, called Q-LEAP, to efficiently find the near-optimal solution. Based on these two algorithms, we design a utility metric to solve the resource allocation problem for multiple S-D pairs, and further design a greedy-based algorithm considering resource allocation and rerouting process for routing requests from multiple S-D pairs. To verify the effectiveness and superiority of the proposed algorithms, extensive simulations are conducted compared to the existing purification-enabled routing algorithm. The simulation results show that, compared with the traditional routing scheme, the proposed algorithms not only can provide fidelity-guaranteed routing solutions under various scenarios, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio.

A Survey of Quantum Entanglement Routing Protocols—Challenges for Wide‐Area Networks

“…The calculation formula for the resulting fidelity F p after purifying two pairs of lower fidelity F can be found, for example, in ref. [18] and is given by…”

“…The authors of ref. [18] propose Q-PATH, probably the first work that studies the fidelity-guaranteed entanglement routing problem for multiple sender-receiver pairs. Considering the high computational complexity of the Q-PATH algorithm, they further propose Q-LEAP, a Low-complExity routing Algorithm from the perspective of "multiPlicative" routing metric of the fidelity degradation.…”

A Connection-Oriented Entanglement Distribution Design in Quantum Networks

“…Unlike the routing problem in quantum networks, which has been investigated in many studies [21], [31]- [33], the specific routing protocol design is still in the early stage. In 2017, Caleffi [34] modeled the entanglement generation through a stochastic framework and derived the closed-form expression of the end-to-end entanglement rate for an arbitrary path.…”