# Simulation of Fidelity in Entanglement-Based Networks with Repeater Chains
## 8 Conclusions  
In this paper, we have argued that simulation is an essential tool for understanding and designing quantum networks--especially, networks based on entanglement distribution--not only as a complement to simplified analytical models but mainly since entanglement is a physical resource inherently different from classical network entities, like conventional protocols or switching devices. Moreover, the efficient generation and distribution of entanglement prompts a thorough rethinking of the internal architectures of quantum repeaters and switches. These architectural alternatives can be also addressed with a good simulation environment.  
We have set the basis for a model using NetSquid for quantum switches and quantum repeaters in general topologies capable of handling an arbitrary number of quantum memory units, using fidelity as the primary decision variable for path selection, and containing depolarization noise in the channels and decoherence in the memory registers. Using this programming environment, fast prototyping and comparisons between alternative network designs can be explored. As an example, we compared the advantages and performance of two typical configurations--a two-hop network with multiple memory positions at the QR versus a standard repeater chain--and determined the achievable end-to-end fidelity in each case. This calculation is virtually intractable with a purely analytical approach. For future work, a more general simulator could be implemented. From an engineering standpoint, this could be used to support more complex topologies and protocols (e.g., the addition of routing protocols [20]), the implementation of teleportation protocols [40], and the modification of the physical structure in cases where purification is present. From a physics standpoint, this could be achieved by adding more control over the experimental parameters that define the network, such as the implementation of different types of quantum channels (e.g., atmospheric channels) and nodes (e.g., in an inhomogeneous network),  
Figure 9: Representation of the theoretical increment in the fidelity after applying several rounds of purification. The total depolarizing probability of the channel is represented in the \(x\)-axis vs. the fidelity output of the process.  
and exploring different technologies for quantum hardware, such as the use of different quantum memories to add a layer of dynamism to the procedure and the obtained results.  
Conceptualization, A.F.V., M.F.V. and R.P.D.R.; Methodology, A.F.V., M.F.V., M.B.R. and R.P.D.R.; Software, D.P.C.; Validation, D.P.C.; Formal analysis, D.P.C., A.F.V. and M.F.V.; Investigation, A.F.V. and M.F.V.; Resources, A.F.V. and M.F.V.; Writing--original draft, D.P.C. and M.B.R.; Writing--review & editing, A.F.V., M.F.V. and R.P.D.R.; Supervision, A.F.V., M.F.V. and R.P.D.R.; Project administration, A.F.V. and M.F.V.; Funding acquisition, A.F.V. and M.F.V. All authors have read and agreed to the published version of the manuscript.  
TED2021-130369B-C31, TED2021-130369 BC32, and TED2021-130369B-C33 were funded by MCIN/AEI/10.13039/501100011033 and by the \"European Union NextGenerationEU/PRTR\". The work is also funded by the Plan Complementario de Comunicaciones Cuanticas, Spanish Ministry of Science and Innovation(MICINN), Plan de Recuperacion NextGenerationEU de la Union Europea (PRTR-C17.I1, CITIC Ref. 305.2022), and Regional Government of Galicia (Agencia Gallega de Innovacion, GAIN, CITIC Ref. 306.2022).3). Additionally, this paper has been also funded by the Galician Regional Government under project ED43 IB 2024/41 (GPC).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflict of interest.