{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:27:32Z","timestamp":1760059652097,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,28]],"date-time":"2025-06-28T00:00:00Z","timestamp":1751068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Quantum repeaters are integral systems to quantum computing and quantum communication as they allow the transfer of information between qubits, particularly over long distances. Because of the \u201cno-cloning theorem,\u201d which says that general quantum states cannot be directly copied, one cannot perform signal amplification in the usual way. The standard approach uses entanglement swapping, in which quantum states are teleported from one (short) segment to the next, using at each step a shared entangled pair. This is the job of the repeater. In general, this requires reliable quantum memories and shared entanglement resources, which are vulnerable to noise and decoherence. It is also difficult to manually create and implement the quantum algorithm for the swap circuit as the size of the system increases. Here, we propose a different approach: to use machine learning to train a repeater node. To demonstrate the feasibility of this method, the system is simulated in MATLAB 2022a. Training is conducted for a system of 2 qubits. It is then scaled up, with no additional training, to systems of 4, 6, and 8 qubits using transfer learning. Finally, the systems are tested in noisy conditions. The results show that the scale-up is very effective and relatively easy, and the effects of noise and decoherence are reduced as the size of the system increases.<\/jats:p>","DOI":"10.3390\/info16070552","type":"journal-article","created":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T13:06:17Z","timestamp":1751288777000},"page":"552","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust and Scalable Quantum Repeaters Using Machine Learning"],"prefix":"10.3390","volume":"16","author":[{"given":"Diego","family":"Fuentealba","sequence":"first","affiliation":[{"name":"Department of Aerospace Engineering, Wichita State University, Wichita, KS 67260, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-2950-2046","authenticated-orcid":false,"given":"Jackson","family":"Dahn","sequence":"additional","affiliation":[{"name":"Wyant College of Optical Sciences, University of Arizona, Tucson, AZ 85719, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7557-0671","authenticated-orcid":false,"given":"James","family":"Steck","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Wichita State University, Wichita, KS 67260, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6195-9122","authenticated-orcid":false,"given":"Elizabeth","family":"Behrman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS 67260, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/0375-9601(82)90084-6","article-title":"Communication by EPR devices","volume":"92","author":"Dieks","year":"1982","journal-title":"Phys. Lett. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1038\/299802a0","article-title":"A single quantum cannot be cloned","volume":"299","author":"Wootters","year":"1982","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Briegel, H.J., D\u00fcr, W., Cirac, J.I., and Zoller, P. (1998). Quantum repeaters for communication. arXiv.","DOI":"10.1007\/978-94-017-1454-9_11"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3891","DOI":"10.1103\/PhysRevLett.80.3891","article-title":"Experimental entanglement swapping: Entangling photons that never interacted","volume":"80","author":"Pan","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","unstructured":"Shi, Y., Patil, A., and Guha, S. (2025). Measurement-Based Entanglement Distillation and Constant-Rate Quantum Repeaters over Arbitrary Distances. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6787","DOI":"10.1038\/ncomms7787","article-title":"All-photonic quantum repeaters","volume":"6","author":"Azuma","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"045006","DOI":"10.1103\/RevModPhys.95.045006","article-title":"Quantum repeaters: From quantum networks to the quantum internet","volume":"95","author":"Azuma","year":"2023","journal-title":"Rev. Mod. Phys."},{"key":"ref_8","unstructured":"Zhang, Y.L., Jie, Q.X., Li, M., Wu, S.H., Wang, Z.B., Zou, X.B., Zhang, P.F., Li, G., Zhang, T., and Guo, G.C. (2024). Proposal of quantum repeater architecture based on Rydberg atom quantum processors. arXiv."},{"key":"ref_9","unstructured":"Zajac, J.M., Huber-Loyola, T., and Hofling, S. (2025). Quantum dots for quantum repeaters. arXiv."},{"key":"ref_10","unstructured":"Cussenot, P., Grivet, B., Lanyon, B.P., Northup, T.E., de Riedmatten, H., S\u00f8rensen, A.S., and Sangouard, N. (2025). Uniting Quantum Processing Nodes of Cavity-coupled Ions with Rare-earth Quantum Repeaters Using Single-photon Pulse Shaping Based on Atomic Frequency Comb. arXiv."},{"key":"ref_11","unstructured":"Chelluri, S.S., Sharma, S., Schmidt, F., Kusminskiy, S.V., and van Loock, P. (2025). Bosonic quantum error correction with microwave cavities for quantum repeaters. arXiv."},{"key":"ref_12","unstructured":"Gan, Y., Azar, M., Chandra, N.K., Jin, X., Cheng, J., Seshadreesan, K.P., and Liu, J. (2025). Quantum repeaters enhanced by vacuum beam guides. arXiv."},{"key":"ref_13","unstructured":"Mor-Ruiz, M.F., Miguel-Ramiro, J., Walln\u00f6fer, J., Coopmans, T., and D\u00fcr, W. (2025). Merging-based quantum repeater. arXiv."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mastriani, M. (2023). Simplified entanglement swapping protocol for the quantum Internet. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-49326-4"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bayrakci, V., and Ozaydin, F. (2022). Quantum Zeno repeaters. Sci. Rep., 12.","DOI":"10.1038\/s41598-022-19170-z"},{"key":"ref_16","first-page":"12","article-title":"Quantum algorithm design using dynamic learning","volume":"8","author":"Behrman","year":"2008","journal-title":"Quantum Inf. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"13344","DOI":"10.1109\/TPAMI.2023.3292075","article-title":"Transfer Learning in Deep Reinforcement Learning: A Survey","volume":"45","author":"Zhu","year":"2023","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s40537-016-0043-6","article-title":"A survey of transfer learning","volume":"3","author":"Weiss","year":"2016","journal-title":"J. Big Data"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1007\/s11128-020-02877-1","article-title":"Experimental pairwise entanglement estimation for an N-qubit system: A machine learning approach for programming quantum hardware","volume":"19","author":"Thompson","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_20","first-page":"36","article-title":"Multiqubit entanglement of a general input state","volume":"13","author":"Behrman","year":"2013","journal-title":"Quantum Inf. Comput."},{"key":"ref_21","unstructured":"Bhattacharyya, S., Maulik, U., and Dutta, P. (2017). Quantum neural computation of entanglement is robust to noise and decoherence. Quantum Inspired Computational Intelligence, Morgan Kaufmann."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42484-020-00013-x","article-title":"Quantum Learning with Noise and Decoherence: A Robust Quantum Neural Network","volume":"2","author":"Nguyen","year":"2020","journal-title":"Quantum Mach. Intell."},{"key":"ref_23","first-page":"32","article-title":"A genetic algorithm for finding pulse sequences for nmr quantum computing","volume":"20","author":"Rethinam","year":"2011","journal-title":"Paritantra\u2014J. Syst. Sci. Eng."},{"key":"ref_24","unstructured":"Nola, J., Sanchez, U., Murthy, A.K., Behrman, E., and Steck, J. (2025). Training microwave pulses using machine learning. Acad. Quantum."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1364\/PRJ.388790","article-title":"Experimental free-space quantum secure direct communication and its security analysis","volume":"8","author":"Pan","year":"2020","journal-title":"Photonics Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/MNET.001.2200144","article-title":"From single-protocol to large-scale multiprotocol quantum networks","volume":"36","author":"Cao","year":"2022","journal-title":"IEEE Netw."},{"key":"ref_27","unstructured":"Chuang, I., and Nielsen, M. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_28","unstructured":"Roweis, S. (2025, June 23). Levenberg-Marquardt Optimization. Available online: https:\/\/people.duke.edu\/~hpgavin\/SystemID\/References\/lm-Roweis.pdf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1090\/qam\/10666","article-title":"A Method for the Solution of Certain Non-Linear Problems in Least Squares","volume":"2","author":"Levenberg","year":"1944","journal-title":"Q. Appl. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An Algorithm for Least-Squares Estimation of Nonlinear Parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"More, J.J. (1978). The Levenberg-Marquardt Algorithm: Implementation and Theory, Springer.","DOI":"10.1007\/BFb0067700"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Steck, J.E., Thompson, N.L., and Behrman, E.C. (2024). Programming Quantum Hardware via Levenberg-Marquardt Machine Learning. Intelligent Quantum Information Processing, CRC Press.","DOI":"10.1201\/9781003373117-5"},{"key":"ref_33","unstructured":"Transtrum, M.K., and Sethna, J.P. (2012). Improvements to the Levenberg Marquardt algorithm for nonlinear least- squares minimization. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"036701","DOI":"10.1103\/PhysRevE.83.036701","article-title":"Geometry of nonlinear least squares with applications to sloppy models and optimization","volume":"83","author":"Transtrum","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Gottesman, D. (2010). An introduction to quantum error correction and fault tolerant quantum computation. Proc. Symp. Appl. Math., 13.","DOI":"10.1090\/psapm\/068\/2762145"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Knill, E., Laflamme, R., and Zurek, W. (1998). Resilient quantum computation: Error models and thresholds. Proc. R. Soc. Lond. A, 454.","DOI":"10.1098\/rspa.1998.0166"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"062432","DOI":"10.1103\/PhysRevA.104.062432","article-title":"Modelling and simulating the noisy behavior of near-term quantum compiuters","volume":"104","author":"Georgopoulos","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"032333","DOI":"10.1103\/PhysRevA.95.032333","article-title":"Quantum noise generated by local random Hamiltonians","volume":"95","author":"Markiewicz","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1016\/j.neunet.2023.06.011","article-title":"Analysis on the inherent noise tolerance of feedforward network and one noise-resilient structure","volume":"165","author":"Lu","year":"2023","journal-title":"Neural Netw."},{"key":"ref_40","unstructured":"Rodriguez, R., Nguyen, N., Behrman, E., Li, A., and Steck, J. (2025). Existence of a robust optimal control process for efficient measurements in a two-qubit system. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"023005","DOI":"10.1103\/PhysRevResearch.3.023005","article-title":"Simulating noisy quantum circuits with matrix product density operators","volume":"3","author":"Cheng","year":"2021","journal-title":"Phys. Rev. Res."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/7\/552\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:00:50Z","timestamp":1760032850000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/7\/552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,28]]},"references-count":41,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["info16070552"],"URL":"https:\/\/doi.org\/10.3390\/info16070552","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2025,6,28]]}}}