Policies for elementary links in a quantum network

Sumeet Khatri

Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana, 70803, USA

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Distributing entanglement over long distances is one of the central tasks in quantum networks. An important problem, especially for near-term quantum networks, is to develop optimal entanglement distribution protocols that take into account the limitations of current and near-term hardware, such as quantum memories with limited coherence time. We address this problem by initiating the study of quantum network protocols for entanglement distribution using the theory of decision processes, such that optimal protocols (referred to as $policies$ in the context of decision processes) can be found using dynamic programming or reinforcement learning algorithms. As a first step, in this work we focus exclusively on the elementary link level. We start by defining a quantum decision process for elementary links, along with figures of merit for evaluating policies. We then provide two algorithms for determining policies, one of which we prove to be optimal (with respect to fidelity and success probability) among all policies. Then we show that the previously-studied memory-cutoff protocol can be phrased as a policy within our decision process framework, allowing us to obtain several new fundamental results about it. The conceptual developments and results of this work pave the way for the systematic study of the fundamental limitations of near-term quantum networks, and the requirements for physically realizing them.

The quantum internet is one of the frontiers of quantum information science. It has the potential to revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet alone, such as quantum teleportation and quantum key distribution. Realizing the quantum internet is a major task, both from the theoretical perspective and from the practical perspective. Understanding the performance of quantum network protocols, particularly with noisy, imperfect near-term devices, is crucial in order to begin realizing small-scale quantum networks. This work sets out on the task of quantifying the performance of quantum network protocols, in particular determining optimal protocols, using the theory of decision processes. As a first step, in this work we focus on the elementary link level. We establish a theoretical framework based on decision processes that allows us to determine an optimal protocol for an elementary link in the presence of device imperfections. This theoretical framework also allows us to determine several new and fundamental results about a well known and heavily studied protocol, which we refer to here as the "memory-cutoff protocol". The developments of this work pave the way for a complete theory of practical quantum network protocols, which we expect will help drive the physical realization of small-scale quantum networks, and eventually lead to the realization of a global-scale quantum internet.

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[2] Simon D. Reiß and Peter van Loock, "Deep reinforcement learning for key distribution based on quantum repeaters", Physical Review A 108 1, 012406 (2023).

[3] Linh Le and Tu N. Nguyen, "DQRA: Deep Quantum Routing Agent for Entanglement Routing in Quantum Networks", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[4] Laszlo Gyongyosi and Sandor Imre, "Resource prioritization and balancing for the quantum internet", Scientific Reports 10 1, 22390 (2020).

[5] Laszlo Gyongyosi, "Decoherence dynamics estimation for superconducting gate-model quantum computers", Quantum Information Processing 19 10, 369 (2020).

[6] Julius Wallnöfer, Frederik Hahn, Mustafa Gündoğan, Jasminder S. Sidhu, Fabian Wiesner, Nathan Walk, Jens Eisert, and Janik Wolters, "Simulating quantum repeater strategies for multiple satellites", Communications Physics 5 1, 169 (2022).

[7] Takla Nateeboon, Chanaprom Cholsuk, Tobias Vogl, and Sujin Suwanna, "Modeling the performance and bandwidth of single-atom adiabatic quantum memories", APL Quantum 1 2, 026107 (2024).

[8] Sara Santos, Francisco A. Monteiro, Bruno C. Coutinho, and Yasser Omar, "Shortest Path Finding in Quantum Networks With Quasi-Linear Complexity", IEEE Access 11, 7180 (2023).

[9] Koji Azuma, Stefan Bäuml, Tim Coopmans, David Elkouss, and Boxi Li, "Tools for quantum network design", AVS Quantum Science 3 1, 014101 (2021).

[10] Laszlo Gyongyosi and Sandor Imre, "Scalable distributed gate-model quantum computers", Scientific Reports 11 1, 5172 (2021).

[11] Stav Haldar, Pratik J. Barge, Sumeet Khatri, and Hwang Lee, "Fast and reliable entanglement distribution with quantum repeaters: Principles for improving protocols using reinforcement learning", Physical Review Applied 21 2, 024041 (2024).

[12] Linh Le, Tu N. Nguyen, Ahyoung Lee, and Braulio Dumba, ICC 2022 - IEEE International Conference on Communications 395 (2022) ISBN:978-1-5386-8347-7.

[13] Laszlo Gyongyosi, "Objective function estimation for solving optimization problems in gate-model quantum computers", Scientific Reports 10 1, 14220 (2020).

[14] Zhen-Qiang Ren, Xian-Liang Lu, and Ze-Liang Xiang, "Heisenberg-limited spin squeezing in a hybrid system with silicon-vacancy centers", Optics Express 32 3, 4013 (2024).

[15] Sumeet Khatri, "On the design and analysis of near-term quantum network protocols using Markov decision processes", AVS Quantum Science 4 3, 030501 (2022).

[16] Julius Wallnöfer, Frederik Hahn, Fabian Wiesner, Nathan Walk, and Jens Eisert, "Faithfully Simulating Near-Term Quantum Repeaters", PRX Quantum 5 1, 010351 (2024).

[17] Bethany Davies, Thomas Beauchamp, Gayane Vardoyan, and Stephanie Wehner, "Tools for the analysis of quantum protocols requiring state generation within a time window", arXiv:2304.12673, (2023).

[18] Zhen-Qiang Ren, Cheng-Rui Feng, and Ze-Liang Xiang, "Deterministic generation of entanglement states between Silicon-Vacancy centers via acoustic modes", Optics Express 30 23, 41685 (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 20:08:40) and SAO/NASA ADS (last updated successfully 2024-05-24 20:08:41). The list may be incomplete as not all publishers provide suitable and complete citation data.