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1. Quantum routing with teleportation

   https://doi.org/10.1103/PhysRevResearch.6.033313  

   Devulapalli, Dhruv; Schoute, Eddie; Bapat, Aniruddha; Childs, Andrew M; Gorshkov, Alexey V (September 2024, Physical Review Research)

   We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation—showing an $O\left(\sqrt{NlogN}\right)$upper bound on the separation in routing time for any interaction graph—and give tighter bounds for some common classes of graphs. Published by the American Physical Society2024 

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2. Quantum routing with fast reversals

   https://doi.org/10.22331/q-2021-08-31-533  

   Bapat, Aniruddha; Childs, Andrew M.; Gorshkov, Alexey V.; King, Samuel; Schoute, Eddie; Shastri, Hrishee (August 2021, Quantum)

   null (Ed.)

   We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n , we show that there exists a constant ϵ ≈ 0.034 such that the quantum routing time is at most ( 1 − ϵ ) n , whereas any swap-based protocol needs at least time n − 1 . This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2 n / 3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k ≤ n qubits and give algorithms with quantum routing time at most n / 3 + O ( k 2 ) on paths and at most 2 r / 3 + O ( k 2 ) on general graphs with radius r . 

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3. Advantages and Limitations of Quantum Routing

   https://doi.org/10.1103/PRXQuantum.4.010313  

   Bapat, Aniruddha; Childs, Andrew M.; Gorshkov, Alexey V.; Schoute, Eddie (February 2023, PRX Quantum)
4. Entanglement Routing Design Over Quantum Networks

   https://doi.org/10.1109/TNET.2023.3282560  

   Zeng, Yiming; Zhang, Jiarui; Liu, Ji; Liu, Zhenhua; Yang, Yuanyuan (February 2024, IEEE/ACM Transactions on Networking)
5. Routing entanglement in the quantum internet

   https://doi.org/10.1038/s41534-019-0139-x  

   Pant, Mihir; Krovi, Hari; Towsley, Don; Tassiulas, Leandros; Jiang, Liang; Basu, Prithwish; Englund, Dirk; Guha, Saikat (December 2019, npj Quantum Information)