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Abstract
We study the problem of implementing arbitrary permutations of qubits under interaction con- straints 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 $O( N \log N )$ upper bound on the separation in routing time for any interaction graph—and give tighter bounds for some common classes of graphs.
Citation
Devulapalli, D., Schoute, E., Bapat, A., Childs, A. M., & Gorshkov, A. V. (2022). “Quantum routing with teleportation”. arXiv preprint arXiv:2204.04185.
@article{devulapalli2022quantum,
title={Quantum routing with teleportation},
author={Devulapalli, Dhruv and Schoute, Eddie and Bapat, Aniruddha and Childs, Andrew M and Gorshkov, Alexey V},
journal={arXiv preprint arXiv:2204.04185},
year={2022}
}