Abstract
Networks of quantum circuits or, more generally, networks transmitting quantum information will need, just like classical networks (e.g. internet), a mechanism for directing data to adequate nodes. Routing, understood as packet switching, is one of the most important processes in classical networks. The issue of routing is also present in quantum networks and an appropriate construction of a quantum router is required to transfer data to specific points in the network. We describe an implementation of a router for qutrits in this chapter. The router is four-qutrit quantum circuit (with one controlling unit). The efficiency and the accuracy of router’s work is tested by the Fidelity measure. The circuit’s dynamics is expressed by a Hamiltonian where the role of generalized Pauli operators is played by the Gell-Mann operators.
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References
Behera, B.K., Seth, S., Das, A., Panigrahi, P.K.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer. arXiv:1712.00854 [quant-ph] (2017)
Behera, B.K., Reza, T., Gupta, A., Panigrahi, P.K.: Designing quantum router in IBM quantum computer. Quantum Inf. Process. 18(11), 1–13 (2019). https://doi.org/10.1007/s11128-019-2436-x
Bergmann, M., van Loock, P.: Hybrid quantum repeater for qudits. Phys. Rev. A 99, 032349 (2019)
Briegel, H.J., Dür, W., Cirac, J.I., Zoller, P.: Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932 (1998)
Bruderer, M., Franke, K., Ragg, S., Belzig, W., Obreschkow, D.: Exploiting boundary states of imperfect spin chains for high-fidelity state transfer. Phys. Rev. A 85, 022312 (2012)
Caleffi, M.: Optimal routing for quantum networks. IEEE Access 5, 22299–22312 (2017)
Christensen, K.S., Rasmussen, S.E., Petrosyan, D., Zinner, N.T.: Coherent router for quantum networks with superconducting qubits. Phys. Rev. Res. 2, 013004 (2020)
Dahlberg, A., Wehner, S.: SimulaQron—a simulator for developing quantum Internet software. Quantum Sci. Technol. 4(1), 015001 (2018). https://doi.org/10.1088/2058-9565/aad56e
Diadamo, S., Nözel, J., Zanger, B., Bese, M.M.: QuNetSim: a software framework for quantum networks. arXiv:abs/2003.06397 (2020)
Diadamo, S., Nözel, J., Zanger, B., Bese, M.M.: Github repository (2020). https://github.com/tqsd/QuNetSim
Domino, K., Gawron, P.: An algorithm for arbitrary-order cumulant tensor calculation in a sliding window of data streams. Int. J. Appl. Math. Comput. Sci. 29(1), 195–206 (2019)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Erhard, M., Malik, M., Zeilinger, A.: A quantum router for high-dimensional entanglement. Quantum Sci. Technol. 2(1), 014001 (2017). https://doi.org/10.1088/2058-9565/aa5917
Goswami, K., et al.: Indefinite causal order in a quantum switch. Phys. Rev. Lett. 121, 090503 (2018)
Gyongyosi, L., Imre, S.: Entanglement-gradient routing for quantum networks. Sci. Rep. 7, 14255 (2017)
Hahn, F., Pappa, A., Eisert, J.: Quantum network routing and local complementation. npj Quantum Inf. 5, 76 (2019)
Hall, B.C.: Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. Springer, New York (2003). https://doi.org/10.1007/978-3-319-13467-3
Hu, C.: Photonic transistor and router using a single quantum-dot-confined spin in a single-sided optical microcavity. Sci. Rep. 7, 45582 (2017)
Jankowski, N., Linowiecki, R.: A fast neural network learning algorithm with approximate singular value decomposition. Int. J. Appl. Math. Comput. Sci. 29(3), 581–594 (2019)
Luo, Y.H., et al.: Quantum teleportation in high dimensions. Phys. Rev. Lett. 123, 070505 (2019)
Marchukov, O., Volosniev, A., Valiente, M., et al.: Quantum spin transistor with a Heisenberg spin chain. Nat. Commun. 7, 13070 (2016)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Pant, M., Krovi, H., Towsley, D., et al.: Routing entanglement in the quantum Internet. npj Quantum Inf. 5, 25 (2019)
Pedersen, L.H., Møller, N.M., Mølmer, K.: Fidelity of quantum operations. Phys. Lett. 384 A 367, 47–51 (2007)
Plenio, M.B., Hartley, J., Eisert, J.: Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom. New J. Phys. 6(1), 36 (2004)
Rasmussen, S.E., Christensen, K.S., Zinner, N.T.: Controllable two-qubit swapping gate using superconducting circuits. Phys. Rev. B 99, 134508 (2019)
Van Meter, R.: Quantum Networking. Wiley, Hoboken (2014). https://doi.org/10.1002/9781118648919
Wallnöfer, J., Zwerger, M., Muschik, C., Sangouard, N., Dür, W.: Two-dimensional quantum repeaters. Phys. Rev. A 94, 052307 (2016)
Wang, M., Chen, X., Luo, S., et al.: Efficient entanglement channel construction schemes for a theoretical quantum network model with d-level system. Quantum Inf. Process. 11, 1715–1739 (2012)
Zhukov, A.A., Kiktenko, E.O., Elistratov, A.A., Pogosov, W.V., Lozovik, Y.E.: Quantum communication protocols as a benchmark for programmable quantum computers. Quantum Inf. Process. 18(1), 1–23 (2018). https://doi.org/10.1007/s11128-018-2144-y
Zwerger, M., Lanyon, B.P., Northup, T.E., Muschik, C.A., Dür, W., Sangouard, N.: Quantum repeaters based on trapped ions with decoherence-free subspace encoding. Quantum Sci. Technol. 2(4), 044001 (2017). https://doi.org/10.1088/2058-9565/aa7983
Acknowledgments
We would like to thank for useful discussions with the Q-INFO group at the Institute of Control and Computation Engineering (ISSI) of the University of Zielona Góra, Poland. We would like also to thank to anonymous referees for useful comments on the preliminary version of this chapter. The numerical results were done using the hardware and software available at the “GPU \(\mu \)-Lab” located at the Institute of Control and Computation Engineering of the University of Zielona Góra, Poland.
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Sawerwain, M., Wiśniewska, J. (2020). Quantum Router for Qutrit Networks. In: Gaj, P., Gumiński, W., Kwiecień, A. (eds) Computer Networks. CN 2020. Communications in Computer and Information Science, vol 1231. Springer, Cham. https://doi.org/10.1007/978-3-030-50719-0_4
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DOI: https://doi.org/10.1007/978-3-030-50719-0_4
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