Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Implementation of a Quantum Addressable Router Using Superconducting Qubits

Connie Miao1,*,†, Sébastien Léger1,*,‡, Ziqian Li1, Gideon Lee2, Liang Jiang2, and David I. Schuster1

  • 1Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
  • 2Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA

  • *These authors contributed equally to this work.
  • †Contact author: cmiao@stanford.edu
  • ‡Contact author: sebleger@stanford.edu

PRX Quantum 6, 040335 – Published 13 November, 2025

DOI: https://doi.org/10.1103/pq3x-cmw9

Abstract

The implementation of a quantum router capable of performing both quantum signal routing and quantum addressing (a Q2-router) represents a key step toward building quantum networks and quantum random access memories. We realize a Q2-router that uses fixed-frequency transmon qubits to implement a routing protocol based on two native controlled-iswap gates. These gates leverage a large ZZ interaction to selectively route information according to a quantum address. We find an estimated average routing fidelity of 95.3%, with errors arising primarily from decoherence or state preparation and measurement. We present a comprehensive calibration and characterization of both the c-iswap gates and the overall routing protocol through randomized benchmarking techniques and state tomography.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Article Text

References (67)

  1. V. Bužek and M. Hillery, Quantum copying: Beyond the no-cloning theorem, Phys. Rev. A 54, 1844 (1996).
  2. K. Lemr, K. Bartkiewicz, A. Černoch, and J. Soubusta, Resource-efficient linear-optical quantum router, Phys. Rev. A 87, 062333 (2013).
  3. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Quantum state transfer and entanglement distribution among distant nodes in a quantum network, Phys. Rev. Lett. 78, 3221 (1997).
  4. H. J. Kimble, The quantum internet, Nature 453, 1023 (2008).
  5. V. Giovannetti, S. Lloyd, and L. Maccone, Architectures for a quantum random access memory, Phys. Rev. A 78, 052310 (2008).
  6. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum random access memory, Phys. Rev. Lett. 100, 160501 (2008).
  7. S. Xu, C. T. Hann, B. Foxman, S. M. Girvin, and Y. Ding, in 56th Annual IEEE/ACM International Symposium on Microarchitecture (2023), pp. 526–538.
  8. L. K. Grover, in Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC ’96 (Association for Computing Machinery, New York, NY, United States, 1996), pp. 212–219.
  9. A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum algorithm for linear systems of equations, Phys. Rev. Lett. 103, 150502 (2009).
  10. N. Wiebe, A. Kapoor, and K. M. Svore, Quantum deep learning, arXiv:1412.3489.
  11. D. W. Berry, C. Gidney, M. Motta, J. R. McClean, and R. Babbush, Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factorization, Quantum 3, 208 (2019).
  12. R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear T complexity, Phys. Rev. X 8, 041015 (2018).
  13. J. Miguel-Ramiro, A. Pirker, and W. Dür, Genuine quantum networks with superposed tasks and addressing, npj Quantum Inf. 7, 1 (2021).
  14. G. Chiribella and H. Kristjánsson, Quantum Shannon theory with superpositions of trajectories, Proc. R. Soc. A: Math., Phys. Eng. Sci. 475, 20180903 (2019).
  15. K. Bartkiewicz, A. Černoch, and K. Lemr, Using quantum routers to implement quantum message authentication and Bell-state manipulation, Phys. Rev. A 90, 022335 (2014).
  16. A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, Stabilization of quantum computations by symmetrization, SIAM J. Comput. 26, 1541 (1997).
  17. H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, Quantum fingerprinting, Phys. Rev. Lett. 87, 167902 (2001).
  18. J. Liu, C. T. Hann, and L. Jiang, Data centers with quantum random access memory and quantum networks, Phys. Rev. A 108, 032610 (2023).
  19. G. Lee, C. T. Hann, S. Puri, S. M. Girvin, and L. Jiang, Error suppression for arbitrary-size black box quantum operations, Phys. Rev. Lett. 131, 190601 (2023).
  20. J. Miguel-Ramiro, Z. Shi, L. Dellantonio, A. Chan, C. A. Muschik, and W. Dür, Superposed quantum error mitigation, Phys. Rev. Lett. 131, 230601 (2023).
  21. X. Wu, H. Yan, G. Andersson, A. Anferov, M.-H. Chou, C. R. Conner, J. Grebel, Y. J. Joshi, S. Li, J. M. Miller, R. G. Povey, H. Qiao, and A. N. Cleland, Modular quantum processor with an all-to-all reconfigurable router, Phys. Rev. X 14, 041030 (2024).
  22. C. Zhou, P. Lu, M. Praquin, T.-C. Chien, R. Kaufman, X. Cao, M. Xia, R. S. K. Mong, W. Pfaff, D. Pekker, and M. Hatridge, Realizing all-to-all couplings among detachable quantum modules using a microwave quantum state router, npj Quantum Inf. 9, 1 (2023).
  23. R. K. Naik, N. Leung, S. Chakram, P. Groszkowski, Y. Lu, N. Earnest, D. C. McKay, J. Koch, and D. I. Schuster, Random access quantum information processors using multimode circuit quantum electrodynamics, Nat. Commun. 8, 1904 (2017).
  24. M. Pechal, J.-C. Besse, M. Mondal, M. Oppliger, S. Gasparinetti, and A. Wallraff, Superconducting switch for fast on-chip routing of quantum microwave fields, Phys. Rev. Appl. 6, 024009 (2016).
  25. B. Kannan, A. Almanakly, Y. Sung, A. Di Paolo, D. A. Rower, J. Braumüller, A. Melville, B. M. Niedzielski, A. Karamlou, K. Serniak, A. Vepsäläinen, M. E. Schwartz, J. L. Yoder, R. Winik, J. I.-J. Wang, T. P. Orlando, S. Gustavsson, J. A. Grover, and W. D. Oliver, On-demand directional microwave photon emission using waveguide quantum electrodynamics, Nat. Phys. 19, 394 (2023).
  26. A. Almanakly, B. Yankelevich, M. Hays, B. Kannan, R. Assouly, A. Greene, M. Gingras, B. M. Niedzielski, H. Stickler, M. E. Schwartz, K. Serniak, J. I.-J. Wang, T. P. Orlando, S. Gustavsson, J. A. Grover, and W. D. Oliver, Deterministic remote entanglement using a chiral quantum interconnect, arXiv:2408.05164.
  27. I.-C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, Demonstration of a single-photon router in the microwave regime, Phys. Rev. Lett. 107, 073601 (2011).
  28. I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, Deterministic photon–emitter coupling in chiral photonic circuits, Nat. Nanotechnol. 10, 775 (2015).
  29. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, Chiral quantum optics, Nature 541, 473 (2017).
  30. R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer, Nat. Commun. 7, 11183 (2016).
  31. K. C. Chen, W. Dai, C. Errando-Herranz, S. Lloyd, and D. Englund, Scalable and high-fidelity quantum random access memory in spin-photon networks, PRX Quantum 2, 030319 (2021).
  32. F.-Y. Hong, Y. Xiang, Z.-Y. Zhu, L.-Z. Jiang, and L.-N. Wu, Robust quantum random access memory, Phys. Rev. A 86, 010306 (2012).
  33. D. Weiss, S. Puri, and S. Girvin, Quantum random access memory architectures using 3D superconducting cavities, PRX Quantum 5, 020312 (2024).
  34. C. T. Hann, C.-L. Zou, Y. Zhang, Y. Chu, R. J. Schoelkopf, S. M. Girvin, and L. Jiang, Hardware-efficient quantum random access memory with hybrid quantum acoustic systems, Phys. Rev. Lett. 123, 250501 (2019).
  35. Y.-J. Wang, S. Zhang, T.-P. Sun, Z.-A. Zhao, X.-F. Xu, X.-N. Zhuang, H.-Y. Liu, C. Xue, P. Duan, Y.-C. Wu, Z.-Y. Chen, and G.-P. Guo, Hardware-efficient quantum random access memory design with a native gate set on superconducting platforms, Adv. Quantum Technol. 8, 2400519 (2025).
  36. Z. Wang, H. Qiao, A. N. Cleland, and L. Jiang, Quantum random access memory with transmon-controlled phonon routing, Phys. Rev. Lett. 134, 210601 (2025).
  37. C.-K. Hu, J. Yuan, B. A. Veloso, J. Qiu, Y. Zhou, L. Zhang, J. Chu, O. Nurbolat, L. Hu, J. Li, Y. Xu, Y. Zhong, S. Liu, F. Yan, D. Tan, R. Bachelard, A. C. Santos, C. Villas-Boas, and D. Yu, Native conditional i swap operation with superconducting artificial atoms, Phys. Rev. Appl. 20, 034072 (2023).
  38. B. J. Chapman, S. J. De Graaf, S. H. Xue, Y. Zhang, J. Teoh, J. C. Curtis, T. Tsunoda, A. Eickbusch, A. P. Read, A. Koottandavida, S. O. Mundhada, L. Frunzio, M. Devoret, S. Girvin, and R. Schoelkopf, High-on-off-ratio beam-splitter interaction for gates on bosonically encoded qubits, PRX Quantum 4, 020355 (2023).
  39. C. W. Warren, J. Fernández-Pendás, S. Ahmed, T. Abad, A. Bengtsson, J. Biznárová, K. Debnath, X. Gu, C. Križan, A. Osman, A. Fadavi Roudsari, P. Delsing, G. Johansson, A. Frisk Kockum, G. Tancredi, and J. Bylander, Extensive characterization and implementation of a family of three-qubit gates at the coherence limit, npj Quantum Inf. 9, 1 (2023).
  40. X. X. Yuan, J.-J. Ma, P.-Y. Hou, X.-Y. Chang, C. Zu, and L.-M. Duan, Experimental demonstration of a quantum router, Sci. Rep. 5, 12452 (2015).
  41. S. Zeytinoğlu, M. Pechal, S. Berger, A. A. Abdumalikov, A. Wallraff, and S. Filipp, Microwave-induced amplitude- and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics, Phys. Rev. A 91, 043846 (2015).
  42. D. Egger, M. Ganzhorn, G. Salis, A. Fuhrer, P. Müller, P. K. Barkoutsos, N. Moll, I. Tavernelli, and S. Filipp, Entanglement generation in superconducting qubits using holonomic operations, Phys. Rev. Appl. 11, 014017 (2019).
  43. T. Tsunoda, J. D. Teoh, W. D. Kalfus, S. J. de Graaf, B. J. Chapman, J. C. Curtis, N. Thakur, S. M. Girvin, and R. J. Schoelkopf, Error-detectable bosonic entangling gates with a noisy ancilla, PRX Quantum 4, 020354 (2023).
  44. E. Magesan, J. M. Gambetta, and J. Emerson, Characterizing quantum gates via randomized benchmarking, Phys. Rev. A 85, 042311 (2012).
  45. E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Randomized benchmarking of quantum gates, Phys. Rev. A 77, 012307 (2008).
  46. Y. Lu, A. Maiti, J. W. O. Garmon, S. Ganjam, Y. Zhang, J. Claes, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, High-fidelity parametric beamsplitting with a parity-protected converter, Nat. Commun. 14, 5767 (2023).
  47. E. Magesan, J. M. Gambetta, B. R. Johnson, C. A. Ryan, J. M. Chow, S. T. Merkel, M. P. da Silva, G. A. Keefe, M. B. Rothwell, T. A. Ohki, M. B. Ketchen, and M. Steffen, Efficient measurement of quantum gate error by interleaved randomized benchmarking, Phys. Rev. Lett. 109, 080505 (2012).
  48. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, 2010).
  49. S. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, Characterizing quantum supremacy in near-term devices, Nat. Phys. 14, 595 (2018).
  50. A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martinez, P. Schindler, T. Monz, J. Emerson, and R. Blatt, Characterizing large-scale quantum computers via cycle benchmarking, Nat. Commun. 10, 5347 (2019).
  51. S. Leger, and C. Miao, Supporting data for “Implementation of a quantum addressable router using superconducting qubits” (2025), https://zenodo.org/records/16954111.
  52. S. Huang, B. Lienhard, G. Calusine, A. Vepsäläinen, J. Braumüller, D. K. Kim, A. J. Melville, B. M. Niedzielski, J. L. Yoder, B. Kannan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Microwave package design for superconducting quantum processors, PRX Quantum 2, 020306 (2021).
  53. M. J. Persky, Review of black surfaces for space-borne infrared systems, Rev. Sci. Instrum. 70, 2193 (1999).
  54. C. Ding, M. Di Federico, M. Hatridge, A. Houck, S. Leger, J. Martinez, C. Miao, D. Schuster I, L. Stefanazzi, C. Stoughton, S. Sussman, K. Treptow, S. Uemura, N. Wilcer, H. Zhang, C. Zhou, and G. Cancelo, Experimental advances with the QICK (Quantum Instrumentation Control Kit) for superconducting quantum hardware, Phys. Rev. Res. 6, 013305 (2024).
  55. L. Stefanazzi, K. Treptow, N. Wilcer, C. Stoughton, S. Montella, C. Bradford, G. Cancelo, S. Saxena, H. Arnaldi, S. Sussman, A. Houck, A. Agrawal, H. Zhang, C. Ding, and D. I. Schuster, The QICK (Quantum Instrumentation Control Kit): Readout and control for qubits and detectors, Rev. Sci. Instrum. 93, 044709 (2022).
  56. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  57. D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. T. Rosen, J. M. Gertler, T. M. Hazard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppressing counter-rotating errors for fast single-qubit gates with fluxonium, PRX Quantum 5, 040342 (2024).
  58. D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta, Efficient Z gates for quantum computing, Phys. Rev. A 96, 022330 (2017).
  59. C. J. Wood and J. M. Gambetta, Quantification and characterization of leakage errors, Phys. Rev. A 97, 032306 (2018).
  60. Y.-H. Chen and C. H. Baldwin, Randomized benchmarking with leakage errors, arXiv:2502.00154.
  61. M. A. Rol, F. Battistel, F. K. Malinowski, C. C. Bultink, B. M. Tarasinski, R. Vollmer, N. Haider, N. Muthusubramanian, A. Bruno, B. M. Terhal, and L. DiCarlo, Fast, high-fidelity conditional-phase gate exploiting leakage interference in weakly anharmonic superconducting qubits, Phys. Rev. Lett. 123, 120502 (2019).
  62. L. B. Nguyen, Y. Kim, A. Hashim, N. Goss, B. Marinelli, B. Bhandari, D. Das, R. K. Naik, J. M. Kreikebaum, A. N. Jordan, D. I. Santiago, and I. Siddiqi, Programmable Heisenberg interactions between Floquet qubits, Nat. Phys. 20, 240 (2024).
  63. G. Aleksandrowicz et al., Qiskit: An open-source framework for quantum computing. Zenodo, 2019.
  64. J. A. Smolin, J. M. Gambetta, and G. Smith, Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise, Phys. Rev. Lett. 108, 070502 (2012).
  65. T. Roy, Z. Li, E. Kapit, and D. I. Schuster, Tomography in the presence of stray inter-qubit coupling, arXiv:2103.13611.
  66. M. Ganzhorn, G. Salis, D. J. Egger, A. Fuhrer, M. Mergenthaler, C. Müller, P. Müller, S. Paredes, M. Pechal, M. Werninghaus, and S. Filipp, Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform, Phys. Rev. Res. 2, 033447 (2020).
  67. C. T. Hann, G. Lee, S. Girvin, and L. Jiang, Resilience of quantum random access memory to generic noise, PRX Quantum 2, 020311 (2021).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation