- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Characterization of a quantum bus between two driven qubits

Alberto Hijano1,*, Henri Lyyra1,2, Juha T. Muhonen1, and Tero T. Heikkilä1,†

  • 1Department of Physics and Nanoscience Center, University of Jyväskylä, P.O. Box 35 (YFL), FI-40014 Jyvaskyla, Finland
  • 2Department of Mechanical and Materials Engineering, University of Turku, FI-20014 Turun yliopisto, Finland

  • *Contact author: alhijano@jyu.fi
  • †Contact author: tero.t.heikkila@jyu.fi
PDF

Phys. Rev. Research 7, 043339 – Published 29 December, 2025

DOI: https://doi.org/10.1103/y648-4111

Abstract

We investigate the use of driven qubits coupled to a harmonic oscillator to implement a iSWAP gate. By dressing the qubits through an external driving field, the qubits and the harmonic oscillator can be selectively coupled, allowing for the measurement of individual qubit states, as well as leading to effective qubit-qubit interactions. We compare the qubit readout on bare and dressed qubits, and demonstrate that when coupled to low-frequency resonators, dressed qubits provide a more robust readout than bare qubits in the presence of damping and thermal effects. Furthermore, we study the impact of various system parameters on the fidelity of the two-qubit gate, identifying an optimal range for quantum computation. Our findings guide the implementation of high-fidelity quantum gates in experimental setups, for example, those employing nanoscale mechanical resonators.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. C. G. Almudever, L. Lao, X. Fu, N. Khammassi, I. Ashraf, D. Iorga, S. Varsamopoulos, C. Eichler, A. Wallraff, L. Geck, A. Kruth, J. Knoch, H. Bluhm, and K. Bertels, The engineering challenges in quantum computing, in Design, Automation & Test in Europe Conference & Exhibition (DATE) (IEEE, Lausanne, Switzerland, 2017), pp. 836–845.
  2. A. D. Córcoles, A. Kandala, A. Javadi-Abhari, D. T. McClure, A. W. Cross, K. Temme, P. D. Nation, M. Steffen, and J. M. Gambetta, Challenges and opportunities of near-term quantum computing systems, Proc. IEEE 108, 1338 (2020).
  3. D. P. DiVincenzo, Two-bit gates are universal for quantum computation, Phys. Rev. A 51, 1015 (1995).
  4. C. P. Williams, Explorations in Quantum Computing, 2nd ed. (Springer, London, 2011), pp. 92–100.
  5. A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52, 3457 (1995).
  6. J. Q. You, C.-H. Lam, and H. Z. Zheng, Superconducting charge qubits: The roles of self and mutual inductances, Phys. Rev. B 63, 180501 (2001).
  7. Y. Makhlin, G. Schön, and A. Shnirman, Quantum-state engineering with Josephson-junction devices, Rev. Mod. Phys. 73, 357 (2001).
  8. J. Q. You, J. S. Tsai, and F. Nori, Scalable quantum computing with Josephson charge qubits, Phys. Rev. Lett. 89, 197902 (2002).
  9. R. Migliore and A. Messina, Quantum superpositions of clockwise and counterclockwise supercurrent states in the dynamics of an rf-SQUID exposed to a quantized electromagnetic field, Phys. Rev. B 67, 134505 (2003).
  10. A. Blais, A. M. van den Brink, and A. M. Zagoskin, Tunable coupling of superconducting qubits, Phys. Rev. Lett. 90, 127901 (2003).
  11. F. Plastina and G. Falci, Communicating Josephson qubits, Phys. Rev. B 67, 224514 (2003).
  12. M. A. Sillanpää, J. I. Park, and R. W. Simmonds, Coherent quantum state storage and transfer between two phase qubits via a resonant cavity, Nature (London) 449, 438 (2007).
  13. J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Coupling superconducting qubits via a cavity bus, Nature (London) 449, 443 (2007).
  14. J. T. Muhonen, A. Laucht, S. Simmons, J. P. Dehollain, R. Kalra, F. E. Hudson, S. Freer, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello, Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking, J. Phys.: Condens. Matter 27, 154205 (2015).
  15. A. Laucht, R. Kalra, S. Simmons, J. P. Dehollain, J. T. Muhonen, F. A. Mohiyaddin, S. Freer, F. E. Hudson, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello, A dressed spin qubit in silicon, Nat. Nanotechnol. 12, 61 (2017).
  16. B. Pigeau, S. Rohr, L. Mercier de Lépinay, A. Gloppe, V. Jacques, and O. Arcizet, Observation of a phononic Mollow triplet in a multimode hybrid spin-nanomechanical system, Nat. Commun. 6, 8603 (2015).
  17. J. T. Muhonen, G. R. La Gala, R. Leijssen, and E. Verhagen, State preparation and tomography of a nanomechanical resonator with fast light pulses, Phys. Rev. Lett. 123, 113601 (2019).
  18. Y.-X. Liu, C. P. Sun, and F. Nori, Scalable superconducting qubit circuits using dressed states, Phys. Rev. A 74, 052321 (2006).
  19. P. R. Eastham, A. O. Spracklen, and J. Keeling, Lindblad theory of dynamical decoherence of quantum-dot excitons, Phys. Rev. B 87, 195306 (2013).
  20. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
  21. D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. M. Girvin, and R. J. Schoelkopf, ac stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field, Phys. Rev. Lett. 94, 123602 (2005).
  22. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Approaching unit visibility for control of a superconducting qubit with dispersive readout, Phys. Rev. Lett. 95, 060501 (2005).
  23. J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting, Phys. Rev. A 74, 042318 (2006).
  24. J. Gambetta, A. Blais, M. Boissonneault, A. A. Houck, D. I. Schuster, and S. M. Girvin, Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect, Phys. Rev. A 77, 012112 (2008).
  25. A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Quantum-information processing with circuit quantum electrodynamics, Phys. Rev. A 75, 032329 (2007).
  26. V. Srinivasa, J. M. Taylor, and J. R. Petta, Cavity-mediated entanglement of parametrically driven spin qubits via sidebands, PRX Quantum 5, 020339 (2024).
  27. E. Rosenfeld, R. Riedinger, J. Gieseler, M. Schuetz, and M. D. Lukin, Efficient entanglement of spin qubits mediated by a hot mechanical oscillator, Phys. Rev. Lett. 126, 250505 (2021).
  28. P. Rabl, P. Cappellaro, M. V. G. Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, Strong magnetic coupling between an electronic spin qubit and a mechanical resonator, Phys. Rev. B 79, 041302(R) (2009).
  29. H. Lyyra, C. Shakespeare, S. Ahopelto, T. Loippo, A. Hijano, R. Inkilä, P. Runko, T. T. Heikkilä, and J. T. Muhonen, Optomechanical quantum bus for donor spins in silicon, arXiv:2503.18764.
  30. C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation, Phys. Rev. A 31, 3761 (1985).
  31. C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer, Berlin/Heidelberg, 2004), Chap. 3.
  32. J. Zhang, S. S. Hegde, F. Jelezko, and D. Suter, Extending and measuring dephasing times of nuclear spins in NV centers of diamond, arXiv:2505.23512.
  33. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, The dressed atom approach, in Atom–Photon Interactions (John Wiley & Sons, Ltd, Weinheim, 1998), Chap. 6, pp. 427–433.
  34. A. Wallraff, D. I. Schuster, A. Blais, R.-S. Frunzio, L. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature (London) 431, 162 (2004).
  35. M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, Č. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, Pulsed quantum optomechanics, Proc. Natl. Acad. Sci. USA 108, 16182 (2011).
  36. M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, Cooling-by-measurement and mechanical state tomography via pulsed optomechanics, Nat. Commun. 4, 2295 (2013).
  37. Computer codes used in this manuscript are available at https://gitlab.jyu.fi/jyucmt/quantum-bus-between-driven-qubits.
  38. M. Lax, Formal theory of quantum fluctuations from a driven state, Phys. Rev. 129, 2342 (1963).
  39. S.-B. Zheng and G.-C. Guo, Efficient scheme for two-atom entanglement and quantum information processing in cavity QED, Phys. Rev. Lett. 85, 2392 (2000).
  40. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53, 2046 (1996).
  41. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54, 3824 (1996).
  42. G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).
  43. M. B. Plenio, Logarithmic negativity: A full entanglement monotone that is not convex, Phys. Rev. Lett. 95, 090503 (2005).
  44. G. Vidal, Entanglement monotones, J. Mod. Opt. 47, 355 (2000).
  45. L. Abdurakhimov et al., Technology and performance benchmarks of IQM’s 20-Qubit quantum computer, arXiv:2408.12433.
  46. D. C. McKay, I. Hincks, E. J. Pritchett, M. Carroll, L. C. G. Govia, and S. T. Merkel, Benchmarking quantum processor performance at scale, arXiv:2311.05933.
  47. R. Barends et al., Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature (London) 508, 500 (2014).
  48. E. Knill, Quantum computing with realistically noisy devices, Nature (London) 434, 39 (2005).
  49. E. Sutcliffe, B. Jonnadula, C. Le Gall, A. E. Moylett, and C. M. Westoby, Distributed quantum error correction based on hyperbolic Floquet codes, in 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, Albuquerque, US, 2025), Vol. 01, pp. 649–657.
  50. A. A. Houck, J. Koch, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Life after charge noise: Recent results with transmon qubits, Quantum Inf. Proc. 8, 105 (2009).
  51. J. T. Muhonen, J. P. Dehollain, A. Laucht, F. E. Hudson, R. Kalra, T. Sekiguchi, K. M. Itoh, D. N. Jamieson, J. C. McCallum, A. S. Dzurak, and A. Morello, Storing quantum information for 30 seconds in a nanoelectronic device, Nat. Nanotechnol. 9, 986 (2014).
  52. J. Mansir, P. Conti, Z. Zeng, J. J. Pla, P. Bertet, M. W. Swift, C. G. Van de Walle, M. L. W. Thewalt, B. Sklenard, Y. M. Niquet, and J. J. L. Morton, Linear hyperfine tuning of donor spins in silicon using hydrostatic strain, Phys. Rev. Lett. 120, 167701 (2018).
  53. Y.-S. Park and H. Wang, Resolved-sideband and cryogenic cooling of an optomechanical resonator, Nat. Phys. 5, 489 (2009).
  54. T. Tanttu et al., Assessment of the errors of high-fidelity two-qubit gates in silicon quantum dots, Nat. Phys. 20, 1804 (2024).
  55. J. Y. Huang et al., High-fidelity spin qubit operation and algorithmic initialization above 1 K, Nature (London) 627, 772 (2024).
  56. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2004), pp. 99–102.
  57. M. Boissonneault, J. M. Gambetta, and A. Blais, Dispersive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates, Phys. Rev. A 79, 013819 (2009).
  58. S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Ann. Phys. 326, 2793 (2011).
  59. A. Sørensen and K. Mølmer, Quantum computation with ions in thermal motion, Phys. Rev. Lett. 82, 1971 (1999).
  60. J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).

Outline

Information

Phys. Rev. Research 7, 043339– Published 29 December, 2025
  • Received 5 May 2025
  • Accepted 4 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation