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Quantum Error Detection in Qubit-Resonator Star Architecture

Florian Vigneau1,*, Sourav Majumder1, Aniket Rath1, Pedro Parrado-Rodríguez2, Francisco Revson Fernandes Pereira1, Hsiang-Sheng Ku1, Fedor Šimkovic, IV1, Stefan Pogorzalek1, Tyler Jones1 et al.

Nicola Wurz1, Michael Renger1, Jeroen Verjauw1, Ping Yang1, William Kindel1, Frank Deppe1,†, and Johannes Heinsoo3,‡

  • *Contact author: florian.vigneau@meetiqm.com
  • †Contact author: frank.deppe@meetiqm.com
  • ‡Contact author: johannes@meetiqm.com
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PRX Quantum 6, 040369 – Published 22 December, 2025

DOI: https://doi.org/10.1103/8m33-wn4g

Abstract

Achieving industrial quantum advantage is unlikely without the use of quantum error correction (QEC). Other QEC codes beyond surface code are being experimentally studied, such as color codes and quantum low-density parity check codes, that could benefit from new quantum processing unit (QPU) architectures. We introduce the six-qubit star lattice architecture that offers parallelism and effective local all-to-all connectivity and thus enables hardware-efficient implementation of certain QEC codes. As a first demonstration of this new architecture, we encode two logical qubits in a six-qubit superconducting QPU with a star topology using the ⟦4,2,2⟧ code and characterize the logical states with the classical shadow framework. Logical lifetime and logical error rate are measured over repeated quantum error detection cycles for various logical states including a logical Bell state. We measure logical state fidelities above 96% for every cardinal logical state, find logical lifetimes above the best physical element, and logical error-per-cycle values ranging from 0.25(2)% to 0.91(3)%. In future, such star units can be tiled into a lattice to enable QEC codes with high-weight and overlapping stabilizers for improved encoding rates.

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Popular Summary

Quantum computers are prone to errors that can destroy the fragile quantum information they process. Unlike classical computers, which use redundancy and error correction codes to detect and correct mistakes, quantum computers require specialized codes that can correct errors without directly measuring the quantum state. Several quantum error correction codes have been developed, with color codes and quantum low-density parity check codes being particularly promising due to their efficient use of qubits. However, these codes often rely on operations that do not match the native functionality of common superconducting qubit-based quantum processors.

To address this challenge, we introduce a novel quantum processor architecture based on a lattice of qubit cells connected in a star topology. This design combines high connectivity and parallelism, enabling the efficient implementation of some quantum error correction codes. The increased connectivity allows for more flexible and efficient detection of qubit errors, which is essential for robust quantum error correction.

In an experimental demonstration, we used a single cell of our architecture to perform an error detection experiment, showcasing the advantages of our design. By leveraging the improved connectivity, we were able to protect, more efficiently, a larger volume of quantum information than previously achieved with comparable-scale quantum processors. Our results demonstrate the potential of the star lattice architecture to enable fault-tolerant quantum computing.

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References (87)

  1. M. E. Beverland, P. Murali, M. Troyer, K. M. Svore, T. Hoefler, V. Kliuchnikov, G. H. Low, M. Soeken, A. Sundaram, and A. Vaschillo, Assessing requirements to scale to practical quantum advantage, arXiv:2211.07629.
  2. J. Preskill, Beyond NISQ: The Megaquop Machine, ACM Trans. Quantum Comput. 6, 1 (2025).
  3. D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology, 1997, arxiv:quant-ph/9705052.
  4. B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
  5. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A–At., Mol. Opt. Phys. 86, 032324 (2012).
  6. S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052.
  7. C. K. Andersen, A. Remm, S. Lazar, S. Krinner, N. Lacroix, G. J. Norris, M. Gabureac, C. Eichler, and A. Wallraff, Repeated quantum error detection in a surface code, Nat. Phys. 16, 875 (2020).
  8. Google Quantum AI and Collaborators, Quantum error correction below the surface code threshold, Nature 638, 1 (2024).
  9. H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Phys. Rev. Lett. 97, 180501 (2006).
  10. S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature 627, 778 (2024).
  11. J. N. Eberhardt, F. R. F. Pereira, and V. Steffan, Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions, arXiv:2412.04181.
  12. C. Gidney and C. Jones, New circuits and an open source decoder for the color code, arXiv:2312.08813.
  13. A. J. Landahl, J. T. Anderson, and P. R. Rice, Fault-tolerant quantum computing with color codes, arXiv:1108.5738.
  14. Y. Takada and K. Fujii, Improving threshold for fault-tolerant color-code quantum computing by flagged weight optimization, PRX Quantum 5, 030352 (2024).
  15. L. Postler, S. Heuβen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. D. Marciniak, R. Stricker, M. Ringbauer, R. Blatt et al., Demonstration of fault-tolerant universal quantum gate operations, Nature 605, 675 (2022).
  16. L. Postler, F. Butt, I. Pogorelov, C. D. Marciniak, S. Heußen, R. Blatt, P. Schindler, M. Rispler, M. Müller, and T. Monz, Demonstration of fault-tolerant Steane quantum error correction, PRX Quantum 5, 030326 (2024).
  17. J. Beugnon, C. Tuchendler, H. Marion, A. Gaëtan, Y. Miroshnychenko, Y. R. Sortais, A. M. Lance, M. P. Jones, G. Messin, A. Browaeys, and P. Grangier, Two-dimensional transport and transfer of a single atomic qubit in optical tweezers, Nat. Phys. 3, 696 (2007).
  18. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024).
  19. M. Takita, A. W. Cross, A. D. Córcoles, J. M. Chow, and J. M. Gambetta, Experimental demonstration of fault-tolerant state preparation with superconducting qubits, Phys. Rev. Lett. 119, 180501 (2017).
  20. C. Vuillot, Is error detection helpful on IBM 5Q chips? Quantum Inf. Comput. 18, 949 (2018).
  21. R. Harper and S. T. Flammia, Fault-tolerant logical gates in the IBM quantum experience, Phys. Rev. Lett. 122, 080504 (2019).
  22. C. Chamberland, A. Kubica, T. J. Yoder, and G. Zhu, Triangular color codes on trivalent graphs with flag qubits, New J. Phys. 22, 023019 (2020).
  23. N. Lacroix, A. Bourassa, F. J. Heras, L. M. Zhang, J. Bausch, A. W. Senior, T. Edlich, N. Shutty, V. Sivak, A. Bengtsson et al., Scaling and logic in the color code on a superconducting quantum processor, Nature 645, 614 (2025).
  24. M. Mathews, L. Pahl, D. Pahl, V. L. Addala, C. Tang, W. D. Oliver, and J. A. Grover, Placing and routing non-local quantum error correcting codes in multi-layer superconducting qubit hardware, arXiv:2507.23011.
  25. K. Wang et al., Demonstration of low-overhead quantum error correction codes, arXiv:2505.09684.
  26. L. Vaidman, L. Goldenberg, and S. Wiesner, Error prevention scheme with four particles, Phys. Rev. A 54, R1745 (1996).
  27. M. Grassl, T. Beth, and T. Pellizzari, Codes for the quantum erasure channel, Phys. Rev. A 56, 33 (1997).
  28. D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, Approximate quantum error correction can lead to better codes, Phys. Rev. A 56, 2567 (1997).
  29. D. Gottesman, Quantum fault tolerance in small experiments, arXiv:1610.03507.
  30. N. M. Linke, M. Gutierrez, K. A. Landsman, C. Figgatt, S. Debnath, K. R. Brown, and C. Monroe, Fault-tolerant quantum error detection, Sci. Adv. 3, e1701074 (2017).
  31. D. Willsch, M. Willsch, F. Jin, H. De Raedt, and K. Michielsen, Testing quantum fault tolerance on small systems, Phys. Rev. A 98, 052348 (2018).
  32. R. Cane, D. Chandra, S. X. Ng, and L. Hanzo, Experimental characterization of fault-tolerant circuits in small-scale quantum processors, IEEE Access 9, 162996 (2021).
  33. M. Bedalov, M. Blakely, P. Buttler, C. Carnahan, F. T. Chong, W. C. Chung, D. C. Cole, P. Goiporia, P. Gokhale, B. Heim et al., Fault-tolerant operation and materials science with neutral atom logical qubits, arXiv:2412.07670.
  34. M. Urbanek, B. Nachman, and W. A. de Jong, Error detection on quantum computers improving the accuracy of chemical calculations, Phys. Rev. A 102, 022427 (2020).
  35. M. Gowrishankar, D. Claudino, J. Wright, and T. Humble, Logical error rates for a [[4, 2, 2]]-encoded variational quantum eigensolver ansatz, arXiv:2405.03032.
  36. R. S. Gupta, N. Sundaresan, T. Alexander, C. J. Wood, S. T. Merkel, M. B. Healy, M. Hillenbrand, T. Jochym-O’Connor, J. R. Wootton, T. J. Yoder, A. W. Cross, M. Takita, and B. J. Brown, Encoding a magic state with beyond break-even fidelity, Nature 625, 259 (2024).
  37. A. Hu, J. Li, and R. Shapiro, Quantum benchmarking on the [[4, 2, 2]] code, Department of Mathematics, Duke University (2018).
  38. B. W. Reichardt, A. Paetznick, D. Aasen, I. Basov, J. M. Bello-Rivas, P. Bonderson, R. Chao, W. van Dam, M. B. Hastings, A. Paz et al., Logical computation demonstrated with a neutral atom quantum processor, arXiv:2411.11822.
  39. A. J. Landahl and C. Ryan-Anderson, Quantum computing by color-code lattice surgery, arXiv:1407.5103.
  40. S. Hazra, A. Bhattacharjee, M. Chand, K. V. Salunkhe, S. Gopalakrishnan, M. P. Patankar, and R. Vijay, Ring-resonator-based coupling architecture for enhanced connectivity in a superconducting multiqubit network, Phys. Rev. Appl. 16, 024018 (2021).
  41. M. G. Algaba, M. Ponce-Martinez, C. Munuera-Javaloy, V. Pina-Canelles, M. J. Thapa, B. G. Taketani, M. Leib, I. de Vega, J. Casanova, and H. Heimonen, Co-design quantum simulation of nanoscale NMR, Phys. Rev. Res. 4, 043089 (2022).
  42. 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).
  43. M. Malekakhlagh, T. Phung, D. Puzzuoli, K. Heya, N. Sundaresan, and J. Orcutt, Enhanced quantum state transfer and Bell-state generation over long-range multimode interconnects via superadiabatic transitionless driving, Phys. Rev. Appl. 22, 024006 (2024).
  44. M. Renger, J. Verjauw, N. Wurz, A. Hosseinkhani, C. Ockeloen-Korppi, W. Liu, A. Rath, M. J. Thapa, F. Vigneau, E. Wybo et al., A superconducting qubit-resonator quantum processor with effective all-to-all connectivity, arXiv:2503.10903.
  45. Y. Xu et al., Observation and modulation of the quantum Mpemba effect on a superconducting quantum processor, arXiv:2508.07707.
  46. M. Papič, M. G. Algaba, E. Godinez-Ramirez, I. de Vega, A. Auer, F. Šimkovic IV, and A. Calzona, Near-term fermionic simulation with subspace noise tailored quantum error mitigation, arXiv:2503.11785.
  47. M. G. Algaba, M. Papič, I. de Vega, A. Calzona, and F. Šimkovic IV, Fermion-to-qubit encodings with arbitrary code distance, arXiv:2505.02916.
  48. J. Leppäkangas, P. Stadler, D. Golubev, R. Reiner, J.-M. Reiner, S. Zanker, N. Wurz, M. Renger, J. Verjauw, D. Gusenkova et al., Quantum algorithms for simulating systems coupled to bosonic modes using a hybrid resonator-qubit quantum computer, arXiv:2503.11507.
  49. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
  50. A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The randomized measurement toolbox, Nat. Rev. Phys. 5, 9 (2023).
  51. F. Yan, P. Krantz, Y. Sung, M. Kjaergaard, D. L. Campbell, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Tunable coupling scheme for implementing high-fidelity two-qubit gates, Phys. Rev. Appl. 10, 054062 (2018).
  52. F. Marxer et al., Long-distance transmon coupler with CZ-gate fidelity above 99.8%, PRX Quantum 4, 010314 (2023).
  53. A. Galiautdinov, A. N. Korotkov, and J. M. Martinis, Resonator–zero-qubit architecture for superconducting qubits, Phys. Rev. A 85, 042321 (2012).
  54. R. Versluis, S. Poletto, N. Khammassi, B. Tarasinski, N. Haider, D. J. Michalak, A. Bruno, K. Bertels, and L. DiCarlo, Scalable quantum circuit and control for a superconducting surface code, Phys. Rev. Appl. 8, 034021 (2017).
  55. R. Chao and B. W. Reichardt, Quantum error correction with only two extra qubits, Phys. Rev. Lett. 121, 050502 (2018).
  56. S. Krinner, N. Lacroix, A. Remm, A. Di Paolo, E. Genois, C. Leroux, C. Hellings, S. Lazar, F. Swiadek, J. Herrmann et al., Realizing repeated quantum error correction in a distance-three surface code, Nature 605, 669 (2022).
  57. A. Gilchrist, N. K. Langford, and M. A. Nielsen, Distance measures to compare real and ideal quantum processes, Phys. Rev. A 71, 062310 (2005).
  58. C. Gidney, Stim: A fast stabilizer circuit simulator, Quantum 5, 497 (2021).
  59. Google Quantum AI and Collaborators, Suppressing quantum errors by scaling a surface code logical qubit, Nature 614, 676 (2023).
  60. 10.5281/zenodo.17476263.
  61. N. M. Linke, D. Maslov, M. Roetteler, S. Debnath, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, Experimental comparison of two quantum computing architectures, Proc. Natl. Acad. Sci. U.S.A. 114, 3305 (2017).
  62. A. Holmes, A. Holmes, S. Johri, G. Guerreschi, J. Clarke, and A. Matsuura, Impact of qubit connectivity on quantum algorithm performance, Quantum Sci. Technol. 5, 025009 (2018).
  63. B. Nash, V. Gheorghiu, and M. Mosca, Quantum circuit optimizations for NISQ architectures, Quantum Sci. Technol. 5, 025010 (2020).
  64. A. Deb, G. W. Dueck, and R. Wille, Exploring the potential benefits of alternative quantum computing architectures, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 40, 1825 (2021).
  65. A. Kotil, F. Simkovic, and M. Leib, Improved qubit routing for QAOA circuits, version: 1, arXiv:2312.15982.
  66. J. Rönkkö, O. Ahonen, V. Bergholm, A. Calzona, A. Geresdi, H. Heimonen, J. Heinsoo, V. Milchakov, S. Pogorzalek, M. Sarsby et al., On-premises superconducting quantum computer for education and research, EPJ Quantum Technol. 11, 32 (2024).
  67. T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing Rényi entanglement entropy via randomized measurements, Science 364, 260 (2019).
  68. K. J. Satzinger, Y.-J. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, C. Gidney, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush et al., Realizing topologically ordered states on a quantum processor, Science 374, 1237 (2021).
  69. M. Yu, D. Li, J. Wang, Y. Chu, P. Yang, M. Gong, N. Goldman, and J. Cai, Experimental estimation of the quantum Fisher information from randomized measurements, Phys. Rev. Res. 3, 043122 (2021).
  70. D. Zhu, Z. P. Cian, C. Noel, A. Risinger, D. Biswas, L. Egan, Y. Zhu, A. M. Green, C. H. Alderete, N. H. Nguyen, Q. Wang, A. Maksymov, Y. Nam, M. Cetina, N. M. Linke, M. Hafezi, and C. Monroe, Cross-platform comparison of arbitrary quantum states, Nat. Commun. 13, 6620 (2022).
  71. L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, and M. K. Joshi, Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett. 133, 010402 (2024).
  72. V. Vitale, A. Rath, P. Jurcevic, A. Elben, C. Branciard, and B. Vermersch, Robust estimation of the quantum Fisher information on a quantum processor, PRX Quantum 5, 030338 (2024).
  73. T. I. Andersen, N. Astrakhantsev, A. H. Karamlou, J. Berndtsson, J. Motruk, A. Szasz, J. A. Gross, A. Schuckert, T. Westerhout, Y. Zhang et al., Thermalization and criticality on an analogue–digital quantum simulator, Nature 638, 79 (2025).
  74. B. Vermersch, A. Rath, B. Sundar, C. Branciard, J. Preskill, and A. Elben, Enhanced estimation of quantum properties with common randomized measurements, PRX Quantum 5, 010352 (2024).
  75. A. Elben, R. Kueng, H.-Y. R. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller, and B. Vermersch, Mixed-state entanglement from local randomized measurements, Phys. Rev. Lett. 125, 200501 (2020).
  76. A. Rath, C. Branciard, A. Minguzzi, and B. Vermersch, Quantum Fisher information from randomized measurements, Phys. Rev. Lett. 127, 260501 (2021).
  77. V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, B. Kraus, P. Zoller, P. Calabrese, B. Vermersch, and M. Dalmonte, Symmetry-resolved dynamical purification in synthetic quantum matter, SciPost Phys. 12, 106 (2022).
  78. K. C. Miao, M. McEwen, J. Atalaya, D. Kafri, L. P. Pryadko, A. Bengtsson, A. Opremcak, K. J. Satzinger, Z. Chen, P. V. Klimov et al., Overcoming leakage in quantum error correction, Nat. Phys. 19, 1780 (2023).
  79. D. Sank et al., Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation, Phys. Rev. Lett. 117, 190503 (2016).
  80. R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. Lewis, G. Vidal, and A. Blais, Dynamics of transmon ionization, Phys. Rev. Appl. 18, 034031 (2022).
  81. B. M. Varbanov, F. Battistel, B. M. Tarasinski, V. P. Ostroukh, T. E. O’Brien, L. DiCarlo, and B. M. Terhal, Leakage detection for a transmon-based surface code, Npj Quantum Inf. 6, 102 (2020).
  82. M. McEwen, D. Kafri, Z. Chen, J. Atalaya, K. Satzinger, C. Quintana, P. V. Klimov, D. Sank, C. Gidney, A. Fowler et al., Removing leakage-induced correlated errors in superconducting quantum error correction, Nat. Commun. 12, 1761 (2021).
  83. P. Magnard, P. Kurpiers, B. Royer, T. Walter, J.-C. Besse, S. Gasparinetti, M. Pechal, J. Heinsoo, S. Storz, A. Blais, and A. Wallraff, Fast and unconditional all-microwave reset of a superconducting qubit, Phys. Rev. Lett. 121, 060502 (2018).
  84. D. Egger, M. Werninghaus, M. Ganzhorn, G. Salis, A. Fuhrer, P. Müller, and S. Filipp, Pulsed reset protocol for fixed-frequency superconducting qubits, Phys. Rev. Appl. 10, 044030 (2018).
  85. Y. Zhou, Z. Zhang, Z. Yin, S. Huai, X. Gu, X. Xu, J. Allcock, F. Liu, G. Xi, Q. Yu, H. Zhang, M. Zhang, H. Li, X. Song, Z. Wang, D. Zheng, S. An, Y. Zheng, and S. Zhang, Rapid and unconditional parametric reset protocol for tunable superconducting qubits, Nat. Commun. 12, 5924 (2021).
  86. N. Lacroix, L. Hofele, A. Remm, O. Benhayoune-Khadraoui, A. McDonald, R. Shillito, S. Lazar, C. Hellings, F. m. c. Swiadek, D. Colao-Zanuz, A. Flasby, M. B. Panah, M. Kerschbaum, G. J. Norris, A. Blais, A. Wallraff, and S. Krinner, Fast flux-activated leakage reduction for superconducting quantum circuits, Phys. Rev. Lett. 134, 120601 (2025).
  87. J. Ghosh, A. G. Fowler, and M. R. Geller, Surface code with decoherence: An analysis of three superconducting architectures, Phys. Rev. A 86, 062318 (2012).

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PRX Quantum 6, 040369– Published 22 December, 2025
  • Received 18 April 2025
  • Revised 26 August 2025
  • Accepted 12 November 2025
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