- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Quantum error correction assisted axion search in CMOS spin qubit arrays

Xiangjun Tan1,* and Zhanning Wang2

  • *Contact author: xiangjun.tan.25@ucl.ac.uk
PDF

Phys. Rev. D 113, 116030 – Published 17 June, 2026

DOI: https://doi.org/10.1103/2y5c-x1kz

Abstract

Searches for axion and axionlike dark matter based on solid-state spin qubits are fundamentally limited by strong longitudinal dephasing, which rapidly suppresses the sensitivity gains offered by entanglement. Here, we show that quantum error correction (QEC) can substantially enhance axion search sensitivity in realistic semiconductor spin qubit platforms by mitigating this dominant noise source. By integrating an optimally chosen repetition code QEC with logical Green berger–Horne–Zeilinger block entanglement, we derive closed-form expressions for the quantum Fisher information that explicitly incorporate the finite coherence time of the axion field. Our analysis demonstrates that modest QEC cycle frequencies are sufficient to significantly reduce the effective dephasing rate, thereby restoring a broad parameter regime in which entanglement-enhanced sensing surpasses the standard quantum limit. Projecting these results onto complementary metal-oxide semiconductor-compatible device parameters, we find that QEC-protected entangled sensing can revive otherwise inaccessible quantum advantages, yielding up to order-of-magnitude improvements in sensitivity to the axion-electron coupling gae. These results establish a practical and theoretically controlled pathway for using QEC to improve qubit array searches for physics beyond the standard model.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (92)

  1. J. L. Feng, Dark matter candidates from particle physics and methods of detection, Annu. Rev. Astron. Astrophys. 48, 495 (2010).
  2. D. J. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
  3. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rep. 870, 1 (2020).
  4. K. Choi, S. H. Im, and C. S. Shin, Recent progress in the physics of axions and axion-like particles, Annu. Rev. Nucl. Part. Sci. 71, 225 (2021).
  5. A. Arbey and F. Mahmoudi, Dark matter and the early universe: A review, Prog. Part. Nucl. Phys. 119, 103865 (2021).
  6. R. D. Peccei and H. R. Quinn, CP conservation in the presence of pseudoparticles, Phys. Rev. Lett. 38, 1440 (1977).
  7. R. D. Peccei and H. R. Quinn, Constraints imposed by CP conservation in the presence of pseudoparticles, Phys. Rev. D 16, 1791 (1977).
  8. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  9. F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  10. Z. G. Berezhiani and M. Y. Khlopov, Cosmology of spontaneously broken gauge family symmetry with axion solution of strong cp-problem, Z. Phys. C Part. Fields 49, 73 (1991).
  11. M. Khlopov, A. Sakharov, and D. Sokoloff, The nonlinear modulation of the density distribution in standard axionic CDM and its cosmological impact, Nucl. Phys. B, Proc. Suppl. 72, 105 (1999).
  12. J. E. Kim and G. Carosi, Axions and the strong CP problem, Rev. Mod. Phys. 82, 557 (2010).
  13. I. G. Irastorza and J. Redondo, New experimental approaches in the search for axion-like particles, Prog. Part. Nucl. Phys. 102, 89 (2018).
  14. L. D. Duffy and K. v. Bibber, Axions as dark matter particles, New J. Phys. 11, 105008 (2009).
  15. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  16. L. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  17. M. Dine and W. Fischler, The not-so-harmless axion, Phys. Lett. 120B, 137 (1983).
  18. F. Chadha-Day, J. Ellis, and D. J. E. Marsh, Axion dark matter: What is it and why now?, Sci. Adv. 8, eabj3618 (2022).
  19. A. J. Brady, C. Gao, R. Harnik, Z. Liu, Z. Zhang, and Q. Zhuang, Entangled sensor-networks for dark-matter searches, PRX Quantum 3, 030333 (2022).
  20. S.-Y. Guo, M. Khlopov, X. Liu, L. Wu, Y. Wu, and B. Zhu, Footprints of axion-like particle in pulsar timing array data and James webb space telescope observations, Sci. China Phys. Mech. Astron. 67, 111011 (2024).
  21. Y. V. Stadnik and V. V. Flambaum, Axion-induced effects in atoms, molecules, and nuclei: Parity nonconservation, anapole moments, electric dipole moments, and spin-gravity and spin-axion momentum couplings, Phys. Rev. D 89, 043522 (2014).
  22. Y. K. Semertzidis and S. Youn, Axion dark matter: How to see it?, Sci. Adv. 8, eabm9928 (2022).
  23. A. B. Balakin and V. A. Popov, Spin-axion coupling, Phys. Rev. D 92, 105025 (2015).
  24. A. Berlin, A. J. Millar, T. Trickle, and K. Zhou, Physical signatures of fermion-coupled axion dark matter, J. High Energy Phys. 05 (2024) 314.
  25. A. Garcon, D. Aybas, J. W. Blanchard, G. Centers, N. L. Figueroa, P. W. Graham, D. F. J. Kimball, S. Rajendran, M. G. Sendra, A. O. Sushkov, L. Trahms, T. Wang, A. Wickenbrock, T. Wu, and D. Budker, The cosmic axion spin precession experiment (CASPEr): A dark-matter search with nuclear magnetic resonance, Quantum Sci. Technol. 3, 014008 (2017).
  26. A. Garcon, J. W. Blanchard, G. P. Centers, N. L. Figueroa, P. W. Graham, D. F. J. Kimball, S. Rajendran, A. O. Sushkov, Y. V. Stadnik, A. Wickenbrock, T. Wu, and D. Budker, Constraints on bosonic dark matter from ultralow-field nuclear magnetic resonance, Sci. Adv. 5, eaax4539 (2019).
  27. J. A. Dror, S. Gori, J. M. Leedom, and N. L. Rodd, Sensitivity of spin-precession axion experiments, Phys. Rev. Lett. 130, 181801 (2023).
  28. Z. Xu, X. Ma, K. Wei, Y. He, X. Heng, X. Huang, T. Ai, J. Liao, W. Ji, J. Liu, X.-P. Wang, and D. Budker, Constraining ultralight dark matter through an accelerated resonant search, Commun. Phys. 7, 226 (2024).
  29. X. Tan, Z. Wang, W. Bai, and H. Zhu, Canceling second-order frequency shifts in ge hole spin qubits via bichromatic control, Appl. Phys. Lett. 128, 124001 (2026).
  30. T. Wu, J. W. Blanchard, G. P. Centers, N. L. Figueroa, A. Garcon, P. W. Graham, D. F. J. Kimball, S. Rajendran, Y. V. Stadnik, A. O. Sushkov, A. Wickenbrock, and D. Budker, Search for axionlike dark matter with a liquid-state nuclear spin comagnetometer, Phys. Rev. Lett. 122, 191302 (2019).
  31. D. Budker, P. W. Graham, M. Ledbetter, S. Rajendran, and A. O. Sushkov, Proposal for a cosmic axion spin precession experiment (CASPEr), Phys. Rev. X 4, 021030 (2014).
  32. D. Aybas et al., Search for axionlike dark matter using solid-state nuclear magnetic resonance, Phys. Rev. Lett. 126, 141802 (2021).
  33. D. Aybas, H. Bekker, J. W. Blanchard, D. Budker, G. P. Centers, N. L. Figueroa, A. V. Gramolin, D. F. Jackson Kimball, A. Wickenbrock, and A. O. Sushkov, Quantum sensitivity limits of nuclear magnetic resonance experiments searching for new fundamental physics, Quantum Sci. Technol. 6, 034007 (2021).
  34. J. W. Blanchard, A. O. Sushkov, and A. Wickenbrock, Magnetic resonance searches, in The Search for Ultralight Bosonic Dark Matter, edited by D. F. Jackson Kimball and K. van Bibber (Springer International Publishing, Cham, 2023), pp. 173–200.
  35. E. Boyers, G. Goldstein, and A. O. Sushkov, Spin squeezing of macroscopic nuclear spin ensembles, Phys. Rev. D 111, 052004 (2025).
  36. R. Barbieri, C. Braggio, G. Carugno, C. Gallo, A. Lombardi, A. Ortolan, R. Pengo, G. Ruoso, and C. Speake, Searching for galactic axions through magnetized media: The quax proposal, Phys. Dark Universe 15, 135 (2017).
  37. N. Crescini, D. Alesini, C. Braggio, G. Carugno, D. Di Gioacchino, C. S. Gallo, U. Gambardella, C. Gatti, G. Iannone, G. Lamanna, C. Ligi, A. Lombardi, A. Ortolan, S. Pagano, R. Pengo, G. Ruoso, C. C. Speake, and L. Taffarello, Operation of a ferromagnetic axion haloscope at ma=58  μeV, Eur. Phys. J. C 78, 703 (2018).
  38. N. Crescini, D. Alesini, C. Braggio, G. Carugno, D. D’Agostino, D. Di Gioacchino, P. Falferi, U. Gambardella, C. Gatti, G. Iannone, C. Ligi, A. Lombardi, A. Ortolan, R. Pengo, G. Ruoso, and L. Taffarello (QUAX Collaboration), Axion search with a quantum-limited ferromagnetic haloscope, Phys. Rev. Lett. 124, 171801 (2020).
  39. S. Chigusa, T. Moroi, and K. Nakayama, Detecting light boson dark matter through conversion into a magnon, Phys. Rev. D 101, 096013 (2020).
  40. S. Chigusa, A. Ito, K. Nakayama, and V. Takhistov, Effects of finite material size on axion-magnon conversion, J. High Energy Phys. 01 (2024) 185.
  41. G. Flower, J. Bourhill, M. Goryachev, and M. E. Tobar, Broadening frequency range of a ferromagnetic axion haloscope with strongly coupled cavity–magnon polaritons, Phys. Dark Universe 25, 100306 (2019).
  42. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  43. T. Ikeda, A. Ito, K. Miuchi, J. Soda, H. Kurashige, and Y. Shikano, Axion search with quantum nondemolition detection of magnons, Phys. Rev. D 105, 102004 (2022).
  44. C. Chang, T. J. Hobbs, D. Jin, Y. Li, M. Lisovenko, V. Novosad, Z. H. Saleem, T. Trickle, and G. Wang, Searching for axion dark matter with array-scalable single magnon detectors, Phys. Rev. D 113, 015016 (2026).
  45. A. V. Dixit, S. Chakram, K. He, A. Agrawal, R. K. Naik, D. I. Schuster, and A. Chou, Searching for dark matter with a superconducting qubit, Phys. Rev. Lett. 126, 141302 (2021).
  46. S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichanugrist, Detecting hidden photon dark matter using the direct excitation of transmon qubits, Phys. Rev. Lett. 131, 211001 (2023).
  47. A. K. Yi et al., Axion dark matter search around 4.55  μeV with dine-fischler-srednicki-zhitnitskii sensitivity, Phys. Rev. Lett. 130, 071002 (2023).
  48. S. Ahn et al., Extensive search for axion dark matter over 1 GHz with CAPP’s main axion experiment, Phys. Rev. X 14, 031023 (2024).
  49. S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichanugrist, Quantum enhancement in dark matter detection with quantum computation, Phys. Rev. Lett. 133, 021801 (2024).
  50. S. Ahn, I. M. C. B. U. Kutlu, S. Lee, S. Youn, S. V. Uchaikin, S. Bae, J. Jeong, A. F. van Loo, Y. Nakamura, S. Oh, J. E. Kim, and Y. K. Semertzidis, Probing kim-shifman-vainshtein-zakharov axion dark matter near 5.9 GHz using an 8-cell cavity haloscope, Phys. Rev. Lett. 135, 211801 (2025).
  51. S. Bae, J. Jeong, Y. Kim, S. Youn, J. Kim, A. F. van Loo, Y. Nakamura, S. Oh, T. Seong, S. Uchaikin, J. E. Kim, and Y. K. Semertzidis, Axion dark matter search with sensitivity near the Kim-Shifman-Vainshtein-Zakharov benchmark using the TM020 mode, Phys. Rev. Lett. 135, 091804 (2025).
  52. C. Braggio, L. Balembois, R. Di Vora, Z. Wang, J. Travesedo, L. Pallegoix, G. Carugno, A. Ortolan, G. Ruoso, U. Gambardella, D. D’Agostino, P. Bertet, and E. Flurin, Quantum-enhanced sensing of axion dark matter with a transmon-based single microwave photon counter, Phys. Rev. X 15, 021031 (2025).
  53. F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Silicon quantum electronics, Rev. Mod. Phys. 85, 961 (2013).
  54. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  55. G. Hu, W. W. Huang, R. Cai, L. Wang, C. H. Yang, G. Cao, X. Xue, P. Huang, and Y. He, Single-electron spin qubits in silicon for quantum computing, Intelligent instruments and computers 4, 0115 (2025).
  56. R. Zhao, T. Tanttu, K. Y. Tan, B. Hensen, K. W. Chan, J. C. C. Hwang, R. C. C. Leon, C. H. Yang, W. Gilbert, F. E. Hudson, K. M. Itoh, A. A. Kiselev, T. D. Ladd, A. Morello, A. Laucht, and A. S. Dzurak, Single-spin qubits in isotopically enriched silicon at low magnetic field, Nat. Commun. 10, 5500 (2019).
  57. A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sammak, G. Scappucci, and S. Tarucha, Fast universal quantum gate above the fault-tolerance threshold in silicon, Nature (London) 601, 338 (2022).
  58. X. Xue, M. Russ, N. Samkharadze, B. Undseth, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Quantum logic with spin qubits crossing the surface code threshold, Nature (London) 601, 343 (2022).
  59. A. M. J. Zwerver et al., Qubits made by advanced semiconductor manufacturing, National electronics review 5, 184 (2022).
  60. W. I. L. Lawrie, M. Rimbach-Russ, F. v. Riggelen, N. W. Hendrickx, S. L. d. Snoo, A. Sammak, G. Scappucci, J. Helsen, and M. Veldhorst, Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold, Nat. Commun. 14, 3617 (2023).
  61. X. Peetroons et al., High fidelity qubit control in a natural si-mos quantum dot using a 300 mm silicon on insulator wafer, arXiv:2512.05052.
  62. P. Steinacker et al., Industry-compatible silicon spin-qubit unit cells exceeding 99% fidelity, Nature (London) 646, 81 (2025).
  63. S. D. Liles, F. Martins, D. S. Miserev, A. A. Kiselev, I. D. Thorvaldson, M. J. Rendell, I. K. Jin, F. E. Hudson, M. Veldhorst, K. M. Itoh, O. P. Sushkov, T. D. Ladd, A. S. Dzurak, and A. R. Hamilton, Electrical control of the g tensor of the first hole in a silicon mos quantum dot, Phys. Rev. B 104, 235303 (2021).
  64. I. K. Jin, J. Hillier, S. D. Liles, Z. Wang, A. Shamim, I. Vorreiter, R. Li, C. Godfrin, S. Kubicek, K. D. Greve, D. Culcer, and A. R. Hamilton, Probing g-tensor reproducibility and spin-orbit effects in planar silicon hole quantum dots, arXiv:2411.06016.
  65. X. Tan and Z. Wang, Axion signal search using hybrid nuclear-electronic spin systems, arXiv:2601.06816.
  66. S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency standards with quantum entanglement, Phys. Rev. Lett. 79, 3865 (1997).
  67. R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, The elusive Heisenberg limit in quantum-enhanced metrology, Nat. Commun. 3, 1063 (2012).
  68. J. Yoneda, K. Takeda, T. Otsuka, T. Nakajima, M. R. Delbecq, G. Allison, T. Honda, T. Kodera, S. Oda, Y. Hoshi, N. Usami, K. M. Itoh, and S. Tarucha, A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%, Nat. Nanotechnol. 13, 102 (2018).
  69. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
  70. E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Quantum error correction for metrology, Phys. Rev. Lett. 112, 150802 (2014).
  71. G. Arrad, Y. Vinkler, D. Aharonov, and A. Retzker, Increasing sensing resolution with error correction, Phys. Rev. Lett. 112, 150801 (2014).
  72. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  73. H. Fukuda, T. Moroi, and T. Sichanugrist, Quantum error correction-like noise mitigation for wave-like dark matter searches with quantum sensors, arXiv:2511.03253.
  74. S. Chen, H. Fukuda, Y. Iiyama, Y. Mino, T. Moroi, M. Nakahara, T. Nitta, and T. Sichanugrist, Background suppression in quantum sensing of dark matter via collective entangled-state projection, Phys. Rev. D 113, 055014 (2026).
  75. G. P. Centers, J. W. Blanchard, J. Conrad, N. L. Figueroa, A. Garcon, A. V. Gramolin, D. F. J. Kimball, M. Lawson, B. Pelssers, J. A. Smiga, A. O. Sushkov, A. Wickenbrock, D. Budker, and A. Derevianko, Stochastic fluctuations of bosonic dark matter, Nat. Commun. 12, 7321 (2021).
  76. W. Chen, Y. Gao, and Q. Yang, Broadband dark matter axion detection using a cylindrical capacitor, Nucl. Phys. B1005, 116602 (2024).
  77. A. V. Gramolin, A. Wickenbrock, D. Aybas, H. Bekker, D. Budker, G. P. Centers, N. L. Figueroa, D. F. Jackson Kimball, and A. O. Sushkov, Spectral signatures of axionlike dark matter, Phys. Rev. D 105, 035029 (2022).
  78. S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichanugrist, Search for QCD axion dark matter with transmon qubits and quantum circuit, Phys. Rev. D 110, 115021 (2024).
  79. A. Quiskamp, B. T. McAllister, P. Altin, E. N. Ivanov, M. Goryachev, and M. E. Tobar, Direct search for dark matter axions excluding alp cogenesis in the 63- to 67-μeV range with the organ experiment, Sci. Adv. 8, eabq3765 (2022).
  80. X. Tan and Z. Wang, Toward axion signal extraction in semiconductor spin qubits via spectral engineering, IEEE Trans. Quantum Eng. 6, 1 (2025).
  81. X. Tan and Z. Wang, Annual-modulation fingerprint of the axion wind induced sideband triplet in quantum dot spin qubit sensors, Phys. Rev. D 113, 016001 (2025).
  82. Z. Wang, S. Gholizadeh, X. Hu, S. Das Sarma, and D. Culcer, Dephasing of planar Ge hole spin qubits due to 1/f charge noise, Phys. Rev. B 111, 155403 (2025).
  83. K. M. Itoh and H. Watanabe, Isotope engineering of silicon and diamond for quantum computing and sensing applications, MRS Commun. 4, 143 (2014).
  84. G. Széchenyi and A. Pályi, Coulomb-blockade and Pauli-blockade magnetometry, Phys. Rev. B 95, 035431 (2017).
  85. J. C. Abadillo-Uriel, E. A. Rodríguez-Mena, B. Martinez, and Y.-M. Niquet, Hole-spin driving by strain-induced spin-orbit interactions, Phys. Rev. Lett. 131, 097002 (2023).
  86. D. J. Reilly, J. M. Taylor, E. A. Laird, J. R. Petta, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Measurement of temporal correlations of the overhauser field in a double quantum dot, Phys. Rev. Lett. 101, 236803 (2008).
  87. B. Shalak, C. Delerue, and Y.-M. Niquet, Modeling of spin decoherence in a Si hole qubit perturbed by a single charge fluctuator, Phys. Rev. B 107, 125415 (2023).
  88. M. Cowie, P. C. Constantinou, N. J. Curson, T. J. Z. Stock, and P. Grütter, Spatially resolved random telegraph fluctuations of a single trap at the Si/SiO2 interface, Proc. Natl. Acad. Sci. U.S.A. 121, e2404456121 (2024).
  89. G. A. Oakes et al., Fast high-fidelity single-shot readout of spins in silicon using a single-electron box, Phys. Rev. X 13, 011023 (2023).
  90. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
  91. F. van Riggelen, W. I. L. Lawrie, M. Russ, N. W. Hendrickx, A. Sammak, M. Rispler, B. M. Terhal, G. Scappucci, and M. Veldhorst, Phase flip code with semiconductor spin qubits, npj Quantum Inf. 8, 124 (2022).
  92. M. Gutiérrez, J. S. Rojas-Arias, D. Obando, and C.-Y. Chang, Comparison of spin-qubit architectures for quantum error-correcting codes, arXiv:2506.17190.

Outline

Information

Phys. Rev. D 113, 116030– Published 17 June, 2026
  • Received 14 December 2025
  • Accepted 20 May 2026
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