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

Mitigation of correlated readout errors without randomized measurements

Adrian Skasberg Aasen1,2,*, Andras Di Giovanni3, Hannes Rotzinger3,4, Alexey V. Ustinov3,4, and Martin Gärttner2,†

  • *Contact author: adrian.aasen@uni-jena.de
  • †Contact author: martin.gaerttner@uni-jena.de

Phys. Rev. A 112, 022601 – Published 4 August, 2025

DOI: https://doi.org/10.1103/6p6s-t8b7

Abstract

Quantum simulation, the study of strongly correlated quantum matter using synthetic quantum systems, has been the most successful application of quantum computers to date. It often requires determining observables with high precision, for example when studying critical phenomena near quantum phase transitions. Thus, readout errors must be carefully characterized and mitigated in data postprocessing, using scalable and noise-model agnostic protocols. We present a readout error-mitigation protocol that uses only single-qubit Pauli measurements and avoids experimentally challenging randomized measurements. The proposed approach captures a very broad class of correlated noise models and is scalable to large qubit systems. It is based on a complete and efficient characterization of few-qubit correlated positive operator-valued measures, using overlapping detector tomography. To assess the effectiveness of the protocol, observables are extracted from simulations involving up to 100 qubits employing readout errors obtained from experiments with superconducting qubits.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (54)

  1. E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Demler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriksson, K.-M. C. Fu, M. Greiner, K. R. Hazzard, R. G. Hulet, A. J. Kollár, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe et al. Quantum simulators: Architectures and opportunities, PRX Quantum 2, 017003 (2021).
  2. K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017).
  3. X. Bonet-Monroig, R. Sagastizabal, M. Singh, and T. E. O'Brien, Low-cost error mitigation by symmetry verification, Phys. Rev. A 98, 062339 (2018).
  4. E. van den Berg, Z. K. Minev, A. Kandala, and K. Temme, Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors, Nat. Phys. 19, 1116 (2023).
  5. Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y. Li, J. R. McClean, and T. E. O'Brien, Quantum error mitigation, Rev. Mod. Phys. 95, 045005 (2023).
  6. Y. Quek, D. Stilck França, S. Khatri, J. J. Meyer, and J. Eisert, Exponentially tighter bounds on limitations of quantum error mitigation, Nat. Phys. 20, 1648 (2024).
  7. Z. Zimborás, B. Koczor, Z. Holmes, E.-M. Borrelli, A. Gilyén, H.-Y. Huang, Z. Cai, A. Acín, L. Aolita, L. Banchi, F. G. S. L. Brandão, D. Cavalcanti, T. Cubitt, S. N. Filippov, G. García-Pérez, J. Goold, O. Kálmán, E. Kyoseva, M. A. C. Rossi, B. Sokolov, I. Tavernelli, and S. Maniscalco, Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't, arXiv:2501.05694.
  8. J. Tuziemski, F. B. Maciejewski, J. Majsak, O. Słowik, M. Kotowski, K. Kowalczyk-Murynka, P. Podziemski, and M. Oszmaniec, Efficient reconstruction, benchmarking and validation of cross-talk models in readout noise in near-term quantum devices, arXiv:2311.10661.
  9. Z. Zhou, R. Sitler, Y. Oda, K. Schultz, and G. Quiroz, Quantum crosstalk robust quantum control, Phys. Rev. Lett. 131, 210802 (2023).
  10. M. R. Geller and M. Sun, Toward efficient correction of multiqubit measurement errors: pair correlation method, Quantum Sci. Technol. 6, 025009 (2021).
  11. M. Sarovar, T. Proctor, K. Rudinger, K. Young, E. Nielsen, and R. Blume-Kohout, Detecting crosstalk errors in quantum information processors, Quantum 4, 321 (2020).
  12. J. Heinsoo, C. K. Andersen, A. Remm, S. Krinner, T. Walter, Y. Salathé, S. Gasparinetti, J.-C. Besse, A. Potočnik, A. Wallraff, and C. Eichler, Rapid high-fidelity multiplexed readout of superconducting qubits, Phys. Rev. Appl. 10, 034040 (2018).
  13. P. C. de Groot, A. F. van Loo, J. Lisenfeld, R. N. Schouten, A. Lupaşcu, C. J. P. M. Harmans, and J. E. Mooij, Low-crosstalk bifurcation detectors for coupled flux qubits, Appl. Phys. Lett. 96, 123508 (2010).
  14. B. Lienhard, A. Vepsäläinen, L. C. G. Govia, C. R. Hoffer, J. Y. Qiu, D. Ristè, M. Ware, D. Kim, R. Winik, A. Melville, B. Niedzielski, J. Yoder, G. J. Ribeill, T. A. Ohki, H. K. Krovi, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Deep-neural-network discrimination of multiplexed superconducting-qubit states, Phys. Rev. Appl. 17, 014024 (2022).
  15. F. B. Maciejewski, Z. Zimborás, and M. Oszmaniec, Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography, Quantum 4, 257 (2020).
  16. P. D. Nation, H. Kang, N. Sundaresan, and J. M. Gambetta, Scalable mitigation of measurement errors on quantum computers, PRX Quantum 2, 040326 (2021).
  17. B. Nachman, M. Urbanek, W. A. de Jong, and C. W. Bauer, Unfolding quantum computer readout noise, npj Quantum Inf. 6, 84 (2020).
  18. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
  19. S. Chen, W. Yu, P. Zeng, and S. T. Flammia, Robust shadow estimation, PRX Quantum 2, 030348 (2021).
  20. H. Jnane, J. Steinberg, Z. Cai, H. C. Nguyen, and B. Koczor, Quantum error mitigated classical shadows, PRX Quantum 5, 010324 (2024).
  21. D. E. Koh and S. Grewal, Classical shadows with noise, Quantum 6, 776 (2022).
  22. A. Arrasmith, A. Patterson, A. Boughton, and M. Paini, Development and demonstration of an efficient readout error mitigation technique for use in NISQ algorithms, arXiv:2303.17741.
  23. H.-Y. Hu, A. Gu, S. Majumder, H. Ren, Y. Zhang, D. S. Wang, Y.-Z. You, Z. Minev, S. F. Yelin, and A. Seif, Demonstration of robust and efficient quantum property learning with shallow shadows, Nat. Commun. 16, 2943 (2025).
  24. E. Onorati, J. Kitzinger, J. Helsen, M. Ioannou, A. H. Werner, I. Roth, and J. Eisert, Noise-mitigated randomized measurements and self-calibrating shadow estimation, arXiv:2403.04751.
  25. A. S. Aasen, A. Di Giovanni, H. Rotzinger, A. V. Ustinov, and M. Gärttner, Readout error mitigated quantum state tomography tested on superconducting qubits, Commun. Phys. 7, 301 (2024).
  26. C. Ding, X.-Y. Xu, Y.-F. Niu, S. Zhang, W.-S. Bao, and H.-L. Huang, Noise-resistant quantum state compression readout, Sci. China Phys. Mech. Astron. 66, 230311 (2023).
  27. H.-L. Huang and C. Ding, Quantum state compression shadow, Eur. Phys. J.: Spec. Top (2025), doi:10.1140/epjs/s11734-025-01715-8.
  28. J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, C. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley, Tomography of quantum detectors, Nat. Phys. 5, 27 (2009).
  29. J. Cotler and F. Wilczek, Quantum overlapping tomography, Phys. Rev. Lett. 124, 100401 (2020).
  30. F. B. Maciejewski, F. Baccari, Z. Zimborás, and M. Oszmaniec, Modeling and mitigation of cross-talk effects in readout noise with applications to the quantum approximate optimization algorithm, Quantum 5, 464 (2021).
  31. I. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  32. A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature (London) 568, 207 (2019).
  33. J. Zhang, S. H. Cantú, F. Liu, A. Bylinskii, B. Braverman, F. Huber, J. Amato-Grill, A. Lukin, N. Gemelke, A. Keesling, S.-T. Wang, Y. Meurice, and S.-W. Tsai, Probing quantum floating phases in Rydberg atom arrays, Nat. Commun. 16, 712 (2025).
  34. A. Schuckert, O. Katz, L. Feng, E. Crane, A. De, M. Hafezi, A. V. Gorshkov, and C. Monroe, Observation of a finite-energy phase transition in a one-dimensional quantum simulator, Nat. Phys. 21, 374 (2025).
  35. P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Non-local propagation of correlations in quantum systems with long-range interactions, Nature (London) 511, 198 (2014).
  36. P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature (London) 511, 202 (2014).
  37. A. Di Giovanni, A. S. Aasen, J. Lisenfeld, M. Gärttner, H. Rotzinger, and A. V. Ustinov, Correlation-conscious optimization of multiplexed qubit readout (unpublished).
  38. J. Fiurášek, Maximum-likelihood estimation of quantum measurement, Phys. Rev. A 64, 024102 (2001).
  39. R. Blume-Kohout, Optimal, reliable estimation of quantum states, New J. Phys. 12, 043034 (2010).
  40. A. I. Lvovsky, Iterative maximum-likelihood reconstruction in quantum homodyne tomography, J. Opt. B: Quantum Semiclassical Opt. 6, S556 (2004).
  41. G. García-Pérez, M. A. C. Rossi, B. Sokolov, E.-M. Borrelli, and S. Maniscalco, Pairwise tomography networks for many-body quantum systems, Phys. Rev. Res. 2, 023393 (2020).
  42. X. Bonet-Monroig, R. Babbush, and T. E. O'Brien, Nearly optimal measurement scheduling for partial tomography of quantum states, Phys. Rev. X 10, 031064 (2020).
  43. R. A. Walker, II and C. J. Colbourn, Perfect hash families: Constructions and existence, J. Math. Cryptol. 1, 125 (2007).
  44. R. Dougherty, Hash families and applications to t-restrictions, Ph.D. thesis, Arizona State University, 2019.
  45. A. Aasen, CREMST, 2025, https://github.com/AdrianAasen/CREMST.
  46. K. Hansenne, R. Qu, L. T. Weinbrenner, C. de Gois, H. Wang, Y. Ming, Z. Yang, P. Horodecki, W. Gao, and O. Gühne, Optimal overlapping tomography, arXiv:2408.05730.
  47. M. Jerger, S. Poletto, P. Macha, U. Hübner, E. Il'ichev, and A. V. Ustinov, Frequency division multiplexing readout and simultaneous manipulation of an array of flux qubits, Appl. Phys. Lett. 101, 042604 (2012).
  48. P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer's guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).
  49. A. D. Giovanni, A. S. Aasen, J. Lisenfeld, M. Gärttner, H. Rotzinger, and A. V. Ustinov, Multiplexed qubit readout quality metric beyond assignment fidelity, arXiv:2502.08589 [Phys. Rev. Appl. (to be published)].
  50. D. Müllner, Modern hierarchical, agglomerative clustering algorithms, arXiv:1109.2378.
  51. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey et al., Scipy 1.0: fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  52. J. Shang, Z. Zhang, and H. K. Ng, Superfast maximum-likelihood reconstruction for quantum tomography, Phys. Rev. A 95, 062336 (2017).
  53. Z. Hou, H.-S. Zhong, Y. Tian, D. Dong, B. Qi, L. Li, Y. Wang, F. Nori, G.-Y. Xiang, C.-F. Li, and G.-C. Guo, Full reconstruction of a 14-qubit state within four hours, New J. Phys. 18, 083036 (2016).
  54. D. H. Mahler, L. A. Rozema, A. Darabi, C. Ferrie, R. Blume-Kohout, and A. M. Steinberg, Adaptive quantum state tomography improves accuracy quadratically, Phys. Rev. Lett. 111, 183601 (2013).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation