- 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
  • Editors' Suggestion
  • Open Access

Error detection without postselection in adaptive quantum circuits

Eli Chertkov*, Andrew C. Potter, David Hayes, and Michael Foss-Feig

  • Quantinuum, 303 South Technology Court, Broomfield, Colorado 80021, USA

  • *Contact author: eli.chertkov@quantinuum.com
PDF

Phys. Rev. Research 8, 023057 – Published 16 April, 2026

DOI: https://doi.org/10.1103/6b14-7wkt

Abstract

Current quantum computers are limited by errors, but have not yet achieved the scale required to benefit from active error correction in large computations. We show how simulations of dissipative quantum circuits can benefit from error detection. In particular, we use Quantinuum’s H2 quantum computer to perform 24-qubit logical simulations of a nonequilibrium phase transition using many [[4,2,2]] code blocks. Importantly, by converting detected errors into random resets, which are an intended part of the dissipative quantum dynamics being studied, we avoid any postselection in our simulations, thereby eliminating the exponential cost typically associated with error detection. The encoded simulations perform near breakeven with unencoded simulations at short times.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (62)

  1. S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
  2. A. D. Córcoles, E. Magesan, S. J. Srinivasan, A. W. Cross, M. Steffen, J. M. Gambetta, and J. M. Chow, Demonstration of a quantum error detection code using a square lattice of four superconducting qubits, Nat. Commun. 6, 6979 (2015).
  3. D. Gottesman, Quantum fault tolerance in small experiments, arXiv:1610.03507.
  4. C. Vuillot, Is error detection helpful on IBM 5Q chips? Quantum Inf. Comput. 18, 0949 (2017).
  5. 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).
  6. R. Harper and S. T. Flammia, Fault-tolerant logical gates in the IBM quantum experience, Phys. Rev. Lett. 122, 080504 (2019).
  7. Y. Wang et al., Fault-tolerant one-bit addition with the smallest interesting color code, Sci. Adv. 10, eado9024 (2024).
  8. D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  9. C. N. Self, M. Benedetti, and D. Amaro, Protecting expressive circuits with a quantum error detection code, Nat. Phys. 20, 219 (2024).
  10. K. Yamamoto, S. Duffield, Y. Kikuchi, and D. M. Ramo, Demonstrating Bayesian quantum phase estimation with quantum error detection, Phys. Rev. Res. 6, 013221 (2024).
  11. Z. He, D. Amaro, R. Shaydulin, and M. Pistoia, Performance of quantum approximate optimization with quantum error detection, Commun. Phys. 8, 217 (2025).
  12. Y. Jin, Z. He, T. Hao, D. Amaro, S. Tannu, R. Shaydulin, and M. Pistoia, Iceberg beyond the tip: Co-compilation of a quantum error detection code and a quantum algorithm, arXiv:2504.21172.
  13. S. Dasu, S. Burton, K. Mayer, D. Amaro, J. A. Gerber, K. Gilmore, D. Gresh, D. DelVento, A. C. Potter, and D. Hayes, Breaking even with magic: Demonstration of a high-fidelity logical non-Clifford gate, arXiv:2506.14688.
  14. T. E. Harris, Contact interactions on a lattice, Ann. Prob. 2, 969 (1974).
  15. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models, Collection Alea-Saclay: Monographs and Texts in Statistical Physics (Cambridge University Press, Cambridge, 1999).
  16. H. Hinrichsen, Non-equilibrium critical phenomena and phase transitions into absorbing states, Adv. Phys. 49, 815 (2000).
  17. G. Ódor, Universality classes in nonequilibrium lattice systems, Rev. Mod. Phys. 76, 663 (2004).
  18. H. Hinrichsen, Non-equilibrium phase transitions, Physica A 369, 1 (2006).
  19. I. Jensen, Low-density series expansions for directed percolation: I. A new efficient algorithm with applications to the square lattice, J. Phys. A 32, 5233 (1999).
  20. M. Marcuzzi, M. Buchhold, S. Diehl, and I. Lesanovsky, Absorbing state phase transition with competing quantum and classical fluctuations, Phys. Rev. Lett. 116, 245701 (2016).
  21. F. Carollo, E. Gillman, H. Weimer, and I. Lesanovsky, Critical behavior of the quantum contact process in one dimension, Phys. Rev. Lett. 123, 100604 (2019).
  22. E. Gillman, F. Carollo, and I. Lesanovsky, Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state, New J. Phys. 21, 093064 (2019).
  23. M. Jo, J. Lee, K. Choi, and B. Kahng, Absorbing phase transition with a continuously varying exponent in a quantum contact process: A neural network approach, Phys. Rev. Res. 3, 013238 (2021).
  24. E. Chertkov, Z. Cheng, A. C. Potter, S. Gopalakrishnan, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, A. Hall, A. Hankin, M. Matheny, T. Mengle, D. Hayes, B. Neyenhuis, R. Stutz, and M. Foss-Feig, Characterizing a non-equilibrium phase transition on a quantum computer, Nat. Phys. 19, 1799 (2023).
  25. B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Phys. Rev. X 9, 031009 (2019).
  26. A. C. Potter and R. Vasseur, Entanglement dynamics in hybrid quantum circuits, in Entanglement in Spin Chains, Quantum Science and Technology, edited by A. Bayat, S. Bose, annd H. Johannesson (Springer International Publishing, Cham, Switzerland, 2022), pp. 211–249.
  27. M. Buchhold, T. Müller, and S. Diehl, Revealing measurement-induced phase transitions by pre-selection, arXiv:2208.10506.
  28. V. Ravindranath, Y. Han, Z.-C. Yang, and X. Chen, Entanglement steering in adaptive circuits with feedback, Phys. Rev. B 108, L041103 (2023).
  29. N. O’Dea, A. Morningstar, S. Gopalakrishnan, and V. Khemani, Entanglement and absorbing-state transitions in interactive quantum dynamics, Phys. Rev. B 109, L020304 (2024).
  30. P. Sierant and X. Turkeshi, Controlling entanglement at absorbing state phase transitions in random circuits, Phys. Rev. Lett. 130, 120402 (2023).
  31. P. Sierant and X. Turkeshi, Entanglement and absorbing state transitions in (d + 1)-dimensional stabilizer circuits, Acta Phys. Pol. A 144, 474 (2023).
  32. D. Qian and J. Wang, Steering-induced phase transition in measurement-only quantum circuits, Phys. Rev. B 109, 024301 (2024).
  33. C. LeMaire, A. A. Allocca, J. H. Pixley, T. Iadecola, and J. H. Wilson, Separate measurement- and feedback-driven entanglement transitions in the stochastic control of chaos, Phys. Rev. B 110, 014310 (2024).
  34. L. Vaidman, L. Goldenberg, and S. Wiesner, Error prevention scheme with four particles, Phys. Rev. A 54, R1745 (1996).
  35. M. Grassl, T. Beth, and T. Pellizzari, Codes for the quantum erasure channel, Phys. Rev. A 56, 33 (1997).
  36. M. DeCross et al., Computational power of random quantum circuits in arbitrary geometries, Phys. Rev. X 15, 021052 (2025).
  37. S. A. Moses et al., A race-track trapped-ion quantum processor, Phys. Rev. X 13, 041052 (2023).
  38. R. Chao and B. W. Reichardt, Fault-tolerant quantum computation with few qubits, npj Quantum Inf. 4, 42 (2018).
  39. D. Gottesman, Opportunities and challenges in fault-tolerant quantum computation, arXiv:2210.15844.
  40. B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Phys. Rev. Lett. 102, 110502 (2009).
  41. Note that the effective logical system size can be larger than expected by two qubits, due to the constrained nature of performing qubit reuse on code blocks with two logical qubits.
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6b14-7wkt for additional details on the quantum error detection code, numerical simulations, and experimental error mitigation, which includes Refs. [3, 4, 6, 24, 36, 37, 38, 51, 52, 53, 59, 60, 61, 62].
  43. M. DeCross, E. Chertkov, M. Kohagen, and M. Foss-Feig, Qubit-reuse compilation with mid-circuit measurement and reset, Phys. Rev. X 13, 041057 (2023).
  44. I. H. Kim, Holographic quantum simulation, arXiv:1702.02093.
  45. M. Foss-Feig, D. Hayes, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, J. M. Pino, and A. C. Potter, Holographic quantum algorithms for simulating correlated spin systems, Phys. Rev. Res. 3, 033002 (2021).
  46. F. Barratt, J. Dborin, M. Bal, V. Stojevic, F. Pollmann, and A. G. Green, Parallel quantum simulation of large systems on small NISQ computers, npj Quantum Inf. 7, 79 (2021).
  47. E. Chertkov, J. Bohnet, D. Francois, J. Gaebler, D. Gresh, A. Hankin, K. Lee, D. Hayes, B. Neyenhuis, R. Stutz, A. C. Potter, and M. Foss-Feig, Holographic dynamics simulations with a trapped-ion quantum computer, Nat. Phys. 18, 1074 (2022).
  48. D. Niu, R. Haghshenas, Y. Zhang, M. Foss-Feig, G. K.-L. Chan, and A. C. Potter, Holographic simulation of correlated electrons on a trapped ion quantum processor, PRX Quantum 3, 030317 (2022).
  49. Y. Zhang, S. Jahanbani, D. Niu, R. Haghshenas, and A. C. Potter, Qubit-efficient simulation of thermal states with quantum tensor networks, Phys. Rev. B 106, 165126 (2022).
  50. R. Stricker, D. Vodola, A. Erhard, L. Postler, M. Meth, M. Ringbauer, P. Schindler, T. Monz, M. Müller, and R. Blatt, Experimental deterministic correction of qubit loss, Nature (London) 585, 207 (2020).
  51. R. Haghshenas et al., Digital quantum magnetism at the frontier of classical simulations, arXiv:2503.20870.
  52. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  53. A. Dua, A. Kubica, L. Jiang, S. T. Flammia, and M. J. Gullans, Clifford-deformed surface codes, PRX Quantum 5, 010347 (2024).
  54. G. Perfetto, F. Carollo, M. Magoni, and I. Lesanovsky, Designing nonequilibrium states of quantum matter through stochastic resetting, Phys. Rev. B 104, L180302 (2021).
  55. M. Magoni, F. Carollo, G. Perfetto, and I. Lesanovsky, Emergent quantum correlations and collective behavior in noninteracting quantum systems subject to stochastic resetting, Phys. Rev. A 106, 052210 (2022).
  56. G. Perfetto, F. Carollo, and I. Lesanovsky, Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting, SciPost Phys. 13, 079 (2022).
  57. S. Wald, L. H. Yao, T. Platini, C. Hooley, and F. Carollo, Stochastic resetting in discrete-time quantum dynamics: Steady states and correlations in few-qubit systems, Quantum 9, 1742 (2025).
  58. Y. Ilin and I. Arad, Dissipative variational quantum algorithms for Gibbs state preparation, IEEE Trans. Quantum Eng. 6, 1 (2025).
  59. C. Chamberland and M. E. Beverland, Flag fault-tolerant error correction with arbitrary distance codes, Quantum 2, 53 (2018).
  60. R. Chao and B. W. Reichardt, Flag fault-tolerant error correction for any stabilizer code, PRX Quantum 1, 010302 (2020).
  61. D. A. Lidar and K. Birgitta Whaley, Decoherence-free subspaces and subsystems, in Irreversible Quantum Dynamics (Springer, Berlin, 2003), pp. 83–120.
  62. Edited by S. Kais, in Quantum Information and Computation for Chemistry (Wiley, Hoboken, New Jersey, 2014).

Outline

Information

Phys. Rev. Research 8, 023057– Published 16 April, 2026
  • Received 9 October 2025
  • Accepted 12 March 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