Improved quantum processor logical error rates via correction and detection

Data availability

The data from the experimental runs are available on request.

Code availability

The quantum circuits used in these experiments are available on request.

References

Reiher, M., Wiebe, N., Svore, K. M., Wecker, D. & Troyer, M. Elucidating reaction mechanisms on quantum computers. Proc. Natl Acad. Sci. USA 114 , 7555–7560 (2016).

Article

ADS

Google Scholar

Beverland, M. E. et al. Assessing requirements to scale to practical quantum advantage. Preprint at https://arxiv.org/abs/2211.07629 (2022).

Aharonov, D. & Ben-Or, M. Fault-tolerant quantum computation with constant error. In Proc. Twenty-Ninth Annual ACM Symposium on Theory of Computing (STOC ‘97) 176–188 (ACM Press, 1997).

Kitaev, A. Y. in Quantum Communication, Computing, and Measurement (eds Hirota, O., Holevo, A. S. & Caves, C. M.) 181–188 (Springer, 1997).

Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279 , 342–345 (1998).

Article

ADS

CAS

Google Scholar

Terhal, B. M. & Burkard, G. Fault-tolerant quantum computation for local non-Markovian noise. Phys. Rev. A 71 , 012336 (2005).

Article

ADS

Google Scholar

Aliferis, P., Gottesman, D. & Preskill, J. Quantum accuracy threshold for concatenated distance-3 codes. Quantum Inf. Comput. 6 , 97–165 (2006).

MathSciNet

Google Scholar

Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98 , 190504 (2007).

Article

ADS

PubMed

Google Scholar

Moses, S. A. et al. A race-track trapped-ion quantum processor. Phys. Rev. X 13 , 041052 (2023).

CAS

Google Scholar

DeCross, M. et al. The computational power of random quantum circuits in arbitrary geometries. Phys. Rev. X 15 , 021052 (2025).

CAS

Google Scholar

Knill, E. Quantum computing with realistically noisy devices. Nature 434 , 39–44 (2004).

Article

ADS

Google Scholar

Delfosse, N. & Reichardt, B. W. Short Shor-style syndrome sequences. Preprint at https://arxiv.org/abs/2008.05051 (2020).

Prabhu, P. & Reichardt, B. W. Distance-four quantum codes with combined postselection and error correction. Phys. Rev. A 110 , 012419 (2024).

Article

ADS

MathSciNet

CAS

Google Scholar

Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2 , 79 (2018).

Article

Google Scholar

Chao, R. & Reichardt, B. W. Fault-tolerant quantum computation with few qubits. npj Quantum Inf. 4 , 42 (2018).

Article

ADS

Google Scholar

Jones, C. et al. Logical qubit in a linear array of semiconductor quantum dots. Phys. Rev. X 8 , 021058 (2018).

CAS

Google Scholar

Reichardt, B. W. Fault-tolerant quantum error correction for Steane’s seven-qubit color code with few or no extra qubits. Quantum Sci. Technol. 6 , 015007 (2021).

Article

ADS

Google Scholar

Knill, E. Scalable quantum computation in the presence of large detected-error rates. Preprint at https://arxiv.org/abs/quant-ph/0312190 (2004).

Gidney, C., Newman, M., Brooks, P. & Jones, C. Yoked surface codes. Nat. Commun. 16 , 4498 (2025).

Egan, L. et al. Fault-tolerant control of an error-corrected qubit. Nature 598 , 281–286 (2021).

Article

ADS

CAS

PubMed

Google Scholar

Ryan-Anderson, C. et al. Realization of real-time fault-tolerant quantum error correction. Phys. Rev. X 11 , 041058 (2021).

CAS

Google Scholar

Ryan-Anderson, C. et al. Implementing fault-tolerant entangling gates on the five-qubit code and the color code. Preprint at https://arxiv.org/abs/2208.01863 (2022).

Acharya, R. et al. Suppressing quantum errors by scaling a surface code logical qubit. Nature 614 , 676–681 (2022).

Google Scholar

Sivak, V. V. et al. Real-time quantum error correction beyond break-even. Nature 616 , 50–55 (2023).

Article

ADS

CAS

PubMed

Google Scholar

Acharya, R. et al. Quantum error correction below the surface code threshold. Nature 638 , 920–926 (2024).

Google Scholar

Eickbusch, A. Demonstration of dynamic surface codes. Nat. Phys. 21 , 1994–2001 (2025).

Article

CAS

Google Scholar

Erhard, A. et al. Entangling logical qubits with lattice surgery. Nature 589 , 220–224 (2020).

Article

ADS

Google Scholar

Postler, L. et al. Demonstration of fault-tolerant universal quantum gate operations. Nature 605 , 675–680 (2022).

Article

ADS

CAS

PubMed

Google Scholar

Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626 , 58–65 (2023).

Article

ADS

PubMed

PubMed Central

Google Scholar

Yamamoto, K., Duffield, S., Kikuchi, Y. & Ramo, D. M. Demonstrating Bayesian quantum phase estimation with quantum error detection. Phys. Rev. Res. 6 , 013221 (2024).

Article

CAS

Google Scholar

Hong, Y., Durso-Sabina, E., Hayes, D. & Lucas, A. Entangling four logical qubits beyond break-even in a nonlocal code. Phys. Rev. Lett. 133 , 180601 (2024).

Article

ADS

MathSciNet

CAS

PubMed

Google Scholar

Self, C. N., Benedetti, M. & Amaro…