quantum-computing

Rare Event Simulation of Quantum Error-Correcting Circuits

Carolyn Mayer, Anand Ganti, Uzoma Onunkwo, Tzvetan Metodi, Benjamin Anker, and Jacek Skryzalin

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In this report, we outline an approach that borrows from earlier work by Bravyi and Vargo [6] to the more complex circuit noise model. We have also generated promising results that are confirmed by standard Monte Carlo simulation under an accessible regime. Toward a union-find decoder for quantum LDPC codes. The list may be incomplete as not all publishers provide suitable and complete citation data.

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AbstractWe describe a practical approach for accessing the logical failure rates of quantum error-correcting (QEC) circuits under low physical (component) failure rate regimes.

Standard Monte Carlo is often the de facto approach for studying the failure rates of quantum circuits. However, in the study of fault-tolerant error-correcting circuits, the ability to extend this approach to low physical failure rates is limited. In particular, the use of Monte Carlo to access circuits that are relatively large or have high correcting power becomes more difficult as we lower the input failure rates of the individual components (gates) in the circuit. For these reasons, many simulations studying the circuit model go no lower than end-to-end logical failure rates in the $10^{-6}$ regime. In this report, we outline an approach that borrows from earlier work by Bravyi and Vargo [6] to the more complex circuit noise model. Earlier works studied both the capacity and phenomenological noise models [6,3,5], but the work is insufficient for generating similar simulations in the circuit-noise model. To the best of our knowledge, our team is the first to develop a full prescription of the rare event simulation by splitting technique for the circuit-based noise model. We have also generated promising results that are confirmed by standard Monte Carlo simulation under an accessible regime. This work shows that we can access noise in the circuit-model prescription of quantum error-correcting code to failure rates below $10^{-20}$ regime.► BibTeX data@article{Mayer2026rareeventsimulation, doi = {10.22331/q-2026-10-15-2237}, url = {https://doi.org/10.22331/q-2026-10-15-2237}, title = {Rare {E}vent {S}imulation of {Q}uantum {E}rror-{C}orrecting {C}ircuits}, author = {Mayer, Carolyn and Ganti, Anand and Onunkwo, Uzoma and Metodi, Tzvetan and Anker, Benjamin and Skryzalin, Jacek}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2237}, month = oct, year = {2026} }► References [1] Muhammad AbuGhanem. IBM quantum computers: evolution, performance, and future directions. The Journal of Supercomputing, 81 (5): 687, 2025. https://doi.org/10.1007/s11227-025-07047-7. https://doi.org/10.1007/s11227-025-07047-7 [2] Charles H Bennett. Efficient estimation of free energy differences from Monte Carlo data. Journal of Computational Physics, 22 (2): 245–268, 1976. ISSN 0021-9991. https://doi.org/10.1016/0021-9991(76)90078-4. https://doi.org/10.1016/0021-9991(76)90078-4 [3] Michael E Beverland, Benjamin J Brown, Michael J Kastoryano, and Quentin Marolleau. The role of entropy in topological quantum error correction. Journal of Statistical Mechanics: Theory and Experiment, 2019 (7): 073404, jul 2019. https://doi.org/10.1088/1742-5468/ab25de. https://doi.org/10.1088/1742-5468/ab25de [4] Michael E Beverland, Malcolm Carroll, Andrew W Cross, and Theodore J Yoder. Fail fast: techniques to probe rare events in quantum error correction. arXiv preprint arXiv:2511.15177, 2025. https://doi.org/10.48550/arXiv.2511.15177. https://doi.org/10.48550/arXiv.2511.15177 arXiv:2511.15177 [5] J Pablo Bonilla Ataides, David K Tuckett, Stephen D Bartlett, Steven T Flammia, and Benjamin J Brown. The XZZX surface code. Nature communications, 12 (1): 2172, 2021. https://doi.org/10.1038/s41467-021-22274-1. https://doi.org/10.1038/s41467-021-22274-1 [6] Sergey Bravyi and Alexander Vargo. Simulation of rare events in quantum error correction. Phys. Rev. A, 88: 062308, Dec 2013. https://doi.org/10.1103/PhysRevA.88.062308. https://doi.org/10.1103/PhysRevA.88.062308 [7] Nikolas P Breuckmann and Jens Niklas Eberhardt. Quantum low-density parity-check codes. PRX Quantum, 2 (4): 040101, 2021. https://doi.org/10.1103/PRXQuantum.2.040101. https://doi.org/10.1103/PRXQuantum.2.040101 [8] Siddhartha Chib and Edward Greenberg. Understanding the Metropolis-Hastings algorithm.

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Physical Review Research, 7 (1): 013029, 2025. https://doi.org/10.1103/PhysRevResearch.7.013029. https://doi.org/10.1103/PhysRevResearch.7.013029Cited by[1] Andrew W. Senior, Thomas Edlich, Francisco J. H. Heras, Lei M. Zhang, Oscar Higgott, James S. Spencer, Taylor Applebaum, Sam Blackwell, Justin Ledford, Akvilė Žemgulytė, Augustin Žídek, Noah Shutty, Andrew Cowie, Yin Li, George Holland, Peter Brooks, Charlie Beattie, Michael Newman, Alex Davies, Cody Jones, Sergio Boixo, Hartmut Neven, Pushmeet Kohli, and Johannes Bausch, "A scalable and real-time neural decoder for topological quantum codes", arXiv:2512.07737, (2025). [2] Michael E. Beverland, Malcolm Carroll, Andrew W. Cross, and Theodore J. Yoder, "Fail fast: techniques to probe rare events in quantum error correction", arXiv:2511.15177, (2025). [3] Xiao Xiao, Dominik Hangleiter, Dolev Bluvstein, Mikhail D. Lukin, and Michael J. Gullans, "In Situ Benchmarking of Fault-Tolerant Quantum Circuits: Clifford Circuits", PRX Quantum 7 3, 033055 (2026). [4] John Zhuoyang Ye and Jens Palsberg, "Scalable testing of quantum error correction", arXiv:2602.04921, (2026). [5] Mark Myers, Mariesa H. Teo, Rajesh Mishra, Jing Hao Chai, and Hui Khoon Ng, "Simulating general noise nearly as cheaply as Pauli noise", arXiv:2512.07304, (2025). [6] Abtin Molavi, Feras Saad, and Aws Albarghouthi, "Analyzing Decoders for Quantum Error Correction", arXiv:2603.20127, (2026). [7] Ge Yan, Shanchuan Li, Pengyue Ma, Qixin Zhang, Pingchuan Ma, Jianping Wang, Min-Hsiu Hsieh, and Yuxuan Du, "OmniQEC: discovering practical quantum error-correcting codes by an AI scientist", arXiv:2607.25865, (2026). [8] Sean R. Garner, Nathan M. Myers, Meng Wang, Samuel Stein, Chenxu Liu, and Ang Li, "Simulation of thermal-relaxation noise for quantum error correction", Physical Review Research 8 2, 023134 (2026). [9] Sean R. Garner, Nathan M. Myers, Meng Wang, Samuel Stein, Chenxu Liu, and Ang Li, "Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction", arXiv:2512.09189, (2025). [10] Matthias C. Löbl, Love A. M. Pettersson, Jan Dragašević, Susan X. Chen, and Oliver A. D. Sandberg, "The subthreshold issue of fusion-based quantum computing", arXiv:2606.28490, (2026). [11] Wang Fang, Huazhe Lou, and Riling Li, "SymFT: Universal Fault-Tolerant Quantum Circuit Simulation via Symbolic Clifford--Pauli Frames and Stabilizer Coordinates", arXiv:2607.28600, (2026). [12] Michael Mullan, Matthew Weippert, and Winton Brown, "Improved Methods for Determining Quantum Error Correcting Code Performance and Fault Tolerance", arXiv:2607.27153, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-10-16 00:11:30). The list may be incomplete as not all publishers provide suitable and complete citation data.On Crossref's cited-by service no data on citing works was found (last attempt 2026-10-16 00:11:28).This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe describe a practical approach for accessing the logical failure rates of quantum error-correcting (QEC) circuits under low physical (component) failure rate regimes.

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Rare Event Simulation of Quantum Error-Correcting Circuits

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