Suppressing quantum errors by scaling a surface code logical qubit
Rajeev Acharya, Igor Aleiner, Richard Allen
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Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Ben Chiaro, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Dripto M. Debroy, Alexander Del Toro Barba, Sean Demura, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Lara Faoro, Edward Farhi, Reza Fatemi, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Michael C. Hamilton, Matthew P. Harrigan, Sean D. Harrington, Oscar Higgott, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Pavol Juhas, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, Paul V. Klimov, Andrey R. Klots, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Lily Laws, Joonho Lee, Kenny Lee, Brian J. Lester, Alexander Lill, Wayne Liu, Aditya Locharla, Erik Lucero, Fionn D. Malone, Jeffrey Marshall, Orion Martin, Jarrod R. McClean, Trevor Mccourt, Matt McEwen, Anthony Megrant, Bernardo Meurer Costa, Xiao Mi, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Alexis Morvan, Emily Mount, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Ani Nersisyan, Hartmut Neven, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Murphy Yuezhen Niu, Thomas E. O'Brien, Alex Opremcak, John Platt, Andre Petukhov, Rebecca Potter, Leonid P. Pryadko, Chris Quintana, Pedram Roushan, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Vladimir Shvarts, Jindra Skruzny, Vadim Smelyanskiy, W. Clarke Smith, George Sterling, Doug Strain, Marco Szalay, Alfredo Torres, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Theodore White, Cheng Xing, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.
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> [0.1% gate error rate] is still wildly out of reach
This is false. When Fowler et al assumed 0.1% gate error rates would be reached for his estimates in 2012 [0], that was ostentatious. Now it's frankly a bit overly conservative. All the big architectures are approaching or surpassing 0.1% gate error rates.
From 2022 to 2024, the google team improved mean two qubit gate error rate from 0.6% [1] to 0.4% [2]. Quantinuum's Helios has a two qubit gate error rate of 0.08% [3]. IBM has Heron processors available on their cloud service with two qubit gate error rates ranging from 0.2% to 0.7% [4]. Neutral atom machines have demonstrated 0.5% gate error rates [5].
[0]:…
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https://arxiv.org/abs/1208.0928
[1]: fig 1c of https://arxiv.org/pdf/2207.06431
[2]: fig 1b of https://arxiv.org/pdf/2408.13687
[3]: https://arxiv.org/abs/2511.05465
[4]: https://quantum.cloud.ibm.com/computers?processorType=Heron (numbers may vary as the website is not static)
[5]: https://arxiv.org/abs/2304.05420
Yes, for some definition of logical qubit.
One of the first example is the experiment of Egan et al where they demonstrated a fault-tolerant QEC measurement using 13 physical qubits. https://arxiv.org/abs/2009.11482 They show improvements in the logical performance on the codes, but it is still a pretty small improvement (factor of 2).
Another example is the experiment we performed at Google https://arxiv.org/abs/2207.06431 where we used superconducting qubits. In that experiment we showed that we were able to go from a small code to a slightly larger code and that the error got "slightly better" as you scaled things up.
Other groups have also demo-ed small scale logical…
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qubits. Notable ones include those done by Quantinuum (trapped ion qubits) and ETH Zurich (superconducting qubits). But all of these show very small improvements in error rates. To truly build "logical" qubits one would hope to get suppression of errors by factors of like 100-1000, and no one is really close to that right now.
You don't need to pay $32. Just click on the article link from the summary page. It loads just fine.
The part to click is this link at the top of the summary page:
This is a summary of: Google Quantum AI. Suppressing quantum errors by
scaling a surface code logical qubit. Nature 614, 676–681 (2023).
That points to: https://www.nature.com/articles/s41586-022-05434-1
The technique developed seems to work for a larger number of qbits (49). With the current systems, increasing the number of qbits does not lead to an increase in computational performance as the extra qbits introduce more noise than can be compensated by error correction codes.
Here, the authors show a small but significant improvement by increasing the number of qbits thanks to their improved ECC.
The paper: https://www.nature.com/articles/s41586-022-05434-1
More or less, we're just before the finish line. About 20% lower noise and we'll be there. For every little bit past that, the overhead gets reduced immensely
https://arxiv.org/abs/2207.06431
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