Suppressing quantum errors by scaling a surface code logical qubit
Authors:   Google Quantum AI, Acharya Rajeev , Aleiner Igor , Allen Richard , Andersen Trond I. , Ansmann Markus , Arute Frank , Arya Kunal , Asfaw Abraham , Atalaya Juan , Babbush Ryan , Bacon Dave , Bardin Joseph C. , Basso Joao , Bengtsson Andreas , Boixo Sergio , Bortoli Gina , Bourassa Alexandre , Bovaird Jenna , Brill Leon , Broughton Michael , Buckley Bob B. , Buell David A. , Burger Tim , Burkett Brian , Bushnell Nicholas , Chen Yu , Chen Zijun , Chiaro Ben , Cogan Josh , Collins Roberto , Conner Paul , Courtney William , Crook Alexander L. , Curtin Ben , Debroy Dripto M. , Del Toro Barba Alexander , Demura Sean , Dunsworth Andrew , Eppens Daniel , Erickson Catherine , Faoro Lara , Farhi Edward , Fatemi Reza , Flores Burgos Leslie , Forati Ebrahim , Fowler Austin G. , Foxen Brooks , Giang William , Gidney Craig , Gilboa Dar , Giustina Marissa , Grajales Dau Alejandro , Gross Jonathan A. , Habegger Steve , Hamilton Michael C. , Harrigan Matthew P. , Harrington Sean D. , Higgott Oscar , Hilton Jeremy , Hoffmann Markus , Hong Sabrina , Huang Trent , Huff Ashley , Huggins William J. , Ioffe Lev B. , Isakov Sergei V. , Iveland Justin , Jeffrey Evan , Jiang Zhang , Jones Cody , Juhas Pavol , Kafri Dvir , Kechedzhi Kostyantyn , Kelly Julian , Khattar Tanuj , Khezri Mostafa , Kieferová Mária , Kim Seon , Kitaev Alexei , Klimov Paul V. , Klots Andrey R. , Korotkov Alexander N. , Kostritsa Fedor , Kreikebaum John Mark , Landhuis David , Laptev Pavel , Lau Kim-Ming , Laws Lily , Lee Joonho , Lee Kenny , Lester Brian J. , Lill Alexander , Liu Wayne , Locharla Aditya , Lucero Erik , Malone Fionn D. , Marshall Jeffrey , Martin Orion , McClean Jarrod R. , McCourt Trevor , McEwen Matt , Megrant Anthony , Meurer Costa Bernardo , Mi Xiao , Miao Kevin C. , Mohseni Masoud , Montazeri Shirin , Morvan Alexis , Mount Emily , Mruczkiewicz Wojciech , Naaman Ofer , Neeley Matthew , Neill Charles , Nersisyan Ani , Neven Hartmut , Newman Michael , Ng Jiun How , Nguyen Anthony , Nguyen Murray , Niu Murphy Yuezhen , O’Brien Thomas E. , Opremcak Alex , Platt John , Petukhov Andre , Potter Rebecca , Pryadko Leonid P. , Quintana Chris , Roushan Pedram , Rubin Nicholas C. , Saei Negar , Sank Daniel , Sankaragomathi Kannan , Satzinger Kevin J. , Schurkus Henry F. , Schuster Christopher , Shearn Michael J. , Shorter Aaron , Shvarts Vladimir , Skruzny Jindra , Smelyanskiy Vadim , Smith W. Clarke , Sterling George , Strain Doug , Szalay Marco , Torres Alfredo , Vidal Guifre , Villalonga Benjamin , Vollgraff Heidweiller Catherine , White Theodore , Xing Cheng , Yao Z. Jamie , Yeh Ping , Yoo Juhwan , Young Grayson , Zalcman Adam , Zhang Yaxing , Zhu Ningfeng 
Published: February 2023

Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which 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 for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10−6 logical error per cycle floor set by a single high-energy event (1.6 × 10−7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.