Exponential suppression of bit or phase errors with cyclic error correction
Authors:   Google Quantum AI, Chen Zijun , Satzinger Kevin J. , Atalaya Juan , Korotkov Alexander N. , Dunsworth Andrew , Sank Daniel , Quintana Chris , McEwen Matt , Barends Rami , Klimov Paul V. , Hong Sabrina , Jones Cody , Petukhov Andre , Kafri Dvir , Demura Sean , Burkett Brian , Gidney Craig , Fowler Austin G. , Paler Alexandru , Putterman Harald , Aleiner Igor , Arute Frank , Arya Kunal , Babbush Ryan , Bardin Joseph C. , Bengtsson Andreas , Bourassa Alexandre , Broughton Michael , Buckley Bob B. , Buell David A. , Bushnell Nicholas , Chiaro Benjamin , Collins Roberto , Courtney William , Derk Alan R. , Eppens Daniel , Erickson Catherine , Farhi Edward , Foxen Brooks , Giustina Marissa , Greene Ami , Gross Jonathan A. , Harrigan Matthew P. , Harrington Sean D. , Hilton Jeremy , Ho Alan , Huang Trent , Huggins William J. , Ioffe L. B. , Isakov Sergei V. , Jeffrey Evan , Jiang Zhang , Kechedzhi Kostyantyn , Kim Seon , Kitaev Alexei , Kostritsa Fedor , Landhuis David , Laptev Pavel , Lucero Erik , Martin Orion , McClean Jarrod R. , McCourt Trevor , Mi Xiao , Miao Kevin C. , Mohseni Masoud , Montazeri Shirin , Mruczkiewicz Wojciech , Mutus Josh , Naaman Ofer , Neeley Matthew , Neill Charles , Newman Michael , Niu Murphy Yuezhen , O’Brien Thomas E. , Opremcak Alex , Ostby Eric , Pató Bálint , Redd Nicholas , Roushan Pedram , Rubin Nicholas C. , Shvarts Vladimir , Strain Doug , Szalay Marco , Trevithick Matthew D. , Villalonga Benjamin , White Theodore , Yao Z. Jamie , Yeh Ping , Yoo Juhwan , Zalcman Adam , Neven Hartmut , Boixo Sergio , Smelyanskiy Vadim , Chen Yu , Megrant Anthony , Kelly Julian 
Published: July 2021

Realizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.