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

description: Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ 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 analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.