Hardware-efficient quantum error correction via concatenated bosonic qubits

Harald Putterman (), Kyungjoo Noh, Connor T. Hann, Gregory S. MacCabe, Shahriar Aghaeimeibodi, Rishi N. Patel, Menyoung Lee, William M. Jones, Hesam Moradinejad, Roberto Rodriguez, Neha Mahuli, Jefferson Rose, John Clai Owens, Harry Levine, Emma Rosenfeld, Philip Reinhold, Lorenzo Moncelsi, Joshua Ari Alcid, Nasser Alidoust, Patricio Arrangoiz-Arriola, James Barnett, Przemyslaw Bienias, Hugh A. Carson, Cliff Chen, Li Chen, Harutiun Chinkezian, Eric M. Chisholm, Ming-Han Chou, Aashish Clerk, Andrew Clifford, R. Cosmic, Ana Valdes Curiel, Erik Davis, Laura DeLorenzo, J. Mitchell D’Ewart, Art Diky, Nathan D’Souza, Philipp T. Dumitrescu, Shmuel Eisenmann, Essam Elkhouly, Glen Evenbly, Michael T. Fang, Yawen Fang, Matthew J. Fling, Warren Fon, Gabriel Garcia, Alexey V. Gorshkov, Julia A. Grant, Mason J. Gray, Sebastian Grimberg, Arne L. Grimsmo, Arbel Haim, Justin Hand, Yuan He, Mike Hernandez, David Hover, Jimmy S. C. Hung, Matthew Hunt, Joe Iverson, Ignace Jarrige, Jean-Christophe Jaskula, Liang Jiang, Mahmoud Kalaee, Rassul Karabalin, Peter J. Karalekas, Andrew J. Keller, Amirhossein Khalajhedayati, Aleksander Kubica, Hanho Lee, Catherine Leroux, Simon Lieu, Victor Ly, Keven Villegas Madrigal, Guillaume Marcaud, Gavin McCabe, Cody Miles, Ashley Milsted, Joaquin Minguzzi, Anurag Mishra, Biswaroop Mukherjee, Mahdi Naghiloo, Eric Oblepias, Gerson Ortuno, Jason Pagdilao, Nicola Pancotti, Ashley Panduro, Paquette Jp, Minje Park, Gregory A. Peairs, David Perello, Eric C. Peterson, Sophia Ponte, John Preskill, Johnson Qiao, Gil Refael, Rachel Resnick, Alex Retzker, Omar A. Reyna, Marc Runyan, Colm A. Ryan, Abdulrahman Sahmoud, Ernesto Sanchez, Rohan Sanil, Krishanu Sankar, Yuki Sato, Thomas Scaffidi, Salome Siavoshi, Prasahnt Sivarajah, Trenton Skogland, Chun-Ju Su, Loren J. Swenson, Stephanie M. Teo, Astrid Tomada, Giacomo Torlai, E. Alex Wollack, Yufeng Ye, Jessica A. Zerrudo, Kailing Zhang, Fernando G. S. L. Brandão, Matthew H. Matheny and Oskar Painter ()
Additional contact information
Harald Putterman: AWS Center for Quantum Computing
Kyungjoo Noh: AWS Center for Quantum Computing
Connor T. Hann: AWS Center for Quantum Computing
Gregory S. MacCabe: AWS Center for Quantum Computing
Shahriar Aghaeimeibodi: AWS Center for Quantum Computing
Rishi N. Patel: AWS Center for Quantum Computing
Menyoung Lee: AWS Center for Quantum Computing
William M. Jones: AWS Center for Quantum Computing
Hesam Moradinejad: AWS Center for Quantum Computing
Roberto Rodriguez: AWS Center for Quantum Computing
Neha Mahuli: AWS Center for Quantum Computing
Jefferson Rose: AWS Center for Quantum Computing
John Clai Owens: AWS Center for Quantum Computing
Harry Levine: AWS Center for Quantum Computing
Emma Rosenfeld: AWS Center for Quantum Computing
Philip Reinhold: AWS Center for Quantum Computing
Lorenzo Moncelsi: AWS Center for Quantum Computing
Joshua Ari Alcid: AWS Center for Quantum Computing
Nasser Alidoust: AWS Center for Quantum Computing
Patricio Arrangoiz-Arriola: AWS Center for Quantum Computing
James Barnett: AWS Center for Quantum Computing
Przemyslaw Bienias: AWS Center for Quantum Computing
Hugh A. Carson: AWS Center for Quantum Computing
Cliff Chen: AWS Center for Quantum Computing
Li Chen: AWS Center for Quantum Computing
Harutiun Chinkezian: AWS Center for Quantum Computing
Eric M. Chisholm: AWS Center for Quantum Computing
Ming-Han Chou: AWS Center for Quantum Computing
Aashish Clerk: AWS Center for Quantum Computing
Andrew Clifford: AWS Center for Quantum Computing
R. Cosmic: AWS Center for Quantum Computing
Ana Valdes Curiel: AWS Center for Quantum Computing
Erik Davis: AWS Center for Quantum Computing
Laura DeLorenzo: AWS Center for Quantum Computing
J. Mitchell D’Ewart: AWS Center for Quantum Computing
Art Diky: AWS Center for Quantum Computing
Nathan D’Souza: AWS Center for Quantum Computing
Philipp T. Dumitrescu: AWS Center for Quantum Computing
Shmuel Eisenmann: AWS Center for Quantum Computing
Essam Elkhouly: AWS Center for Quantum Computing
Glen Evenbly: AWS Center for Quantum Computing
Michael T. Fang: AWS Center for Quantum Computing
Yawen Fang: AWS Center for Quantum Computing
Matthew J. Fling: AWS Center for Quantum Computing
Warren Fon: AWS Center for Quantum Computing
Gabriel Garcia: AWS Center for Quantum Computing
Alexey V. Gorshkov: AWS Center for Quantum Computing
Julia A. Grant: AWS Center for Quantum Computing
Mason J. Gray: AWS Center for Quantum Computing
Sebastian Grimberg: AWS Center for Quantum Computing
Arne L. Grimsmo: AWS Center for Quantum Computing
Arbel Haim: AWS Center for Quantum Computing
Justin Hand: AWS Center for Quantum Computing
Yuan He: AWS Center for Quantum Computing
Mike Hernandez: AWS Center for Quantum Computing
David Hover: AWS Center for Quantum Computing
Jimmy S. C. Hung: AWS Center for Quantum Computing
Matthew Hunt: AWS Center for Quantum Computing
Joe Iverson: AWS Center for Quantum Computing
Ignace Jarrige: AWS Center for Quantum Computing
Jean-Christophe Jaskula: AWS Center for Quantum Computing
Liang Jiang: AWS Center for Quantum Computing
Mahmoud Kalaee: AWS Center for Quantum Computing
Rassul Karabalin: AWS Center for Quantum Computing
Peter J. Karalekas: AWS Center for Quantum Computing
Andrew J. Keller: AWS Center for Quantum Computing
Amirhossein Khalajhedayati: AWS Center for Quantum Computing
Aleksander Kubica: AWS Center for Quantum Computing
Hanho Lee: AWS Center for Quantum Computing
Catherine Leroux: AWS Center for Quantum Computing
Simon Lieu: AWS Center for Quantum Computing
Victor Ly: AWS Center for Quantum Computing
Keven Villegas Madrigal: AWS Center for Quantum Computing
Guillaume Marcaud: AWS Center for Quantum Computing
Gavin McCabe: AWS Center for Quantum Computing
Cody Miles: AWS Center for Quantum Computing
Ashley Milsted: AWS Center for Quantum Computing
Joaquin Minguzzi: AWS Center for Quantum Computing
Anurag Mishra: AWS Center for Quantum Computing
Biswaroop Mukherjee: AWS Center for Quantum Computing
Mahdi Naghiloo: AWS Center for Quantum Computing
Eric Oblepias: AWS Center for Quantum Computing
Gerson Ortuno: AWS Center for Quantum Computing
Jason Pagdilao: AWS Center for Quantum Computing
Nicola Pancotti: AWS Center for Quantum Computing
Ashley Panduro: AWS Center for Quantum Computing
Paquette Jp: AWS Center for Quantum Computing
Minje Park: AWS Center for Quantum Computing
Gregory A. Peairs: AWS Center for Quantum Computing
David Perello: AWS Center for Quantum Computing
Eric C. Peterson: AWS Center for Quantum Computing
Sophia Ponte: AWS Center for Quantum Computing
John Preskill: AWS Center for Quantum Computing
Johnson Qiao: AWS Center for Quantum Computing
Gil Refael: AWS Center for Quantum Computing
Rachel Resnick: AWS Center for Quantum Computing
Alex Retzker: AWS Center for Quantum Computing
Omar A. Reyna: AWS Center for Quantum Computing
Marc Runyan: AWS Center for Quantum Computing
Colm A. Ryan: AWS Center for Quantum Computing
Abdulrahman Sahmoud: AWS Center for Quantum Computing
Ernesto Sanchez: AWS Center for Quantum Computing
Rohan Sanil: AWS Center for Quantum Computing
Krishanu Sankar: AWS Center for Quantum Computing
Yuki Sato: AWS Center for Quantum Computing
Thomas Scaffidi: AWS Center for Quantum Computing
Salome Siavoshi: AWS Center for Quantum Computing
Prasahnt Sivarajah: AWS Center for Quantum Computing
Trenton Skogland: AWS Center for Quantum Computing
Chun-Ju Su: AWS Center for Quantum Computing
Loren J. Swenson: AWS Center for Quantum Computing
Stephanie M. Teo: AWS Center for Quantum Computing
Astrid Tomada: AWS Center for Quantum Computing
Giacomo Torlai: AWS Center for Quantum Computing
E. Alex Wollack: AWS Center for Quantum Computing
Yufeng Ye: AWS Center for Quantum Computing
Jessica A. Zerrudo: AWS Center for Quantum Computing
Kailing Zhang: AWS Center for Quantum Computing
Fernando G. S. L. Brandão: AWS Center for Quantum Computing
Matthew H. Matheny: AWS Center for Quantum Computing
Oskar Painter: AWS Center for Quantum Computing

Nature, 2025, vol. 638, issue 8052, 927-934

Abstract: Abstract To solve problems of practical importance1,2, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits3–5. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches6–18. Here, using a superconducting quantum circuit19, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance d = 5 (ref. 10). A stabilizing circuit passively protects cat qubits against bit flips20–24. The repetition code, using ancilla transmons for syndrome measurement, corrects cat qubit phase flips. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below the threshold. The logical bit-flip error is suppressed with increasing cat qubit mean photon number, enabled by our realization of a cat-transmon noise-biased CX gate. The minimum measured logical error per cycle is on average 1.75(2)% for the distance-3 code sections, and 1.65(3)% for the distance-5 code. Despite the increased number of fault locations of the distance-5 code, the high degree of noise bias preserved during error correction enables comparable performance. These results, where the intrinsic error suppression of the bosonic encodings enables us to use a hardware-efficient outer error-correcting code, indicate that concatenated bosonic codes can be a compelling model for reaching fault-tolerant quantum computation.

Date: 2025
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DOI: 10.1038/s41586-025-08642-7

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