Hardware-efficient quantum error correction via concatenated bosonic qubits

To solve problems of practical importance<sup>1,2</sup>, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits<sup>3-5</sup>. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches<sup>6-18</sup>. Here, using a superconducting quantum circuit<sup>19</sup>, 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. <sup>10</sup>). A stabilizing circuit passively protects cat qubits against bit flips<sup>20-24</sup>. 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.

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Publication Details

Journal
Nature
Published
2025-02-26
DOI
https://doi.org/10.1038/s41586-025-08642-7
Citations
74
Primary Topic
Quantum Computing Algorithms and Architecture
Type
article
Field-Weighted Citation Impact
183.59

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article

Hardware-efficient quantum error correction via concatenated bosonic qubits

Alexey Vyacheslavovich Gorshkov, Jana Marie Iverson, Harry Levine, James W. Barnett et al.
74 citations
Nature
Quantum Computing Algorithms and Architecture
183.59
article

Hardware-efficient quantum error correction via concatenated bosonic qubits

Alexey Vyacheslavovich Gorshkov, Jana Marie Iverson, Harry Levine, James W. Barnett, W C Fon, Salvatore Ponte, Prasahnt Sivarajah, Peter J. Karalekas, Mason Gray, Thomas Scaffidi, Eric M. Chisholm, Marco A. Panduro, Stephanie M. Teo, Aleksander Kubica, Yufeng Ye, Menyoung Lee, Kyungjoo Noh, Mahdi Naghiloo, Ana Valdés Curiel, Biswaroop Mukherjee, R. B. Karabalin, J. L. Hand, Arbel Haim, Yawen Fang, Haifeng Qiao, John D'Ewart, Ming-Han Chou, Krishanu Sankar, Guillaume Marcaud, Harald Putterman, Amirhossein Khalajhedayati, Fernando G. S. L. Brandão, Patricio Arrangoiz-Arriola, Philipp T. Dumitrescu, Ernesto Sánchez, Philip Reinhold, Emma Rosenfeld, Matthew A. Hunt, Arne L. Grimsmo, Laura DeLorenzo, Chris Miles, L. J. Swenson, Lorenzo Moncelsi, Nasser Alidoust, JP Paquette, Ashley Milsted, Jimmy S. C. Hung, David Hover, David Perello, Erik Davis, Kailing Zhang, Alex Retzker, Connor T. Hann, Catherine Leroux, John Clai Owens, Hesam Moradinejad, Matthew H. Matheny, Aashish A. Clerk, Michael Fang, John P. Preskill, He Yuan, Joaquín Minguzzi, Shahriar Aghaeimeibodi, Glen Evenbly, G. A. Peairs, Noel D’Souza, Yūki Sato, William M. Jones, Przemysław Bienias, Gregory S. MacCabe, Hanho Lee, Gabriel García, Mahmoud Kalaee, Gil Refael, Jean-Christophe Jaskula, R. Cosmic, Hugh A. Carson, Liang Jiang, M. C. Runyan, Nicola Pancotti, Sebastian Grimberg, Rishi N. Patel, Rachel Resnick, E. S. Elkhouly, Giacomo Torlai, Art Diky, Colm A. Ryan, Andrew J. Keller, Mike Hernández, Minje Park, Anurag Mishra, Rohan Sanil, Trenton Skogland, Astrid Tomada, Joshua Ari Alcid, Harutiun Chinkezian, Matthew J. Fling, Neha Mahuli, Eric Oblepias, Gerson Ortuno, Jason Pagdilao, Omar A. Reyna, Abdulrahman Sahmoud, Salome Siavoshi, Li Chen, Eric C. Peterson, James P. Grant, Victoria Ly, E. Alex Wollack, Gavin McCabe, Roberto Rodríguez, Oskar Painter, Chun‐Ju Su, Andrew J. Clifford, Simon Lieu, Ignace Jarrige, J. Rose, Jessica A. Zerrudo, Shmuel Eisenmann, Keven Villegas Madrigal, Cliff Chen
article en
74 citations

Abstract

To solve problems of practical importance<sup>1,2</sup>, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits<sup>3-5</sup>. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches<sup>6-18</sup>. Here, using a superconducting quantum circuit<sup>19</sup>, 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. <sup>10</sup>). A stabilizing circuit passively protects cat qubits against bit flips<sup>20-24</sup>. 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.

NatureVol. 638(8052)
California Institute of Technology (US), Google (United States) (US), Amazon (United States) (US), Hebrew University of Jerusalem (IL), University of California, Irvine (US), Yale University (US), University of Chicago (US)
California Institute of Technology
Affordable and clean energy
Openalex Percentile: Top 0%
Quantum Computing Algorithms and Architecture
183.59
DOIOpen Access PDFOpenAlex
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