Hardware-efficient quantum error correction via concatenated bosonic qubits

Creators: Putterman, Harald¹; Noh, Kyungjoo¹; Hann, Connor T.¹; MacCabe, Gregory S.¹; Aghaeimeibodi, Shahriar¹; Patel, Rishi N.¹; Lee, Menyoung¹; Jones, William M.¹; Moradinejad, Hesam¹; Rodriguez, Roberto¹; Mahuli, Neha¹; Rose, Jefferson¹; Owens, John Clai¹; Levine, Harry¹; Rosenfeld, Emma^{1, 2}; Reinhold, Philip¹; Moncelsi, Lorenzo¹; Alcid, Joshua Ari¹; Alidoust, Nasser¹; Arrangoiz-Arriola, Patricio¹; Barnett, James¹; Bienias, Przemyslaw¹; Carson, Hugh A.¹; Chen, Cliff¹; Chen, Li¹; Chinkezian, Harutiun¹; Chisholm, Eric M.¹; Chou, Ming-Han¹; Clerk, Aashish^{1, 3}; Clifford, Andrew¹; Cosmic, R.¹; Curiel, Ana Valdes¹; Davis, Erik¹; DeLorenzo, Laura^{1, 2}; D'Ewart, J. Mitchell¹; Diky, Art¹; D'Souza, Nathan¹; Dumitrescu, Philipp T.¹; Eisenmann, Shmuel¹; Elkhouly, Essam¹; Evenbly, Glen¹; Fang, Michael T.¹; Fang, Yawen¹; Fling, Matthew J.¹; Fon, Warren¹; Garcia, Gabriel¹; Gorshkov, Alexey V.¹; Grant, Julia A.¹; Gray, Mason J.¹; Grimberg, Sebastian¹; Grimsmo, Arne L.¹; Haim, Arbel¹; Hand, Justin¹; He, Yuan¹; Hernandez, Mike¹; Hover, David¹; Hung, Jimmy S. C.¹; Hunt, Matthew¹; Iverson, Joe¹; Jarrige, Ignace¹; Jaskula, Jean-Christophe¹; Jiang, Liang^{1, 3}; Kalaee, Mahmoud¹; Karabalin, Rassul¹; Karalekas, Peter J.¹; Keller, Andrew J.¹; Khalajhedayati, Amirhossein¹; Kubica, Aleksander^{1, 4}; Lee, Hanho¹; Leroux, Catherine¹; Lieu, Simon¹; Ly, Victor¹; Madrigal, Keven Villegas¹; Marcaud, Guillaume¹; McCabe, Gavin¹; Miles, Cody¹; Milsted, Ashley¹; Minguzzi, Joaquin¹; Mishra, Anurag¹; Mukherjee, Biswaroop¹; Naghiloo, Mahdi¹; Oblepias, Eric¹; Ortuno, Gerson¹; Pagdilao, Jason¹; Pancotti, Nicola¹; Panduro, Ashley¹; Paquette, JP¹; Park, Minje¹; Peairs, Gregory A.¹; Perello, David¹; Peterson, Eric C.¹; Ponte, Sophia¹; Preskill, John^{1, 5}; Qiao, Johnson¹; Refael, Gil^{1, 5}; Resnick, Rachel^{1, 2}; Retzker, Alex^{1, 6}; Reyna, Omar A.¹; Runyan, Marc¹; Ryan, Colm A.¹; Sahmoud, Abdulrahman¹; Sanchez, Ernesto¹; Sanil, Rohan¹; Sankar, Krishanu¹; Sato, Yuki¹; Scaffidi, Thomas^{1, 7}; Siavoshi, Salome¹; Sivarajah, Prasahnt¹; Skogland, Trenton¹; Su, Chun-Ju¹; Swenson, Loren J.¹; Teo, Stephanie M.¹; Tomada, Astrid¹; Torlai, Giacomo¹; Wollack, E. Alex¹; Ye, Yufeng¹; Zerrudo, Jessica A.¹; Zhang, Kailing¹; Brandão, Fernando G. S. L.^{1, 5}; Matheny, Matthew H.¹; Painter, Oskar^{1, 5}

1. Amazon (United States)
2. Google (United States)
3. University of Chicago
4. Yale University
5. California Institute of Technology
6. Hebrew University of Jerusalem
7. University of California, Irvine

Abstract

To solve problems of practical importance, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches. Here, using a superconducting quantum circuit, 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 flips. 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.

Copyright and License

© The Author(s) 2025. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Acknowledgement

We thank the staff from across the AWS Center for Quantum Computing that enabled this project. We also thank F. Harrison, H. Atwater, D. Tirrell and T. Rosenbaum at Caltech and S. Severini, B. Vass, J. Hamilton, N. Bshara and P. DeSantis at AWS for their involvement and support of the research activities at the AWS Center for Quantum Computing.

Data Availability

Data for the logical qubit memory experiment can be found at Zenodo (https://doi.org/10.5281/zenodo.14257632; ref. ⁶⁶).

Supplemental Material

Supplementary Information

This file contains Supplementary Sections A–K, including Supplementary Figs. 1–41 and Supplementary References – see Contents page for details.

Peer Review File

Files

s41586-025-08642-7.pdf

Files (28.7 MB)

Name	Size	Download all
s41586-025-08642-7.pdf md5:c95db72c453659aa2fa7dab089075c9d	3.4 MB	Preview Download
41586_2025_8642_MOESM1_ESM.pdf md5:d8bc8e839b978873ff7d94cb315bb625	25.3 MB	Preview Download

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes