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 Rodríguez, Neha Mahuli, J. Rose, John Clai Owens, Harry Levine, Emma Rosenfeld, Philip Reinhold, Lorenzo Moncelsi, Joshua Ari Alcid, Nasser Alidoust, Patricio Arrangoiz-Arriola, James W. Barnett, Przemysław Bienias, Hugh A. Carson, Cliff Chen, Li Chen, Harutiun Chinkezian, Eric M. Chisholm, Ming-Han Chou, Aashish A. Clerk, Andrew J. Clifford, R. Cosmic, Ana Valdés Curiel, Erik Davis, Laura DeLorenzo, John D'Ewart, Art Diky, Nathan D’Souza, Philipp T. Dumitrescu, Shmuel Eisenmann, E. S. Elkhouly, Glen Evenbly, Michael Fang, Yawen Fang, Matthew J. Fling, W C Fon, Gabriel García, Alexey V. Gorshkov, Julia A. Grant, Mason Gray, Sebastian Grimberg, Arne L. Grimsmo, Arbel Haim, Justin Hand, He Yuan, Mike Hernández, David Hover, Jimmy S. C. Hung, Matthew A. Hunt, Joe Iverson, Ignace Jarrige, Jean-Christophe Jaskula, Liang Jiang, Mahmoud Kalaee, R. B. Karabalin, Peter J. Karalekas, Andrew J. Keller, Amirhossein Khalajhedayati, Aleksander Kubica, Hanho Lee, Catherine Leroux, Simon Lieu, Victoria Ly, Keven Villegas Madrigal, Guillaume Marcaud, Gavin McCabe, Cody Miles, Ashley Milsted, Joaquín Minguzzi, Anurag Mishra, Biswaroop Mukherjee, Mahdi Naghiloo, Eric Oblepias, Gerson Ortuno, Jason Pagdilao, Nicola Pancotti, Ashley Panduro, JP Paquette, Minje Park, G. A. Peairs, David Perello, Eric C. Peterson, Sophia Ponte, John Preskill, Haifeng Qiao, Gil Refael, Rachel Resnick, Alex Retzker, Omar A. Reyna, M. C. Runyan, Colm A. Ryan
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. Bosonic qubits can be engineered to feature intrinsic protection against certain kinds of errors, which makes quantum error correction across many bosonic qubits possible with less overhead.