Hardware-efficient quantum error correction via concatenated bosonic qubits
Creators: name: Putterman, Harald
name: Noh, Kyungjoo
name: Hann, Connor T.
name: MacCabe, Gregory S.
name: Aghaeimeibodi, Shahriar
name: Patel, Rishi N.
name: Lee, Menyoung
name: Jones, William M.
name: Moradinejad, Hesam
name: Rodriguez, Roberto
name: Mahuli, Neha
name: Rose, Jefferson
name: Owens, John Clai
name: Levine, Harry
name: Rosenfeld, Emma
name: Reinhold, Philip
name: Moncelsi, Lorenzo
name: Alcid, Joshua Ari
name: Alidoust, Nasser
name: Arrangoiz-Arriola, Patricio
name: Barnett, James
name: Bienias, Przemyslaw
name: Carson, Hugh A.
name: Chen, Cliff
name: Chen, Li
name: Chinkezian, Harutiun
name: Chisholm, Eric M.
name: Chou, Ming-Han
name: Clerk, Aashish
name: Clifford, Andrew
name: Cosmic, R.
name: Curiel, Ana Valdes
name: Davis, Erik
name: DeLorenzo, Laura
name: D'Ewart, J. Mitchell
name: Diky, Art
name: D'Souza, Nathan
name: Dumitrescu, Philipp T.
name: Eisenmann, Shmuel
name: Elkhouly, Essam
name: Evenbly, Glen
name: Fang, Michael T.
name: Fang, Yawen
name: Fling, Matthew J.
name: Fon, Warren
name: Garcia, Gabriel
name: Gorshkov, Alexey V.
name: Grant, Julia A.
name: Gray, Mason J.
name: Grimberg, Sebastian
name: Grimsmo, Arne L.
name: Haim, Arbel
name: Hand, Justin
name: He, Yuan
name: Hernandez, Mike
name: Hover, David
name: Hung, Jimmy S. C.
name: Hunt, Matthew
name: Iverson, Joe
name: Jarrige, Ignace
name: Jaskula, Jean-Christophe
name: Jiang, Liang
name: Kalaee, Mahmoud
name: Karabalin, Rassul
name: Karalekas, Peter J.
name: Keller, Andrew J.
name: Khalajhedayati, Amirhossein
name: Kubica, Aleksander
name: Lee, Hanho
name: Leroux, Catherine
name: Lieu, Simon
name: Ly, Victor
name: Madrigal, Keven Villegas
name: Marcaud, Guillaume
name: McCabe, Gavin
name: Miles, Cody
name: Milsted, Ashley
name: Minguzzi, Joaquin
name: Mishra, Anurag
name: Mukherjee, Biswaroop
name: Naghiloo, Mahdi
name: Oblepias, Eric
name: Ortuno, Gerson
name: Pagdilao, Jason
name: Pancotti, Nicola
name: Panduro, Ashley
name: Paquette, JP
name: Park, Minje
name: Peairs, Gregory A.
name: Perello, David
name: Peterson, Eric C.
name: Ponte, Sophia
name: Preskill, John
name: Qiao, Johnson
name: Refael, Gil
name: Resnick, Rachel
name: Retzker, Alex
name: Reyna, Omar A.
name: Runyan, Marc
name: Ryan, Colm A.
name: Sahmoud, Abdulrahman
name: Sanchez, Ernesto
name: Sanil, Rohan
name: Sankar, Krishanu
name: Sato, Yuki
name: Scaffidi, Thomas
name: Siavoshi, Salome
name: Sivarajah, Prasahnt
name: Skogland, Trenton
name: Su, Chun-Ju
name: Swenson, Loren J.
name: Teo, Stephanie M.
name: Tomada, Astrid
name: Torlai, Giacomo
name: Wollack, E. Alex
name: Ye, Yufeng
name: Zerrudo, Jessica A.
name: Zhang, Kailing
name: Brandão, Fernando G. S. L.
name: Matheny, Matthew H.
name: Painter, Oskar
Publisher: name: arXiv
Year: 2024
Subjects: subject: Quantum Physics (quant-ph)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated 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 $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. 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 longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation.