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Here, we investigate a lattice-surgery-based CNOT operation between two surface code patches under phenomenological error models. (i) For two-qubit logical Pauli measurements \u2013 the elementary building block of the CNOT \u2013 we optimize the number of stabilizer measurement rounds, usually taken equal to d<\/mml:mi><\/mml:math>, the size (code distance) of each patch. We find that the optimal number can be greater or smaller than d<\/mml:mi><\/mml:math>, depending on the rate of physical and readout errors, and the separation between the code patches. (ii) We fully characterize the two-qubit logical error channel of the lattice-surgery-based CNOT. We find a symmetry of the CNOT protocol, that results in a symmetry of the logical error channel. We also find that correlations between X and Z errors on the logical level are suppressed under minimum weight decoding.<\/jats:p>","DOI":"10.22331\/q-2024-12-27-1577","type":"journal-article","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T16:55:51Z","timestamp":1735318551000},"page":"1577","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Characterization of errors in a CNOT between surface code patches"],"prefix":"10.22331","volume":"8","author":[{"given":"B\u00e1lint","family":"Domokos","sequence":"first","affiliation":[{"name":"Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, M\u0171egyetem rkp. 3., H-1111 Budapest, Hungary"}]},{"given":"\u00c1ron","family":"M\u00e1rton","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, M\u0171egyetem rkp. 3., H-1111 Budapest, Hungary"}]},{"given":"J\u00e1nos K.","family":"Asb\u00f3th","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, M\u0171egyetem rkp. 3., H-1111 Budapest, Hungary"},{"name":"HUN-REN Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49., Hungary"}]}],"member":"9598","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A.Yu. Kitaev. ``Fault-tolerant quantum computation by anyons''. Annals of Physics 303, 2\u201330 (2003).","DOI":"10.1016\/s0003-4916(02)00018-0"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. ``Surface codes: Towards practical large-scale quantum computation''. Physical Review A 86 (2012).","DOI":"10.1103\/physreva.86.032324"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Rajeev Acharya et al. ``Suppressing quantum errors by scaling a surface code logical qubit''. Nature 614, 676 \u2013 681 (2022).","DOI":"10.1038\/s41586-022-05434-1"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Dolev Bluvstein, Harry Levine, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Marcin Kalinowski, Alexander Keesling, Nishad Maskara, Hannes Pichler, Markus Greiner, Vladan Vuleti\u0107, and Mikhail D. Lukin. ``A quantum processor based on coherent transport of entangled atom arrays''. Nature 604, 451\u2013456 (2022).","DOI":"10.1038\/s41586-022-04592-6"},{"key":"4","doi-asserted-by":"publisher","unstructured":"J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, F. Battistel, M. Beekman, N. Haider, W. Vlothuizen, A. Bruno, B. M. Terhal, and L. DiCarlo. ``Logical-qubit operations in an error-detecting surface code''. Nature Physics 18, 80\u201386 (2021).","DOI":"10.1038\/s41567-021-01423-9"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Sebastian Krinner, Nathan Lacroix, Ants Remm, Agustin Di Paolo, Elie Genois, Catherine Leroux, Christoph Hellings, Stefania Lazar, Francois Swiadek, Johannes Herrmann, et al. ``Realizing repeated quantum error correction in a distance-three surface code''. 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