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Quantum error correction (QEC) and fault-tolerant (FT) mechanisms are essential for reliable quantum computing. However, QEC considerably increases the computation size up to four orders of magnitude. Moreover, FT implementation has…

Quantum Physics · Physics 2018-09-20 L. Lao , B. van Wee , I. Ashraf , J. van Someren , N. Khammassi , K. Bertels , C. G. Almudever

Quantum code surgery is a promising technique to perform fault-tolerant computation on quantum low-density parity-check codes. Recent developments have significantly reduced the space overhead of surgery. However, generic surgery operations…

Quantum Physics · Physics 2025-10-17 Alexander Cowtan , Zhiyang He , Dominic J. Williamson , Theodore J. Yoder

In universal fault-tolerant quantum computing, implementing logical non-Clifford gates often demands substantial spacetime resources for many error-correcting codes, including the high-threshold surface code. A critical mission for…

Quantum Physics · Physics 2026-01-07 Sheng-Jie Huang , Alison Warman , Sakura Schafer-Nameki , Yanzhu Chen

Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching…

Quantum Physics · Physics 2025-10-10 Shi Jie Samuel Tan , Yifan Hong , Ting-Chun Lin , Michael J. Gullans , Min-Hsiu Hsieh

Quantum error correction is necessary for large-scale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e.,…

Quantum Physics · Physics 2024-09-04 Daniel Bochen Tan , Murphy Yuezhen Niu , Craig Gidney

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…

Quantum Physics · Physics 2016-08-24 Benjamin J. Brown , Naomi H. Nickerson , Dan E. Browne

Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes, which generalises lattice surgery. In this work, we present a code surgery scheme, applicable to any qubit…

Quantum Physics · Physics 2026-05-12 Alexander Cowtan , Zhiyang He , Dominic J. Williamson , Theodore J. Yoder

For planar architectures surface code-based quantum error correction is one of the most promising approaches to fault-tolerant quantum computation. This is partially due to the variety of fault-tolerant logical protocols that can be…

Quantum Physics · Physics 2025-09-22 Áron Márton , Luis Colmenarez , Lukas Bödeker , Markus Müller

Quantum error correction allows inherently noisy quantum devices to emulate an ideal quantum computer with reasonable resource overhead. As a crucial component, decoding architectures have received significant attention recently. In this…

Quantum Physics · Physics 2025-09-05 Kai Zhang , Jubo Xu , Fang Zhang , Linghang Kong , Zhengfeng Ji , Jianxin Chen

Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist…

Quantum Physics · Physics 2022-05-04 Christopher Chamberland , Earl T. Campbell

Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…

Resource consumption of the conventional surface code is expensive, in part due to the need to separate the defects that create the logical qubit far apart on the physical qubit lattice. We propose that instantiating the deformation-based…

Quantum Physics · Physics 2017-01-25 Shota Nagayama , Takahiko Satoh , Rodney Van Meter

Surface quantum error-correcting codes are the leading proposal for fault-tolerance within quantum computers. We present OpenSurgery, a scalable tool for the preparation of circuits protected by the surface code operated through lattice…

Quantum Physics · Physics 2020-08-27 Alexandru Paler , Austin G. Fowler

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…

Quantum Physics · Physics 2026-03-20 Nathan Lacroix , Alexandre Bourassa , Francisco J. H. Heras , Lei M. Zhang , Johannes Bausch , Andrew W. Senior , Thomas Edlich , Noah Shutty , Volodymyr Sivak , Andreas Bengtsson , Matt McEwen , Oscar Higgott , Dvir Kafri , Jahan Claes , Alexis Morvan , Zijun Chen , Adam Zalcman , Sid Madhuk , Rajeev Acharya , Laleh Aghababaie Beni , Georg Aigeldinger , Ross Alcaraz , Trond I. Andersen , Markus Ansmann , Frank Arute , Kunal Arya , Abraham Asfaw , Juan Atalaya , Ryan Babbush , Brian Ballard , Joseph C. Bardin , Alexander Bilmes , Sam Blackwell , Jenna Bovaird , Dylan Bowers , Leon Brill , Michael Broughton , David A. Browne , Brett Buchea , Bob B. Buckley , Tim Burger , Brian Burkett , Nicholas Bushnell , Anthony Cabrera , Juan Campero , Hung-Shen Chang , Ben Chiaro , Liang-Ying Chih , Agnetta Y. Cleland , Josh Cogan , Roberto Collins , Paul Conner , William Courtney , Alexander L. Crook , Ben Curtin , Sayan Das , Sean Demura , Laura De Lorenzo , Agustin Di Paolo , Paul Donohoe , Ilya Drozdov , Andrew Dunsworth , Alec Eickbusch , Aviv Moshe Elbag , Mahmoud Elzouka , Catherine Erickson , Vinicius S. Ferreira , Leslie Flores Burgos , Ebrahim Forati , Austin G. Fowler , Brooks Foxen , Suhas Ganjam , Gonzalo Garcia , Robert Gasca , Élie Genois , William Giang , Dar Gilboa , Raja Gosula , Alejandro Grajales Dau , Dietrich Graumann , Alex Greene , Jonathan A. Gross , Tan Ha , Steve Habegger , Monica Hansen , Matthew P. Harrigan , Sean D. Harrington , Stephen Heslin , Paula Heu , Reno Hiltermann , Jeremy Hilton , Sabrina Hong , Hsin-Yuan Huang , Ashley Huff , William J. Huggins , Evan Jeffrey , Zhang Jiang , Xiaoxuan Jin , Chaitali Joshi , Pavol Juhas , Andreas Kabel , Hui Kang , Amir H. Karamlou , Kostyantyn Kechedzhi , Trupti Khaire , Tanuj Khattar , Mostafa Khezri , Seon Kim , Paul V. Klimov , Bryce Kobrin , Alexander N. Korotkov , Fedor Kostritsa , John Mark Kreikebaum , Vladislav D. Kurilovich , David Landhuis , Tiano Lange-Dei , Brandon W. Langley , Pavel Laptev , Kim-Ming Lau , Justin Ledford , Kenny Lee , Brian J. Lester , Loïck Le Guevel , Wing Yan Li , Yin Li , Alexander T. Lill , William P. Livingston , Aditya Locharla , Erik Lucero , Daniel Lundahl , Aaron Lunt , Ashley Maloney , Salvatore Mandrà , Leigh S. Martin , Orion Martin , Cameron Maxfield , Jarrod R. McClean , Seneca Meeks , Anthony Megrant , Kevin C. Miao , Reza Molavi , Sebastian Molina , Shirin Montazeri , Ramis Movassagh , Charles Neill , Michael Newman , Anthony Nguyen , Murray Nguyen , Chia-Hung Ni , Murphy Y. Niu , Logan Oas , William D. Oliver , Raymond Orosco , Kristoffer Ottosson , Alex Pizzuto , Rebecca Potter , Orion Pritchard , Chris Quintana , Ganesh Ramachandran , Matthew J. Reagor , Rachel Resnick , David M. Rhodes , Gabrielle Roberts , Eliott Rosenberg , Emma Rosenfeld , Elizabeth Rossi , Pedram Roushan , Kannan Sankaragomathi , Henry F. Schurkus , Michael J. Shearn , Aaron Shorter , Vladimir Shvarts , Spencer Small , W. Clarke Smith , Sofia Springer , George Sterling , Jordan Suchard , Aaron Szasz , Alex Sztein , Douglas Thor , Eifu Tomita , Alfredo Torres , M. Mert Torunbalci , Abeer Vaishnav , Justin Vargas , Sergey Vdovichev , Guifre Vidal , Catherine Vollgraff Heidweiller , Steven Waltman , Jonathan Waltz , Shannon X. Wang , Brayden Ware , Travis Weidel , Theodore White , Kristi Wong , Bryan W. K. Woo , Maddy Woodson , Cheng Xing , Z. Jamie Yao , Ping Yeh , Bicheng Ying , Juhwan Yoo , Noureldin Yosri , Grayson Young , Yaxing Zhang , Ningfeng Zhu , Nicholas Zobrist , Hartmut Neven , Pushmeet Kohli , Alex Davies , Sergio Boixo , Julian Kelly , Cody Jones , Craig Gidney , Kevin J. Satzinger

Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery…

Quantum Physics · Physics 2025-12-12 Laura S. Herzog , Lucas Berent , Aleksander Kubica , Robert Wille

Due to the high error rate of a qubit, detecting and correcting errors on it is essential for fault-tolerant quantum computing (FTQC). Among several FTQC techniques, lattice surgery (LS) using surface code (SC) is currently promising. To…

Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…

Quantum Physics · Physics 2023-07-26 Adam Siegel , Armands Strikis , Thomas Flatters , Simon Benjamin

Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…

Quantum Physics · Physics 2014-02-14 Ashley M. Stephens

Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We…

Quantum Physics · Physics 2025-10-07 Nouédyn Baspin , Lucas Berent , Lawrence Z. Cohen

The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in…

Quantum Physics · Physics 2015-05-13 H. Bombin , M. A. Martin-Delgado