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We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…

Quantum Physics · Physics 2011-08-31 Andrew J. Landahl , Jonas T. Anderson , Patrick R. Rice

Scalability of flying photonic quantum systems in generating quantum entanglement offers a potential for implementing large-scale fault-tolerant quantum computation, especially by means of measurement-based quantum computation (MBQC).…

Quantum Physics · Physics 2020-06-11 Hayata Yamasaki , Kosuke Fukui , Yuki Takeuchi , Seiichiro Tani , Masato Koashi

We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade-offs between the number of physical qubits and the fault-tolerant execution time of a…

Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…

Quantum Physics · Physics 2013-03-12 Tomas Jochym-O'Connor , Yafei Yu , Bassam Helou , Raymond Laflamme

Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources…

Quantum Physics · Physics 2026-04-06 Hai Xu , Tao Chen , Junkai Zeng , Xiu-Hao Deng , Fang Gao , Xin Wang , Zheng-Yuan Xue , Chengxian Zhang

Majorana-based quantum computation in nanowires and neutral atoms has gained prominence as a promising platform to encode qubits and protect them against noise. In order to run computations reliably on such devices, a fully fault-tolerant…

Quantum Physics · Physics 2025-09-17 Maryam Mudassar , Alexander Schuckert , Daniel Gottesman

Measurement-based quantum computation with continuous variables in an optical setup shows the great promise towards implementation of large-scale quantum computation, where the time-domain multiplexing approach enables us to generate the…

Quantum Physics · Physics 2020-09-11 Kosuke Fukui , Warit Asavanant , Akira Furusawa

Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…

We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…

Quantum Physics · Physics 2019-12-11 Xiaosi Xu , Qi Zhao , Xiao Yuan , Simon C. Benjamin

We study the code obtained by concatenating the standard single-mode Gottesman-Kitaev-Preskill (GKP) code with the surface code. We show that the noise tolerance of this surface-GKP code with respect to (Gaussian) displacement errors…

Quantum Physics · Physics 2020-11-18 Lisa Hänggli , Margret Heinze , Robert Koenig

We analyse a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal…

Quantum Physics · Physics 2015-12-07 Paul Webster , Stephen D. Bartlett , David Poulin

We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…

Quantum Physics · Physics 2019-08-29 Theodoros Kapourniotis , Animesh Datta

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

Macronode cluster states are promising for fault-tolerant continuous-variable quantum computation, combining gate teleportation via homodyne detection with the Gottesman-Kitaev-Preskill code for universality and error correction. While the…

We introduce and implement a technique to extend the quantum computational power of cluster states by replacing some projective measurements with generalized quantum measurements (POVMs). As an experimental demonstration we fully realize an…

We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap encompasses four generations of devices: a single-qubit…

Quantum Physics · Physics 2025-07-22 David Aasen , Morteza Aghaee , Zulfi Alam , Mariusz Andrzejczuk , Andrey Antipov , Mikhail Astafev , Lukas Avilovas , Amin Barzegar , Bela Bauer , Jonathan Becker , Juan M. Bello-Rivas , Umesh Bhaskar , Alex Bocharov , Srini Boddapati , David Bohn , Jouri Bommer , Parsa Bonderson , Jan Borovsky , Leo Bourdet , Samuel Boutin , Tom Brown , Gary Campbell , Lucas Casparis , Srivatsa Chakravarthi , Rui Chao , Benjamin J. Chapman , Sohail Chatoor , Anna Wulff Christensen , Patrick Codd , William Cole , Paul Cooper , Fabiano Corsetti , Ajuan Cui , Wim van Dam , Tareq El Dandachi , Sahar Daraeizadeh , Adrian Dumitrascu , Andreas Ekefjärd , Saeed Fallahi , Luca Galletti , Geoff Gardner , Raghu Gatta , Haris Gavranovic , Michael Goulding , Deshan Govender , Flavio Griggio , Ruben Grigoryan , Sebastian Grijalva , Sergei Gronin , Jan Gukelberger , Jeongwan Haah , Marzie Hamdast , Esben Bork Hansen , Matthew Hastings , Sebastian Heedt , Samantha Ho , Justin Hogaboam , Laurens Holgaard , Kevin Van Hoogdalem , Jinnapat Indrapiromkul , Henrik Ingerslev , Lovro Ivancevic , Sarah Jablonski , Thomas Jensen , Jaspreet Jhoja , Jeffrey Jones , Kostya Kalashnikov , Ray Kallaher , Rachpon Kalra , Farhad Karimi , Torsten Karzig , Seth Kimes , Vadym Kliuchnikov , Maren Elisabeth Kloster , Christina Knapp , Derek Knee , Jonne Koski , Pasi Kostamo , Jamie Kuesel , Brad Lackey , Tom Laeven , Jeffrey Lai , Gijs de Lange , Thorvald Larsen , Jason Lee , Kyunghoon Lee , Grant Leum , Kongyi Li , Tyler Lindemann , Marijn Lucas , Roman Lutchyn , Morten Hannibal Madsen , Nash Madulid , Michael Manfra , Signe Brynold Markussen , Esteban Martinez , Marco Mattila , Jake Mattinson , Robert McNeil , Antonio Rodolph Mei , Ryan V. Mishmash , Gopakumar Mohandas , Christian Mollgaard , Michiel de Moor , Trevor Morgan , George Moussa , Anirudh Narla , Chetan Nayak , Jens Hedegaard Nielsen , William Hvidtfelt Padkær Nielsen , Frédéric Nolet , Mike Nystrom , Eoin O'Farrell , Keita Otani , Adam Paetznick , Camille Papon , Andres Paz , Karl Petersson , Luca Petit , Dima Pikulin , Diego Olivier Fernandez Pons , Sam Quinn , Mohana Rajpalke , Alejandro Alcaraz Ramirez , Katrine Rasmussen , David Razmadze , Ben Reichardt , Yuan Ren , Ken Reneris , Roy Riccomini , Ivan Sadovskyy , Lauri Sainiemi , Juan Carlos Estrada Saldaña , Irene Sanlorenzo , Simon Schaal , Emma Schmidgall , Cristina Sfiligoj , Marcus P. da Silva , Shilpi Singh , Sarat Sinha , Mathias Soeken , Patrick Sohr , Tomas Stankevic , Lieuwe Stek , Patrick Strøm-Hansen , Eric Stuppard , Aarthi Sundaram , Henri Suominen , Judith Suter , Satoshi Suzuki , Krysta Svore , Sam Teicher , Nivetha Thiyagarajah , Raj Tholapi , Mason Thomas , Dennis Tom , Emily Toomey , Josh Tracy , Matthias Troyer , Michelle Turley , Matthew D. Turner , Shivendra Upadhyay , Ivan Urban , Alexander Vaschillo , Dmitrii Viazmitinov , Dominik Vogel , Zhenghan Wang , John Watson , Alex Webster , Joseph Weston , Timothy Williamson , Georg W. Winkler , David J. van Woerkom , Brian Paquelet Wütz , Chung Kai Yang , Richard Yu , Emrah Yucelen , Jesús Herranz Zamorano , Roland Zeisel , Guoji Zheng , Justin Zilke , Andrew Zimmerman

Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…

Quantum Physics · Physics 2016-06-30 Christopher Chamberland , Tomas Jochym-O'Connor , Raymond Laflamme

We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the…

Quantum Physics · Physics 2022-07-13 Omar Fawzi , Antoine Grospellier , Anthony Leverrier

Modular architectures offer a scalable path toward fault-tolerant quantum computing by interconnecting smaller quantum processing units (QPUs) provided that high-rate, fault-tolerant interfaces can be realized across modules. We present a…

Quantum Physics · Physics 2026-05-05 Frederik K. Marqversen , Gefen Baranes , Maxim Sirotin , Johannes Borregaard

Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…

Quantum Physics · Physics 2024-11-07 Matthias Christandl , Alexander Müller-Hermes