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The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…

Quantum Physics · Physics 2025-06-03 Satoshi Yoshida , Shiro Tamiya , Hayata Yamasaki

Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians.…

Quantum Physics · Physics 2026-02-27 Yongtao Zhan , Zhiyan Ding , Jakob Huhn , Johnnie Gray , John Preskill , Garnet Kin-Lic Chan , Lin Lin

Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…

Quantum Physics · Physics 2025-10-16 Trond Hjerpekjøn Haug , Timo Hillmann , Anton Frisk Kockum , Raphaël Van Laer

Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…

Quantum Physics · Physics 2017-11-08 Maika Takita , Andrew W. Cross , A. D. Córcoles , Jerry M. Chow , Jay M. Gambetta

Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…

Magic states enable universal, fault-tolerant quantum computation within the stabilizer framework. Their non-stabilizerness supplies the resource needed to bypass the Eastin-Knill theorem while allowing fault-tolerant distillation. Although…

Quantum Physics · Physics 2026-02-27 Muhammad Erew , Moshe Goldstein

Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement of a large number of clean ancilla states of…

Quantum Physics · Physics 2018-03-23 Yi-Cong Zheng , Ching-Yi Lai , Todd A. Brun

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…

Distributed architecture is a promising route to scaling fault-tolerant quantum computing (FTQC) beyond the inherent limitations of single processors. For practical implementation of distributed FTQC, logical Bell pair preparation must be…

Quantum Physics · Physics 2026-05-05 Shinichi Sunami , Yutaka Hirano , Toshihide Hinokuma , Hayata Yamasaki

In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant…

Quantum Physics · Physics 2025-07-02 Sheng-Jie Huang , Yanzhu Chen

Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…

Quantum Physics · Physics 2020-05-12 Adam Holmes , A. Y. Matsuura

Magic is a non-classical resource whose efficient manipulation is fundamental to advancing efficient and scalable fault-tolerant quantum computing. Quantum advantage is possible only if both magic and entanglement are present. Of particular…

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

We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant quantum computers (EFTQCs) in the context of models of their implementations on a surface code architecture. We estimate the logical and physical…

Quantum Physics · Physics 2024-03-04 Jacob S. Nelson , Andrew D. Baczewski

Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then…

Quantum Physics · Physics 2024-03-29 Vadym Kliuchnikov , Eddie Schoute

We describe an efficient, fully fault-tolerant implementation of Measurement-Based Quantum Computation (MBQC) in the 3D cluster state. The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and…

Quantum Physics · Physics 2026-02-11 Gabrielle Tournaire , Marvin Schwiering , Robert Raussendorf , Sven Bachmann

The degradation of entanglement in quantum memories due to decoherence is a critical challenge for scalable quantum networks. We present an entanglement distillation protocol based on the [[4,2,2]] quantum error-detecting code, deriving…

Quantum Physics · Physics 2025-09-09 Huidan Zheng , Gunsik Min , Ilkwon Sohn , Jun Heo

We study the task of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC). Establishing a general formalism which allows…

Quantum Physics · Physics 2019-10-15 Bartosz Regula , Kun Fang , Xin Wang , Mile Gu

Future quantum computers will require quantum error correction for faithful operation. The correction capabilities come with an overhead for performing fault-tolerant logical operations on the encoded qubits. One of the most resource…

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited…

Quantum Physics · Physics 2024-08-28 Riki Toshio , Yutaro Akahoshi , Jun Fujisaki , Hirotaka Oshima , Shintaro Sato , Keisuke Fujii