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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 computers capable of solving classically intractable problems are under construction, and intermediate-scale devices are approaching completion. Current efforts to design large-scale devices require allocating immense resources to…

Leading approaches to fault-tolerant quantum computation dedicate a significant portion of the hardware to computational factories that churn out high-fidelity ancillas called magic states. Consequently, efficient and realistic factory…

Quantum Physics · Physics 2017-04-04 Joe O'Gorman , Earl T. Campbell

The leading approach to fault tolerant quantum computing requires a continual supply of magic states. When a new magic state is first encoded, its initial fidelity will be too poor for use in the computation. This necessitates a…

Quantum Physics · Physics 2015-03-24 Ying Li

Quantum error correction is a cornerstone of reliable quantum computing, with surface codes emerging as a prominent method for protecting quantum information. Surface codes are efficient for Clifford gates but require magic state…

Quantum Physics · Physics 2025-03-13 Avimita Chatterjee , Archisman Ghosh , Swaroop Ghosh

Practical quantum computation requires high-fidelity instruction executions on qubits. Among them, Clifford instructions are relatively easy to perform, while non-Clifford instructions require the use of magic states. This makes magic state…

Quantum Physics · Physics 2025-09-30 Junshi Wang , Prakash Murali

Fault-tolerant quantum computation relies on the assumption of time-invariant, sufficiently low physical error rates. However, current superconducting quantum computers suffer from frequent disruptive noise events, including cosmic ray…

The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient…

Quantum Physics · Physics 2020-10-30 Christopher Chamberland , Kyungjoo Noh

Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple…

Quantum Physics · Physics 2026-02-25 Shifan Xu , Kun Liu , Patrick Rall , Zhiyang He , Yongshan Ding

To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from…

Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery…

Quantum Physics · Physics 2026-02-02 Dominic J. Williamson

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is…

Quantum Physics · Physics 2026-04-06 Younghun Kim , Martin Sevior , Muhammad Usman

Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to…

Quantum Physics · Physics 2019-12-04 Daniel Litinski

Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient…

Quantum Physics · Physics 2025-12-17 Emma Rosenfeld , Craig Gidney , Gabrielle Roberts , Alexis Morvan , Nathan Lacroix , Dvir Kafri , Jeffrey Marshall , Ming Li , Volodymyr Sivak , Dmitry Abanin , Amira Abbas , Rajeev Acharya , Laleh Aghababaie Beni , Georg Aigeldinger , Ross Alcaraz , Sayra Alcaraz , Trond I. Andersen , Markus Ansmann , Frank Arute , Kunal Arya , Walt Askew , Nikita Astrakhantsev , Juan Atalaya , Ryan Babbush , Brian Ballard , Joseph C. Bardin , Hector Bates , Andreas Bengtsson , Majid Bigdeli Karimi , Alexander Bilmes , Simon Bilodeau , Felix Borjans , Jenna Bovaird , Dylan Bowers , Leon Brill , Peter Brooks , Michael Broughton , David A. Browne , Brett Buchea , Bob B. Buckley , Tim Burger , Brian Burkett , Nicholas Bushnell , Jamal Busnaina , Anthony Cabrera , Juan Campero , Hung-Shen Chang , Silas Chen , Zijun Chen , Ben Chiaro , Liang-Ying Chih , Agnetta Y. Cleland , Bryan Cochrane , Matt Cockrell , Josh Cogan , Paul Conner , Harold Cook , Rodrigo G. Cortiñas , William Courtney , Alexander L. Crook , Ben Curtin , Martin Damyanov , Sayan Das , Dripto M. Debroy , Sean Demura , Paul Donohoe , Ilya Drozdov , Andrew Dunsworth , Valerie Ehimhen , Alec Eickbusch , Aviv Moshe Elbag , Lior Ella , Mahmoud Elzouka , David Enriquez , Catherine Erickson , Lara Faoro , Vinicius S. Ferreira , Marcos Flores , Leslie Flores Burgos , Sam Fontes , Ebrahim Forati , Jeremiah Ford , Brooks Foxen , Masaya Fukami , Alan Wing Lun Fung , Lenny Fuste , Suhas Ganjam , Gonzalo Garcia , Christopher Garrick , Robert Gasca , Helge Gehring , Robert Geiger , Élie Genois , William Giang , Dar Gilboa , James E. Goeders , Edward C. Gonzales , Raja Gosula , Stijn J. de Graaf , Alejandro Grajales Dau , Dietrich Graumann , Joel Grebel , Alex Greene , Jonathan A. Gross , Jose Guerrero , Loïck Le Guevel , Tan Ha , Steve Habegger , Tanner Hadick , Ali Hadjikhani , Michael C. Hamilton , Monica Hansen , Matthew P. Harrigan , Sean D. Harrington , Jeanne Hartshorn , Stephen Heslin , Paula Heu , Oscar Higgott , Reno Hiltermann , Jeremy Hilton , Hsin-Yuan Huang , Mike Hucka , Christopher Hudspeth , Ashley Huff , William J. Huggins , Lev B. Ioffe , Evan Jeffrey , Shaun Jevons , Zhang Jiang , Xiaoxuan Jin , Chaitali Joshi , Pavol Juhas , Andreas Kabel , Hui Kang , Kiseo Kang , Amir H. Karamlou , Ryan Kaufman , Kostyantyn Kechedzhi , Tanuj Khattar , Mostafa Khezri , Seon Kim , Paul V. Klimov , Can M. Knaut , Bryce Kobrin , Alexander N. Korotkov , Fedor Kostritsa , John Mark Kreikebaum , Ryuho Kudo , Ben Kueffler , Arun Kumar , Vladislav D. Kurilovich , Vitali Kutsko , Tiano Lange-Dei , Brandon W. Langley , Pavel Laptev , Kim-Ming Lau , Emma Leavell , Justin Ledford , Joy Lee , Kenny Lee , Brian J. Lester , Wendy Leung , Lily Li , Wing Yan Li , Alexander T. Lill , William P. Livingston , Matthew T. Lloyd , Aditya Locharla , Laura De Lorenzo , Erik Lucero , Daniel Lundahl , Aaron Lunt , Sid Madhuk , Aniket Maiti , Ashley Maloney , Salvatore Mandrà , Leigh S. Martin , Orion Martin , Eric Mascot , Paul Masih Das , Dmitri Maslov , Melvin Mathews , Cameron Maxfield , Jarrod R. McClean , Matt McEwen , Seneca Meeks , Anthony Megrant , Kevin C. Miao , Zlatko K. Minev , Reza Molavi , Sebastian Molina , Shirin Montazeri , Charles Neill , Michael Newman , Anthony Nguyen , Murray Nguyen , Chia-Hung Ni , Murphy Yuezhen Niu , Nicholas Noll , Logan Oas , William D. Oliver , Raymond Orosco , Kristoffer Ottosson , Alice Pagano , Agustin Di Paolo , Sherman Peek , David Peterson , Alex Pizzuto , Elias Portoles , Rebecca Potter , Orion Pritchard , Michael Qian , Chris Quintana , Ganesh Ramachandran , Arpit Ranadive , Matthew J. Reagor , Rachel Resnick , David M. Rhodes , Daniel Riley , Roberto Rodriguez , Emma Ropes , Lucia B. De Rose , Eliott Rosenberg , Dario Rosenstock , Elizabeth Rossi , Pedram Roushan , David A. Rower , Robert Salazar , Kannan Sankaragomathi , Murat Can Sarihan , Max Schaefer , Sebastian Schroeder , Henry F. Schurkus , Aria Shahingohar , Michael J. Shearn , Aaron Shorter , Noah Shutty , Vladimir Shvarts , Spencer Small , W. Clarke Smith , David A. Sobel , Barrett Spells , Sofia Springer , George Sterling , Jordan Suchard , Aaron Szasz , Alexander Sztein , Madeline Taylor , Jothi Priyanka Thiruraman , Douglas Thor , Dogan Timucin , Eifu Tomita , Alfredo Torres , M. Mert Torunbalci , Hao Tran , Abeer Vaishnav , Justin Vargas , Sergey Vdovichev , Guifre Vidal , Benjamin Villalonga , Catherine Vollgraff Heidweiller , Meghan Voorhees , Steven Waltman , Jonathan Waltz , Shannon X. Wang , Danni Wang , Brayden Ware , James D. Watson , Yonghua Wei , Travis Weidel , Theodore White , Kristi Wong , Bryan W. K. Woo , Christopher J. Wood , Maddy Woodson , Cheng Xing , Z. Jamie Yao , Ping Yeh , Bicheng Ying , Juhwan Yoo , Noureldin Yosri , Elliot Young , Grayson Young , Adam Zalcman , Ran Zhang , Yaxing Zhang , Ningfeng Zhu , Nicholas Zobrist , Zhenjie Zou , Hartmut Neven , Sergio Boixo , Cody Jones , Julian Kelly , Alexandre Bourassa , Kevin J. Satzinger

Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and…

Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction…

Quantum Physics · Physics 2025-10-29 Yutaka Hirano , Riki Toshio , Tomohiro Itogawa , Keisuke Fujii

Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but…

Quantum Physics · Physics 2026-01-09 Seok-Hyung Lee , Felix Thomsen , Nicholas Fazio , Benjamin J. Brown , Stephen D. Bartlett

Erasure qubits constitute a promising approach for tackling the daunting resources required for fault-tolerant quantum computing. By heralding erasure errors, both the error-correction threshold and the sub-threshold scaling of the logical…

Quantum Physics · Physics 2026-01-16 Shoham Jacoby , Yotam Vaknin , Alex Retzker , Arne L. Grimsmo

Magic state distillation (MSD) is a cornerstone of fault-tolerant quantum computing, enabling non-Clifford gates via state injection into stabilizer circuits. However, the substantial overhead of current MSD protocols remains a major…

Quantum Physics · Physics 2026-05-26 Muhammad Erew , Moshe Goldstein , Yaron Oz , Haim Suchowski

Magic state distillation (MSD) is an essential element for universal fault-tolerant quantum computing, which distills a high-fidelity magic state from noisy magic states using ideal (error-corrected) Clifford operations. For ideal Clifford…

Quantum Physics · Physics 2025-06-23 Tomohiro Itogawa , Yugo Takada , Yutaka Hirano , Keisuke Fujii
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