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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

Magic state cultivation is a state-of-the-art protocol to prepare ultra-high fidelity non-Clifford resource states for universal quantum computation. It offers a significant reduction in spacetime overhead compared to traditional magic…

Quantum Physics · Physics 2026-03-25 Kaavya Sahay , Pei-Kai Tsai , Kathleen Chang , Qile Su , Thomas B. Smith , Shraddha Singh , Shruti Puri

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

Developing space- and time-efficient logical magic state preparation protocols will likely be an essential step towards building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for…

Quantum Physics · Physics 2026-05-26 Samyak Surti , Lucas Daguerre , Isaac H. Kim

Magic state distillation uses special codes to suppress errors in input states, which are often tailored to a Clifford-twirled error model. We present detailed measurement sequences for magic state distillation protocols which can suppress…

Quantum Physics · Physics 2021-01-27 Jeongwan Haah , Matthew B. Hastings

We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling…

Quantum Physics · Physics 2012-11-30 Sergey Bravyi , Jeongwan Haah

We apply the cutting stabiliser decomposition techniques [arXiv:2403.10964] to the quantum states generated from magic state cultivation [arXiv:2409.17595], post-selected upon all $+1$ measured values for simplicity. The resultant states to…

Quantum Physics · Physics 2025-09-23 Kwok Ho Wan , Zhenghao Zhong

Magic state cultivation is a leading approach for generating the resource states required for fault-tolerant quantum computation. Here we present a new cultivation protocol that increases the success probability of magic-state generation in…

Quantum Physics · Physics 2026-02-02 Yotam Vaknin , Shoham Jacoby , Arne Grimsmo , Alex Retzker

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

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

We refine ideas from Knill 1996, Jones 2016, Chamberland 2020, Gidney 2023+2024, Bombin 2024, and Hirano 2024 to efficiently prepare good $|T\rangle$ states. We call our construction "magic state cultivation" because it gradually grows the…

Quantum Physics · Physics 2024-09-27 Craig Gidney , Noah Shutty , Cody Jones

Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…

Quantum Physics · Physics 2026-03-11 Shiroman Prakash , Rishabh Singhal

Building upon [arXiv:2509.01224], we present a few methods on how to simulate the non-Clifford $d=5$ magic state cultivation circuits [arXiv:2409.17595] with a sum of $\approx 8$ Clifford ZX-diagrams on average, at $0.1\%$ noise. Compared…

Quantum Physics · Physics 2026-04-03 Kwok Ho Wan , Zhenghao Zhong , Ainhoa Zapirain

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

High-fidelity T magic states are a key requirement for fault-tolerant quantum computing in 2D. It has generally been assumed that preparing high-fidelity T states requires noisy injection of T states followed by lengthy distillation…

Quantum Physics · Physics 2025-09-17 Jahan Claes

Magic state distillation (MSD) is a quantum algorithm that enables performing logical non-Clifford gates with in principle arbitrarily low noise level. It is herein typically assumed that logical Clifford gates can be executed without…

Quantum Physics · Physics 2025-05-13 Sascha Heußen

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

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…

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

Preparing high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among prior attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC), a recently proposed protocol for…

Quantum Physics · Physics 2025-03-25 Zi-Han Chen , Ming-Cheng Chen , Chao-Yang Lu , Jian-Wei Pan
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