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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

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

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

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

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

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

Quantum low-density parity-check (qLDPC) codes can encode many logical qubits within a single code block at low physical qubit overhead, yet magic state injection into such codes remains largely underexplored. Existing state injection…

Quantum Physics · Physics 2026-04-08 Kun Liu , Shifan Xu , Tomas Jochym-O'Connor , Zhiyang He , Shraddha Singh , Yongshan Ding

Magic state distillation is a resource intensive subroutine that consumes noisy input states to produce high-fidelity resource states that are used to perform logical operations in practical quantum-computing architectures. The resource…

Quantum Physics · Physics 2022-05-17 Shraddha Singh , Andrew S. Darmawan , Benjamin J. Brown , Shruti Puri

Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage…

Quantum Physics · Physics 2026-05-29 Masari Watanabe , Hirofumi Nishi , Taichi Kosugi , Shinji Tsuneyuki , Yu-ichiro Matsushita

Logical T state preparation is a major overhead source in fault tolerant architectures built from stabilizer operations. Existing protocols, however, are reported under different code families, noise models, postselection rules, and cost…

Quantum Physics · Physics 2026-05-27 Jianshuo Gao , Xiao Yuan , Yuan Yao

Magic state distillation, a process for preparing magic states needed to implement non-Clifford gates fault-tolerantly, plays a crucial role in fault-tolerant quantum computation. Historically, it has been a major bottleneck, leading to the…

Quantum Physics · Physics 2025-12-04 Yutaka Hirano , Keisuke Fujii

Magic states are essential yet resource-intensive components for realizing universal fault-tolerant quantum computation. Preparing magic states within emerging quantum low-density parity-check (qLDPC) codes poses additional challenges, due…

Quantum Physics · Physics 2025-05-13 Guo Zhang , Yuanye Zhu , Xiao Yuan , Ying Li

Fault-tolerant quantum computation on surface codes requires magic states for universal computation. Traditional distillation factories deliver magic states deterministically but consume large areas of logical qubits, forcing static,…

Quantum Physics · Physics 2026-05-20 Steven Hofmeyr , Mathias Weiden , Justin Kalloor , John Kubiatowicz , Costin Iancu

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

The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In…

Quantum Physics · Physics 2026-05-01 Earl T. Campbell , Mark Howard

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, which is a probabilistic process used to generate magic states, plays an important role in universal fault-tolerant quantum computers. On the other hand, to solve interesting problems, we need to run complex…

Quantum Physics · Physics 2024-07-11 Yutaka Hirano , Yasunari Suzuki , Keisuke Fujii

Quantum resource distillation is a fundamental task in quantum information science and technology. Minimizing the overhead of distillation is crucial for the realization of quantum computation and other technologies. Here we explicitly…

Quantum Physics · Physics 2025-10-15 Kun Fang , Zi-Wen Liu

Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…

Quantum Physics · Physics 2026-01-27 Seok-Hyung Lee , Lucas H. English , Stephen D. Bartlett
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