Efficient fault-tolerant code switching via one-way transversal CNOT gates

Sascha Heußen; Janine Hilder

doi:10.22331/q-2025-09-03-1846

Efficient fault-tolerant code switching via one-way transversal CNOT gates

¹neQxt, 50670 Cologne, Germany
²neQxt, 63906 Erlenbach am Main, Germany
³QUANTUM, Institut für Physik, Universität Mainz, 55128 Mainz, Germany

Published:	2025-09-03, volume 9, page 1846
Editor:	Joschka Roffe
Eprint:	arXiv:2409.13465v2
Doi:	https://doi.org/10.22331/q-2025-09-03-1846
Citation:	Quantum 9, 1846 (2025).

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Abstract

Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this work, we present a code switching scheme that respects the constraints of FT circuit design by only making use of transversal gates. These gates are intrinsically FT without additional qubit overhead. We analyze application of the scheme to low-distance color codes, which are suitable for operation in existing quantum processors, for instance based on trapped ions or neutral atoms. We briefly discuss connectivity constraints that arise for architectures based on superconducting qubits. Numerical simulations of circuit-level noise indicate that a logical $T$-gate, facilitated by our scheme, could outperform both flag-FT magic state injection protocols and a physical $T$-gate at low physical error rates. Transversal code switching naturally scales to code pairs of arbitrary code distance. We observe improved performance of a distance-5 protocol compared to both the distance-3 implementation and the physical gate for realistically attainable physical entangling gate error rates. We discuss how the scheme can be implemented with a large degree of parallelization, provided that logical auxiliary qubits can be prepared reliably enough. Our logical $T$-gate circumvents potentially costly magic state factories. The requirements to perform QEC and to achieve an FT universal gate set are then essentially the same: Prepare logical auxiliary qubits offline, execute transversal gates and perform fast-enough measurements. Transversal code switching thus serves to enable more practical hardware realizations of FT universal quantum computation. The scheme alleviates resource requirements for experimental demonstrations of quantum algorithms run on logical qubits.

Featured image: A universal set of fault-tolerant quantum gate operations is realized by switching between a 2D and a 3D color code.

Popular summary

Quantum error correction provides a scalable way to make quantum computers work reliably. By encoding logical information across many physical qubits, fragile quantum states are protected against errors that naturally arise in any physical architecture. Implementing a universal set of quantum gate operations on logical qubits remains challenging. Some gates are "easy" to perform fault-tolerantly, while others, like the T-gate, typically require additional costly procedures such as preparing special "magic states".

In our work, we analyze an alternative paradigm to realize a universal gate set by transferring an encoded quantum state at will between two types of quantum error correction codes that can, in conjunction, facilitate all required gates easily. Importantly, the code switching scheme relies on transversal gates only, acting on each qubit independently, and is therefore naturally fault-tolerant without extra circuitry. Also, this property allows one to use the scheme for codes of arbitrary distance without increasing the circuit depth. We show through simulations that this method can outperform existing alternatives at realistically attainable physical error rates.

This matters because it offers a path to more practical and scalable fault-tolerant quantum computing. Transversal code switching reduces hardware requirements and could therefore make experimental demonstrations of logical quantum algorithms more accessible in the near future.

► BibTeX data

@article{Heussen2025efficientfault,
  doi = {10.22331/q-2025-09-03-1846},
  url = {https://doi.org/10.22331/q-2025-09-03-1846},
  title = {Efficient fault-tolerant code switching via one-way transversal {CNOT} gates},
  author = {Heu{\ss{}}en, Sascha and Hilder, Janine},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1846},
  month = sep,
  year = {2025}
}

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Cited by

[1] Sascha Heußen, "Magic state distillation without measurements and post-selection", APL Quantum 2 4, 046113 (2025).

[2] Samyak Surti, Lucas Daguerre, and Isaac H. Kim, "Efficient Simulation of Logical Magic State Preparation Protocols", PRX Quantum 7 2, 020329 (2026).

[3] Zi-Han Chen, Ming-Cheng Chen, Chao-Yang Lu, and Jian-Wei Pan, "Efficient Magic State Cultivation on RP2", PRX Quantum 7 1, 010315 (2026).

[4] Christopher Gerhard and Todd A. Brun, "Weakly fault-tolerant computation in a quantum error-detecting code", Physical Review A 114 1, 012429 (2026).

[5] Tom Peham, Erik Weilandt, and Robert Wille, "Optimizing fault-tolerant cat state preparation", Physical Review A 113 6, 062426 (2026).

[6] Varun Menon, J. Pablo Bonilla Ataides, Rohan Mehta, Andi Gu, Daniel Bochen Tan, and Mikhail D. Lukin, "Magic Tricycles: Efficient Magic-State Generation with Finite Block-Length Quantum LDPC Codes", Physical Review X 16 2, 021014 (2026).

[7] Craig Gidney, Noah Shutty, and Cody Jones, "Magic state cultivation: growing T states as cheap as CNOT gates", arXiv:2409.17595, (2024).

[8] Lucas Daguerre, Robin Blume-Kohout, Natalie C. Brown, David Hayes, and Isaac H. Kim, "Experimental Demonstration of High-Fidelity Logical Magic States from Code Switching", Physical Review X 15 4, 041008 (2025).

[9] Shubham P. Jain and Victor V. Albert, "Transversal Clifford and T-gate codes of short length and high distance", arXiv:2408.12752, (2024).

[10] 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, and Kevin J. Satzinger, "Magic state cultivation on a superconducting quantum processor", arXiv:2512.13908, (2025).

[11] Christine Li, John Preskill, and Qian Xu, "Transversal dimension jump for product qLDPC codes", arXiv:2510.07269, (2025).

[12] Clément Poirson, Joschka Roffe, and Robert I. Booth, "Engineering CSS surgery: compiling any CNOT in any code", arXiv:2505.01370, (2025).

[13] Lucas Daguerre and Isaac H. Kim, "Code switching revisited: Low-overhead magic state preparation using color codes", arXiv:2410.07327, (2024).

[14] Yingkai Ouyang, Yumang Jing, and Gavin K. Brennen, "Measurement-Free Code-Switching Protocol for Low-Overhead Quantum Computation Using Permutation-Invariant Codes", PRX Quantum 6 4, 040341 (2025).

[15] Ludwig Schmid, Tom Peham, Lucas Berent, Markus Müller, and Robert Wille, "Deterministic Fault-Tolerant State Preparation for Near-Term Quantum Error Correction: Automatic Synthesis Using Boolean Satisfiability", arXiv:2501.05527, (2025).

[16] Sascha Heußen, "Magic state distillation without measurements and post-selection", arXiv:2504.17509, (2025).

[17] Junshi Wang and Prakash Murali, "Orchestrating multi-level magic state distillation: a dynamic pipeline architecture", arXiv:2509.24402, (2025).

[18] Victor V. Albert and Philippe Faist, "Handbook of Error-Correcting Codes", arXiv:2606.11484, (2026).

[19] Lucas Daguerre and Isaac H. Kim, "Code switching revisited: Low-overhead magic state preparation using color codes", Physical Review Research 7 2, 023080 (2025).

[20] Jacob S. Nelson, Andrew J. Landahl, and Andrew D. Baczewski, "A small and interesting architecture for early fault-tolerant quantum computers", arXiv:2507.20387, (2025).

[21] Friederike Butt, David F. Locher, Katharina Brechtelsbauer, Hans Peter Büchler, and Markus Müller, "Measurement-free, scalable, and fault-tolerant universal quantum computing", Science Advances 11 33, eadv2590 (2025).

[22] Shubham P. Jain and Victor V. Albert, "Transversal Clifford and T-Gate Codes of Short Length and High Distance", IEEE Journal on Selected Areas in Information Theory 6, 127 (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 12:30:55) and SAO/NASA ADS (last updated successfully 2026-08-09 12:31:07). The list may be incomplete as not all publishers provide suitable and complete citation data.

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