Magic State Distillation: Not as Costly as You Think

Daniel Litinski

doi:10.22331/q-2019-12-02-205

Magic State Distillation: Not as Costly as You Think

Daniel Litinski

Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Published:	2019-12-02, volume 3, page 205
Eprint:	arXiv:1905.06903v3
Doi:	https://doi.org/10.22331/q-2019-12-02-205
Citation:	Quantum 3, 205 (2019).

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Abstract

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 demonstrate that this is not true. By writing distillation circuits in a form that separates qubits that are capable of error detection from those that are not, most logical qubits used for distillation can be encoded at a very low code distance. This significantly reduces the space-time cost of distillation, as well as the number of qubits. In extreme cases, it can cost less to distill a magic state than to perform a logical Clifford gate on full-distance logical qubits.

► BibTeX data

@article{Litinski2019magicstate,
  doi = {10.22331/q-2019-12-02-205},
  url = {https://doi.org/10.22331/q-2019-12-02-205},
  title = {Magic {S}tate {D}istillation: {N}ot as {C}ostly as {Y}ou {T}hink},
  author = {Litinski, Daniel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {205},
  month = dec,
  year = {2019}
}

► References

[1] J. Preskill, Reliable quantum computers, Proc. Roy. Soc. Lond. A 454, 385 (1998).
https://doi.org/10.1098/rspa.1998.0167

[2] B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
https://doi.org/10.1103/RevModPhys.87.307

[3] E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature 549, 172 (2017).
https://doi.org/10.1038/nature23460

[4] A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
https://doi.org/10.1016/S0003-4916(02)00018-0

[5] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
https://doi.org/10.1103/PhysRevA.86.032324

[6] C. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
https://doi.org/10.1088/1367-2630/14/12/123011

[7] D. Litinski and F. v. Oppen, Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes, Quantum 2, 62 (2018).
https://doi.org/10.22331/q-2018-05-04-62

[8] A. G. Fowler and C. Gidney, Low overhead quantum computation using lattice surgery, arXiv:1808.06709 (2018).
arXiv:1808.06709

[9] S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
https://doi.org/10.1103/PhysRevA.71.022316

[10] R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear T complexity, Phys. Rev. X 8, 041015 (2018).
https://doi.org/10.1103/PhysRevX.8.041015

[11] S. Bravyi and J. Haah, Magic-state distillation with low overhead, Phys. Rev. A 86, 052329 (2012).
https://doi.org/10.1103/PhysRevA.86.052329

[12] A. G. Fowler, S. J. Devitt, and C. Jones, Surface code implementation of block code state distillation, Scientific Rep. 3, 1939 (2013).
https://doi.org/10.1038/srep01939

[13] A. M. Meier, B. Eastin, and E. Knill, Magic-state distillation with the four-qubit code, Quant. Inf. Comp. 13, 195 (2013).
arXiv:1204.4221

[14] C. Jones, Multilevel distillation of magic states for quantum computing, Phys. Rev. A 87, 042305 (2013a).
https://doi.org/10.1103/PhysRevA.87.042305

[15] G. Duclos-Cianci and K. M. Svore, Distillation of nonstabilizer states for universal quantum computation, Phys. Rev. A 88, 042325 (2013).
https://doi.org/10.1103/PhysRevA.88.042325

[16] G. Duclos-Cianci and D. Poulin, Reducing the quantum-computing overhead with complex gate distillation, Phys. Rev. A 91, 042315 (2015).
https://doi.org/10.1103/PhysRevA.91.042315

[17] E. T. Campbell and M. Howard, Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost, Phys. Rev. A 95, 022316 (2017a).
https://doi.org/10.1103/PhysRevA.95.022316

[18] J. O'Gorman and E. T. Campbell, Quantum computation with realistic magic-state factories, Phys. Rev. A 95, 032338 (2017).
https://doi.org/10.1103/PhysRevA.95.032338

[19] J. Haah and M. B. Hastings, Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates, Quantum 2, 71 (2018).
https://doi.org/10.22331/q-2018-06-07-71

[20] E. T. Campbell and M. Howard, Magic state parity-checker with pre-distilled components, Quantum 2, 56 (2018).
https://doi.org/10.22331/q-2018-03-14-56

[21] C. Gidney and A. G. Fowler, Efficient magic state factories with a catalyzed $|CCZ\rangle$ to $2|T\rangle$ transformation, Quantum 3, 135 (2019).
https://doi.org/10.22331/q-2019-04-30-135

[22] C. Jones, P. Brooks, and J. Harrington, Gauge color codes in two dimensions, Phys. Rev. A 93, 052332 (2016).
https://doi.org/10.1103/PhysRevA.93.052332

[23] S. Bravyi and A. Cross, Doubled color codes, arXiv:1509.03239 (2015).
arXiv:1509.03239

[24] T. Jochym-O'Connor and S. D. Bartlett, Stacked codes: Universal fault-tolerant quantum computation in a two-dimensional layout, Phys. Rev. A 93, 022323 (2016).
https://doi.org/10.1103/PhysRevA.93.022323

[25] H. Bombin, 2D quantum computation with 3D topological codes, arXiv:1810.09571 (2018).
arXiv:1810.09571

[26] C. Chamberland and A. W. Cross, Fault-tolerant magic state preparation with flag qubits, Quantum 3, 143 (2019).
https://doi.org/10.22331/q-2019-05-20-143

[27] B. J. Brown, A fault-tolerant non-Clifford gate for the surface code in two dimensions, arXiv:1903.11634 (2019).
arXiv:1903.11634

[28] D. Litinski, A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery, Quantum 3, 128 (2019).
https://doi.org/10.22331/q-2019-03-05-128

[29] M. Amy and M. Mosca, T-count optimization and Reed-Muller codes, IEEE Transactions on Information Theory , 1 (2019).
https://doi.org/10.1109/TIT.2019.2906374

[30] J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, Magic state distillation with low space overhead and optimal asymptotic input count, Quantum 1, 31 (2017).
https://doi.org/10.22331/q-2017-10-03-31

[31] A. J. Landahl and C. Ryan-Anderson, Quantum computing by color-code lattice surgery, arXiv:1407.5103 (2014).
arXiv:1407.5103

[32] Y. Li, A magic state’s fidelity can be superior to the operations that created it, New J. Phys. 17, 023037 (2015).
https://doi.org/10.1088/1367-2630/17/2/023037

[33] J. Lodyga, P. Mazurek, A. Grudka, and M. Horodecki, Simple scheme for encoding and decoding a qubit in unknown state for various topological codes, Scientific Rep. 5, 8975 (2015).
https://doi.org/10.1038/srep08975

[34] L. Lao et al., Preparing high-fidelity magic states with low costs, in preparation.

[35] Cramming more power into a quantum device, https://www.ibm.com/blogs/research/2019/03/ power-quantum-device/, accessed: 2019-05-09.
https://www.ibm.com/blogs/research/2019/03/power-quantum-device/

[36] K. Wright, K. Beck, S. Debnath, J. Amini, Y. Nam, N. Grzesiak, J.-S. Chen, N. Pisenti, M. Chmielewski, C. Collins, et al., Benchmarking an 11-qubit quantum computer, arXiv:1903.08181 (2019).
arXiv:1903.08181

[37] The Python script and Mathematica notebook can be found on GitHub, see https://github.com/litinski/magicstates.
https://github.com/litinski/magicstates

[38] E. T. Campbell and M. Howard, Unifying gate synthesis and magic state distillation, Phys. Rev. Lett. 118, 060501 (2017b).
https://doi.org/10.1103/PhysRevLett.118.060501

[39] P. Selinger, Quantum circuits of $T$-depth one, Phys. Rev. A 87, 042302 (2013).
https://doi.org/10.1103/PhysRevA.87.042302

[40] C. Jones, Low-overhead constructions for the fault-tolerant Toffoli gate, Phys. Rev. A 87, 022328 (2013b).
https://doi.org/10.1103/PhysRevA.87.022328

[41] C. Gidney, Halving the cost of quantum addition, Quantum 2, 74 (2018).
https://doi.org/10.22331/q-2018-06-18-74

[42] B. J. Brown and S. Roberts, Universal fault-tolerant measurement-based quantum computation, arXiv:1811.11780 (2018).
arXiv:1811.11780

Cited by

[1] T. R. Scruby, D. E. Browne, P. Webster, and M. Vasmer, "Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code", Quantum 6, 721 (2022).

[2] Dimiter Ostrev, Davide Orsucci, Francisco Lázaro, and Balazs Matuz, "Classical product code constructions for quantum Calderbank-Shor-Steane codes", Quantum 8, 1420 (2024).

[3] Satvik Maurya, Abtin Molavi, Aws Albarghouthi, and Swamit Tannu, Proceedings of the 21st European Conference on Computer Systems 514 (2026) ISBN:9798400722127.

[4] Victor Barizien, Hugo Jacinto, and Nicolas Sangouard, "Accessible Quantum Gates on Classical Stabilizer Codes", Physical Review Letters 136 3, 030602 (2026).

[5] Jiaxuan Zhang, Zhao-Yun Chen, Yun-Jie Wang, Bin-Han Lu, Hai-Feng Zhang, Jia-Ning Li, Peng Duan, Yu-Chun Wu, and Guo-Ping Guo, "Demonstrating a universal logical gate set in error-detecting surface codes on a superconducting quantum processor", npj Quantum Information 11 1, 177 (2025).

[6] Lewis W. Anderson, Martin Kiffner, Tom O'Leary, Jason Crain, and Dieter Jaksch, "Solving lattice gauge theories using the quantum Krylov algorithm and qubitization", Quantum 9, 1669 (2025).

[7] Amara Katabarwa, Katerina Gratsea, Athena Caesura, and Peter D. Johnson, "Early Fault-Tolerant Quantum Computing", PRX Quantum 5 2, 020101 (2024).

[8] Lan Luo, Zhi Ma, Dongdai Lin, and Hong Wang, "Fault-tolerance thresholds for code conversion schemes with quantum Reed–Muller codes", Quantum Science and Technology 5 4, 045022 (2020).

[9] Adam Wills, Min-Hsiu Hsieh, and Hayata Yamasaki, "Constant-overhead magic state distillation", Nature Physics 21 11, 1842 (2025).

[10] Korbinian Staudacher, Tobias Guggemos, Sophia Grundner-Culemann, and Wolfgang Gehrke, "Reducing 2-QuBit Gate Count for ZX-Calculus based Quantum Circuit Optimization", Electronic Proceedings in Theoretical Computer Science 394, 29 (2023).

[11] Jungmin Cho, Hyeonseong Jeong, Junpyo Kim, Junhyuk Choi, Juwon Hong, and Jangwoo Kim, Proceedings of the 31st ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 59 (2026) ISBN:9798400723599.

[12] 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).

[13] Diego Ruiz, Jérémie Guillaud, Christophe Vuillot, and Mazyar Mirrahimi, "Unfolded distillation: very low-cost magic state preparation for biased-noise qubits", npj Quantum Information 12 1, 53 (2026).

[14] S Flannigan, N Pearson, G H Low, A Buyskikh, I Bloch, P Zoller, M Troyer, and A J Daley, "Propagation of errors and quantitative quantum simulation with quantum advantage", Quantum Science and Technology 7 4, 045025 (2022).

[15] Timothy N. Georges, Marius Bothe, Christoph Sünderhauf, Bjorn K. Berntson, Róbert Izsák, and Aleksei V. Ivanov, "Quantum simulations of chemistry in first quantization with any basis set", npj Quantum Information 11 1, 55 (2025).

[16] Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, "Quantum computational chemistry", Reviews of Modern Physics 92 1, 015003 (2020).

[17] Eric Kubischta and Ian Teixeira, "Flexible fault-tolerant gate gadgets", Physical Review A 113 2, 022421 (2026).

[18] Abhoy Kole, Till Schnittka, and Rolf Drechsler, 2026 IEEE 29th International Symposium on Design and Diagnostics of Electronic Circuits and Systems (DDECS) 1 (2026) ISBN:979-8-3315-8229-6.

[19] Seok-Hyung Lee, Andrew Li, and Stephen D. Bartlett, "Color code decoder with improved scaling for correcting circuit-level noise", Quantum 9, 1609 (2025).

[20] Kou Hamada, Yasunari Suzuki, and Yuuki Tokunaga, "Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice", Quantum 10, 2061 (2026).

[21] Christopher Chamberland, Luis Goncalves, Prasahnt Sivarajah, Eric Peterson, and Sebastian Grimberg, "Techniques for combining fast local decoders with global decoders under circuit-level noise", Quantum Science and Technology 8 4, 045011 (2023).

[22] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien, "Quantum error mitigation", Reviews of Modern Physics 95 4, 045005 (2023).

[23] Mu-Te Lau, Hsiang-Chun Yang, Hsin-Yu Chen, and Chung-Yang Huang, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 481 (2025) ISBN:979-8-3315-5736-2.

[24] William J. Huggins and Jarrod R. McClean, "Accelerating Quantum Algorithms with Precomputation", Quantum 8, 1264 (2024).

[25] Julio C. Magdalena de la Fuente, Jens Eisert, and Andreas Bauer, "Bulk-to-boundary anyon fusion from microscopic models", Journal of Mathematical Physics 64 11, 111904 (2023).

[26] Archisman Ghosh, Avimita Chatterjee, and Swaroop Ghosh, Design Automation for Quantum Computing 155 (2026) ISBN:978-3-032-09302-8.

[27] Mauricio Gutiérrez, Juan S. Rojas-Arias, David Obando, and Chien-Yuan Chang, "Comparison of spin-qubit architectures for quantum error-correcting codes", Physical Review A 113 6, 062464 (2026).

[28] Avimita Chatterjee, Archisman Ghosh, and Swaroop Ghosh, 2026 27th International Symposium on Quality Electronic Design (ISQED) 1 (2026) ISBN:979-8-3315-8361-3.

[29] Mohamad Mousa, Amit Jamadagni, and Eugene Dumitrescu, "Composite-dimensional topological codes with boundaries and defects", Physical Review A 114 1, 012438 (2026).

[30] Shiroman Prakash and Tanay Saha, "Low Overhead Qutrit Magic State Distillation", Quantum 9, 1768 (2025).

[31] Shifan Xu, Kun Liu, Patrick Rall, Zhiyang He, and Yongshan Ding, 2026 ACM/IEEE 53rd Annual International Symposium on Computer Architecture (ISCA) 2081 (2026) ISBN:979-8-3315-5065-3.

[32] Seok-Hyung Lee and Hyunseok Jeong, "Universal hardware-efficient topological measurement-based quantum computation via color-code-based cluster states", Physical Review Research 4 1, 013010 (2022).

[33] Elena Berardini, Reza Dastbasteh, Josu Etxezarreta Martinez, Shreyas Jain, and Olatz Sanz Larrarte, "Asymptotically Good CSS-T Codes and a New Construction of Triorthogonal Codes", IEEE Journal on Selected Areas in Information Theory 6, 189 (2025).

[34] Andrew S. Darmawan, Yoshifumi Nakata, Shiro Tamiya, and Hayata Yamasaki, "Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder", Physical Review Research 6 2, 023055 (2024).

[35] Yujin Kang, Youshin Chung, Huidan Zheng, Sungyeon Kook, and Jun Heo, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 416 (2024) ISBN:979-8-3315-4137-8.

[36] David Aasen, Morteza Aghaee, Zulfi Alam, Mariusz Andrzejczuk, Andrey Antipov, Mikhail Astafev, Lukas Avilovas, Amin Barzegar, Bela Bauer, Jonathan Becker, Juan M. Bello-Rivas, Umesh Bhaskar, Alex Bocharov, Srini Boddapati, David Bohn, Jouri Bommer, Parsa Bonderson, Jan Borovsky, Leo Bourdet, Samuel Boutin, Tom Brown, Gary Campbell, Lucas Casparis, Srivatsa Chakravarthi, Rui Chao, Benjamin J. Chapman, Sohail Chatoor, Anna Wulff Christensen, Patrick Codd, William Cole, Paul Cooper, Fabiano Corsetti, Ajuan Cui, Wim van Dam, Tareq El Dandachi, Sahar Daraeizadeh, Adrian Dumitrascu, Andreas Ekefjärd, Saeed Fallahi, Luca Galletti, Geoff Gardner, Raghu Gatta, Haris Gavranovic, Michael Goulding, Deshan Govender, Flavio Griggio, Ruben Grigoryan, Sebastian Grijalva, Sergei Gronin, Jan Gukelberger, Jeongwan Haah, Marzie Hamdast, Esben Bork Hansen, Matthew Hastings, Sebastian Heedt, Samantha Ho, Justin Hogaboam, Laurens Holgaard, Kevin Van Hoogdalem, Jinnapat Indrapiromkul, Henrik Ingerslev, Lovro Ivancevic, Sarah Jablonski, Thomas Jensen, Jaspreet Jhoja, Jeffrey Jones, Kostya Kalashnikov, Ray Kallaher, Rachpon Kalra, Farhad Karimi, Torsten Karzig, Seth Kimes, Vadym Kliuchnikov, Maren Elisabeth Kloster, Christina Knapp, Derek Knee, Jonne Koski, Pasi Kostamo, Jamie Kuesel, Brad Lackey, Tom Laeven, Jeffrey Lai, Gijs de Lange, Thorvald Larsen, Jason Lee, Kyunghoon Lee, Grant Leum, Kongyi Li, Tyler Lindemann, Marijn Lucas, Roman Lutchyn, Morten Hannibal Madsen, Nash Madulid, Michael Manfra, Signe Brynold Markussen, Esteban Martinez, Marco Mattila, Jake Mattinson, Robert McNeil, Antonio Rodolph Mei, Ryan V. Mishmash, Gopakumar Mohandas, Christian Mollgaard, Michiel de Moor, Trevor Morgan, George Moussa, Anirudh Narla, Chetan Nayak, Jens Hedegaard Nielsen, William Hvidtfelt Padkær Nielsen, Frédéric Nolet, Mike Nystrom, Eoin O’Farrell, Keita Otani, Adam Paetznick, Camille Papon, Andres Paz, Karl Petersson, Luca Petit, Dima Pikulin, Diego Olivier Fernandez Pons, Sam Quinn, Mohana Rajpalke, Alejandro Alcaraz Ramirez, Katrine Rasmussen, David Razmadze, Ben Reichardt, Yuan Ren, Ken Reneris, Roy Riccomini, Ivan Sadovskyy, Lauri Sainiemi, Juan Carlos Estrada Saldaña, Irene Sanlorenzo, Simon Schaal, Emma Schmidgall, Cristina Sfiligoj, Marcus P. da Silva, Shilpi Singh, Sarat Sinha, Mathias Soeken, Patrick Sohr, Tomas Stankevic, Lieuwe Stek, Patrick Strøm-Hansen, Eric Stuppard, Aarthi Sundaram, Henri Suominen, Judith Suter, Satoshi Suzuki, Krysta Svore, Sam Teicher, Nivetha Thiyagarajah, Raj Tholapi, Mason Thomas, Dennis Tom, Emily Toomey, Josh Tracy, Matthias Troyer, Michelle Turley, Matthew D. Turner, Shivendra Upadhyay, Ivan Urban, Alexander Vaschillo, Dmitrii Viazmitinov, Dominik Vogel, Zhenghan Wang, John Watson, Alex Webster, Joseph Weston, Timothy Williamson, Georg W. Winkler, David J. van Woerkom, Brian Paquelet Wütz, Chung Kai Yang, Richard Yu, Emrah Yucelen, Jesús Herranz Zamorano, Roland Zeisel, Guoji Zheng, Justin Zilke, and Andrew Zimmerman, "Blueprint for fault-tolerant quantum computation with topological qubit arrays", Physical Review Research 7 4, 041002 (2025).

[37] Joshua Viszlai, Willers Yang, Sophia Lin, Junyu Liu, Natalia Nottingham, Jonathan Baker, and Frederic Chong, "qSIEVE: Efficient qLDPC Memory via Systolic Movement in Atom Arrays", ACM Transactions on Quantum Computing 7 2, 1 (2026).

[38] Tyler Leblond, Christopher Dean, George Watkins, and Ryan Bennink, "Realistic Cost to Execute Practical Quantum Circuits using Direct Clifford+T Lattice Surgery Compilation", ACM Transactions on Quantum Computing 5 4, 1 (2024).

[39] Andreas Bauer, "Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases", Quantum 9, 1673 (2025).

[40] Principles of Superconducting Quantum Computers 327 (2022) ISBN:9781119750727.

[41] Kwok Ho Wan, Zhenghao Zhong, and Ainhoa Zapirain, "Simulating magic state cultivation with few Clifford terms", Quantum 10, 2134 (2026).

[42] Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, and Keisuke Fujii, "Efficient Magic State Distillation by Zero-Level Distillation", PRX Quantum 6 2, 020356 (2025).

[43] Isaac H. Kim, Ye-Hua Liu, Sam Pallister, William Pol, Sam Roberts, and Eunseok Lee, "Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules", Physical Review Research 4 2, 023019 (2022).

[44] Diego Ristè, Luke C. G. Govia, Brian Donovan, Spencer D. Fallek, William D. Kalfus, Markus Brink, Nicholas T. Bronn, and Thomas A. Ohki, "Real-time processing of stabilizer measurements in a bit-flip code", npj Quantum Information 6 1, 71 (2020).

[45] Yotam Vaknin, Shoham Jacoby, Arne Grimsmo, and Alex Retzker, "High Rate Magic State Cultivation on the Surface Code", PRX Quantum 7 1, 010353 (2026).

[46] Samuel C. Smith, Benjamin J. Brown, and Stephen D. Bartlett, "Mitigating errors in logical qubits", Communications Physics 7 1, 386 (2024).

[47] Daniel Bochen Tan, Murphy Yuezhen Niu, and Craig Gidney, 2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA) 325 (2024) ISBN:979-8-3503-2658-1.

[48] Tathagata Karmakar, Philippe Lewalle, Yipei Zhang, and K. Birgitta Whaley, "Noise-canceling quantum feedback: Non-Hermitian dynamics with applications to state preparation and magic state distillation", Physical Review A 113 4, 042403 (2026).

[49] Nick S. Blunt, György P. Gehér, and Alexandra E. Moylett, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 290 (2023) ISBN:979-8-3503-4323-6.

[50] Matthew Sullivan, "Code conversion with the quantum Golay code for a universal transversal gate set", Physical Review A 109 4, 042416 (2024).

[51] S.N. Saadatmand, Tyler L. Wilson, Mark J. Hodson, Mark Field, Simon J. Devitt, Madhav Krishnan Vijayan, Alan Robertson, Thinh P. Le, Jannis Ruh, Alexandru Paler, Arshpreet Singh Maan, Ioana Moflic, Athena Caesura, and Josh Y. Mutus, "Superconducting qubits in the millions: The potential and limitations of modularity", Physical Review Applied 25 6, 064038 (2026).

[52] Rini Wisnu Wardhani, Dedy Septono Catur Putranto, and Howon Kim, Lecture Notes in Computer Science 15596, 209 (2025) ISBN:978-981-96-5565-6.

[53] Siyuan Niu, Di Wu, Ozgur Kilic, and Kwangmin Yu, Proceedings of the 16th ACM International Green and Sustainable Computing Conference 132 (2026) ISBN:9798400725203.

[54] Manoj G. Gowda and Pradeep Kiran Sarvepalli, "Color codes with twists: Construction and universal-gate-set implementation", Physical Review A 104 1, 012603 (2021).

[55] Jakob Günther, Freek Witteveen, Alexander Schmidhuber, Marek Miller, Matthias Christandl, and Aram W. Harrow, "Phase Estimation with Partially Randomized Time Evolution", PRX Quantum 7 2, 020332 (2026).

[56] Pedro Sales Rodriguez, John M. Robinson, Paul Niklas Jepsen, Zhiyang He, Casey Duckering, Chen Zhao, Kai-Hsin Wu, Joseph Campo, Kevin Bagnall, Minho Kwon, Thomas Karolyshyn, Phillip Weinberg, Madelyn Cain, Simon J. Evered, Alexandra A. Geim, Marcin Kalinowski, Sophie H. Li, Tom Manovitz, Jesse Amato-Grill, James I. Basham, Liane Bernstein, Boris Braverman, Alexei Bylinskii, Adam Choukri, Robert J. DeAngelo, Fang Fang, Connor Fieweger, Paige Frederick, David Haines, Majd Hamdan, Julian Hammett, Ning Hsu, Ming-Guang Hu, Florian Huber, Ningyuan Jia, Dhruv Kedar, Milan Kornjača, Fangli Liu, John Long, Jonathan Lopatin, Pedro L. S. Lopes, Xiu-Zhe Luo, Tommaso Macrì, Ognjen Marković, Luis A. Martínez-Martínez, Xianmei Meng, Stefan Ostermann, Evgeny Ostroumov, David Paquette, Zexuan Qiang, Vadim Shofman, Anshuman Singh, Manuj Singh, Nandan Sinha, Henry Thoreen, Noel Wan, Yiping Wang, Daniel Waxman-Lenz, Tak Wong, Jonathan Wurtz, Andrii Zhdanov, Laurent Zheng, Markus Greiner, Alexander Keesling, Nathan Gemelke, Vladan Vuletić, Takuya Kitagawa, Sheng-Tao Wang, Dolev Bluvstein, Mikhail D. Lukin, Alexander Lukin, Hengyun Zhou, and Sergio H. Cantú, "Experimental demonstration of logical magic state distillation", Nature 645 8081, 620 (2025).

[57] Eric Kubischta and Ian Teixeira, "Quantum Codes from Twisted Unitary t -Groups", Physical Review Letters 133 3, 030602 (2024).

[58] Satvik Maurya and Swamit Tannu, Proceedings of the 52nd Annual International Symposium on Computer Architecture 1370 (2025) ISBN:9798400712616.

[59] Emanuel Dallas and Paolo Zanardi, "Nonlocal nonstabilizerness generation and information scrambling in noisy Clifford circuits", Physical Review A 113 4, 042429 (2026).

[60] Chenghong Zhu, Xian Wu, Jiahan Chen, Keming He, Junjie Wu, Xin Wang, and Lingling Lao, 2026 ACM/IEEE 53rd Annual International Symposium on Computer Architecture (ISCA) 2096 (2026) ISBN:979-8-3315-5065-3.

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

[62] Paul Renault, Patrick Yard, Raphael C. Pooser, Miller Eaton, and Hussain Asim Zaidi, "End-to-end switchless architecture for fault-tolerant photonic quantum computing", Quantum 9, 1796 (2025).

[63] Shin Ho Choe and Robert König, "Long-range data transmission in a fault-tolerant quantum bus architecture", npj Quantum Information 10 1, 132 (2024).

[64] Nicholas Fazio, Robin Harper, and Stephen D. Bartlett, "Logical Noise Bias in Magic State Injection", Quantum 9, 1779 (2025).

[65] Matthew Otten, Byeol Kang, Dmitry Fedorov, Joo-Hyoung Lee, Anouar Benali, Salman Habib, Stephen K. Gray, and Yuri Alexeev, "QREChem: quantum resource estimation software for chemistry applications", Frontiers in Quantum Science and Technology 2, 1232624 (2023).

[66] Francisco Orts, Gloria Ortega, Elías F. Combarro, Ignacio F. Rúa, and Ester M. Garzón, "Quantum circuits for computing Hamming distance requiring fewer T gates", The Journal of Supercomputing 80 9, 12527 (2024).

[67] Kyungjoo Noh, Liang Jiang, and Bill Fefferman, "Efficient classical simulation of noisy random quantum circuits in one dimension", Quantum 4, 318 (2020).

[68] M. Lostaglio and A. Ciani, "Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime", Physical Review Letters 127 20, 200506 (2021).

[69] Jacob S. Nelson and Andrew D. Baczewski, "Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers", Physical Review A 110 4, 042420 (2024).

[70] Sanaa Sharma and Prakash Murali, 2026 IEEE/ACM International Symposium on Code Generation and Optimization (CGO) 281 (2026) ISBN:979-8-3315-9288-2.

[71] Yasunori Lee and Keita Kanno, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 2170 (2025) ISBN:979-8-3315-5736-2.

[72] Armanda O. Quintavalle, Paul Webster, and Michael Vasmer, "Partitioning qubits in hypergraph product codes to implement logical gates", Quantum 7, 1153 (2023).

[73] Poetri Sonya Tarabunga, Martina Frau, Tobias Haug, Emanuele Tirrito, and Lorenzo Piroli, "A nonstabilizerness monotone from stabilizerness asymmetry", Quantum Science and Technology 10 4, 045026 (2025).

[74] Krishna Kumar, 2025 International Conference on Computing Technologies (ICOCT) 1 (2025) ISBN:979-8-3315-1637-6.

[75] Gökhan Torun, Hüseyin Talha Şenyaşa, and Ali Yildiz, "Resource theory of superposition: State transformations", Physical Review A 103 3, 032416 (2021).

[76] Nick S. Blunt, Joan Camps, Ophelia Crawford, Róbert Izsák, Sebastian Leontica, Arjun Mirani, Alexandra E. Moylett, Sam A. Scivier, Christoph Sünderhauf, Patrick Schopf, Jacob M. Taylor, and Nicole Holzmann, "Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications", Journal of Chemical Theory and Computation 18 12, 7001 (2022).

[77] Dominik Szombathy, Angelo Valli, Cătălin Paşcu Moca, János Asbóth, Lóránt Farkas, Tibor Rakovszky, and Gergely Zaránd, "Spectral properties versus magic generation in T -doped random Clifford circuits", Physical Review Research 7 4, 043080 (2025).

[78] Nikolaos Koukoulekidis and David Jennings, "Constraints on magic state protocols from the statistical mechanics of Wigner negativity", npj Quantum Information 8 1, 42 (2022).

[79] Su-un Lee, Ming Yuan, Senrui Chen, Kento Tsubouchi, and Liang Jiang, "Efficient Benchmarking of Logical Magic State", Physical Review Letters 136 5, 050602 (2026).

[80] Campbell K. McLauchlan and Benjamin Béri, "Fermion-Parity-Based Computation and Its Majorana-Zero-Mode Implementation", Physical Review Letters 128 18, 180504 (2022).

[81] Jérémie Guillaud and Mazyar Mirrahimi, "Error rates and resource overheads of repetition cat qubits", Physical Review A 103 4, 042413 (2021).

[82] Christopher Chamberland, Kyungjoo Noh, Patricio Arrangoiz-Arriola, Earl T. Campbell, Connor T. Hann, Joseph Iverson, Harald Putterman, Thomas C. Bohdanowicz, Steven T. Flammia, Andrew Keller, Gil Refael, John Preskill, Liang Jiang, Amir H. Safavi-Naeini, Oskar Painter, and Fernando G.S.L. Brandão, "Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes", PRX Quantum 3 1, 010329 (2022).

[83] Gaurav Saxena and Gilad Gour, "Quantifying multiqubit magic channels with completely stabilizer-preserving operations", Physical Review A 106 4, 042422 (2022).

[84] Héctor Bombín, Chris Dawson, Ryan V. Mishmash, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Logical Blocks for Fault-Tolerant Topological Quantum Computation", PRX Quantum 4 2, 020303 (2023).

[85] Michael Hanks, Marta P. Estarellas, William J. Munro, and Kae Nemoto, "Effective Compression of Quantum Braided Circuits Aided by ZX-Calculus", Physical Review X 10 4, 041030 (2020).

[86] Shinichi Sunami, Yutaka Hirano, Toshihide Hinokuma, and Hayata Yamasaki, "Entanglement Boosting: Low-Volume Logical Bell Pair Preparation for Distributed Fault-Tolerant Quantum Computation", PRX Quantum 7 3, 033014 (2026).

[87] Xiao Huang, Guanhua Chen, and Yao Yao, "Advantage of utilizing nonlocal magic resource in Haar-random circuits", Journal of Physics A: Mathematical and Theoretical 59 2, 025302 (2026).

[88] Armands Strikis, Simon C. Benjamin, and Benjamin J. Brown, "Quantum Computing is Scalable on a Planar Array of Qubits with Fabrication Defects", Physical Review Applied 19 6, 064081 (2023).

[89] Yiran Wang and Yongming Li, "Stabilizer Rényi entropy on qudits", Quantum Information Processing 22 12, 444 (2023).

[90] Campbell McLauchlan and Benjamin Béri, "A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation", Quantum 8, 1400 (2024).

[91] Samuel Stein, Sara Sussman, Teague Tomesh, Charles Guinn, Esin Tureci, Sophia Fuhui Lin, Wei Tang, James Ang, Srivatsan Chakram, Ang Li, Margaret Martonosi, Fred Chong, Andrew A. Houck, Isaac L. Chuang, and Michael Demarco, 56th Annual IEEE/ACM International Symposium on Microarchitecture 539 (2023) ISBN:9798400703294.

[92] Haiyue Kang, Younghun Kim, Eromanga Adermann, Martin Sevior, and Muhammad Usman, "Almost fault-tolerant quantum machine learning with drastic overhead reduction", Quantum Science and Technology 11 1, 015021 (2026).

[93] Hassan Soubra, Hatem Elsayed, Yousef Elbrolosy, Youssef Adel, and Zeyad Attia, "Comprehensive Review of Metrics and Measurements of Quantum Systems", Metrics 2 2, 9 (2025).

[94] Jason Gavriel, Daniel Herr, Alexis Shaw, Michael J. Bremner, Alexandru Paler, and Simon J. Devitt, "Transversal injection for direct encoding of ancilla states for non-Clifford gates using stabilizer codes", Physical Review Research 5 3, 033019 (2023).

[95] Riddhi S. Gupta, Neereja Sundaresan, Thomas Alexander, Christopher J. Wood, Seth T. Merkel, Michael B. Healy, Marius Hillenbrand, Tomas Jochym-O’Connor, James R. Wootton, Theodore J. Yoder, Andrew W. Cross, Maika Takita, and Benjamin J. Brown, "Encoding a magic state with beyond break-even fidelity", Nature 625 7994, 259 (2024).

[96] Christopher Chamberland and Kyungjoo Noh, "Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits", npj Quantum Information 6 1, 91 (2020).

[97] Tanay Saha and Shiroman Prakash, "Sublogarithmic distillation in all prime dimensions using punctured Reed-Muller codes", Physical Review A 113 4, 042405 (2026).

[98] Laura M. Donaire, Gloria Ortega, and Francisco Orts, Lecture Notes in Computer Science 15386, 367 (2025) ISBN:978-3-031-90202-4.

[99] Surabhi Luthra, Alexandra E Moylett, Dan E Browne, and Earl T Campbell, "Unlocking early fault-tolerant quantum computing with mitigated magic dilution", Quantum Science and Technology 10 4, 045066 (2025).

[100] You‐Seok Lee, Jongheon Lee, and Yousung Kang, "QCrypton: An integrated platform for resource‐based quantum security strength evaluation of cryptographic algorithms", ETRI Journal 48 3, 397 (2026).

[101] Felix Thomsen, Markus S. Kesselring, Stephen D. Bartlett, and Benjamin J. Brown, "Low-overhead quantum computing with the color code", Physical Review Research 6 4, 043125 (2024).

[102] Jiaxuan Zhang, Yu-Chun Wu, and Guo-Ping Guo, "Facilitating practical fault-tolerant quantum computing based on color codes", Physical Review Research 6 3, 033086 (2024).

[103] Riki Toshio, Yutaro Akahoshi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, and Keisuke Fujii, "Practical Quantum Advantage on Partially Fault-Tolerant Quantum Computer", Physical Review X 15 2, 021057 (2025).

[104] Keyi Yin, Xiang Fang, Zhuo Chen, David Hayes, Eneet Kaur, Reza Nejabati, Hartmut Haeffner, Wes Campbell, Eric Hudson, Jens Palsberg, Travis Humble, and Yufei Ding, Proceedings of the 31st ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 1007 (2026) ISBN:9798400723599.

[105] Jia‐Ning Li, Tian‐Hao Wei, Zi‐Hao Mei, Qi Zhou, Wei‐Cheng Kong, Jiaxuan Zhang, Yu‐Chun Wu, and Guo‐Ping Guo, "Real‐Time Decoding For Surface Code", Advanced Quantum Technologies 9 5, e00806 (2026).

[106] Michael Vasmer and Aleksander Kubica, "Morphing Quantum Codes", PRX Quantum 3 3, 030319 (2022).

[107] Kazuki Sakamoto, Hayata Morisaki, Junichi Haruna, Etsuko Itou, Keisuke Fujii, and Kosuke Mitarai, "End-to-end complexity for simulating the Schwinger model on quantum computers", Quantum 8, 1474 (2024).

[108] Christophe Piveteau, David Sutter, Sergey Bravyi, Jay M. Gambetta, and Kristan Temme, "Error Mitigation for Universal Gates on Encoded Qubits", Physical Review Letters 127 20, 200505 (2021).

[109] Ilkwon Byun, Junpyo Kim, Dongmoon Min, Ikki Nagaoka, Kosuke Fukumitsu, Iori Ishikawa, Teruo Tanimoto, Masamitsu Tanaka, Koji Inoue, and Jangwoo Kim, Proceedings of the 49th Annual International Symposium on Computer Architecture 366 (2022) ISBN:9781450386104.

[110] Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D. Bartlett, "Universal fault-tolerant quantum computing with stabilizer codes", Physical Review Research 4 1, 013092 (2022).

[111] Zhu Sun and Bálint Koczor, "Space and time cost of continuous rotations in surface codes", Quantum Science and Technology 11 2, 025046 (2026).

[112] Alexander J. Malcolm, Andrew N. Glaudell, Patricio Fuentes, Daryus Chandra, Alexis Schotte, Colby DeLisle, Rafael Haenel, Amir Ebrahimi, Joschka Roffe, Armanda O. Quintavalle, Stefanie J. Beale, Nicholas R. Lee-Hone, and Stephanie Simmons, "Computing efficiently in QLDPC codes", Nature Communications 17 1, 7286 (2026).

[113] Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Darío Gil, and Zaira Nazario, "The future of quantum computing with superconducting qubits", Journal of Applied Physics 132 16, 160902 (2022).

[114] César Benito, Esperanza López, Borja Peropadre, and Alejandro Bermudez, "Comparative study of quantum error correction strategies for the heavy-hexagonal lattice", Quantum 9, 1623 (2025).

[115] Lingling Lao and Ben Criger, Proceedings of the 19th ACM International Conference on Computing Frontiers 113 (2022) ISBN:9781450393386.

[116] Jeongwan Haah and Matthew B. Hastings, "Measurement sequences for magic state distillation", Quantum 5, 383 (2021).

[117] Mikkel V. Larsen, Christopher Chamberland, Kyungjoo Noh, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen, "Fault-Tolerant Continuous-Variable Measurement-based Quantum Computation Architecture", PRX Quantum 2 3, 030325 (2021).

[118] György P. Gehér, Campbell McLauchlan, Earl T. Campbell, Alexandra E. Moylett, and Ophelia Crawford, "Error-corrected Hadamard gate simulated at the circuit level", Quantum 8, 1394 (2024).

[119] Samuel Stein, Shifan Xu, Andrew W. Cross, Theodore J. Yoder, Ali Javadi-Abhari, Chenxu Liu, Kun Liu, Zeyuan Zhou, Charlie Guinn, Yufei Ding, Yongshan Ding, and Ang Li, Proceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 515 (2025) ISBN:9798400710797.

[120] George Watkins, Hoang Minh Nguyen, Keelan Watkins, Steven Pearce, Hoi-Kwan Lau, and Alexandru Paler, "A High Performance Compiler for Very Large Scale Surface Code Computations", Quantum 8, 1354 (2024).

[121] Paul Webster and Stephen D. Bartlett, "Fault-tolerant quantum gates with defects in topological stabilizer codes", Physical Review A 102 2, 022403 (2020).

[122] Takumi Kobori, Yasunari Suzuki, Yosuke Ueno, Teruo Tanimoto, Synge Todo, and Yuuki Tokunaga, 2025 IEEE International Symposium on High Performance Computer Architecture (HPCA) 304 (2025) ISBN:979-8-3315-0647-6.

[123] 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).

[124] David Aram Korbany, Michael J. Gullans, and Lorenzo Piroli, "Long-Range Nonstabilizerness and Phases of Matter", Physical Review Letters 135 16, 160404 (2025).

[125] Hengyun Zhou, Madelyn Cain, and Mikhail D. Lukin, "Opportunities in full-stack design of low-overhead fault-tolerant quantum computation", Nature Computational Science 5 12, 1110 (2025).

[126] S. Pathak, A. E. Russo, S. K. Seritan, and A. D. Baczewski, "Quantifying T -gate-count improvements for ground-state-energy estimation with near-optimal state preparation", Physical Review A 107 4, L040601 (2023).

[127] Y. Herasymenko and T.E. O'Brien, "A diagrammatic approach to variational quantum ansatz construction", Quantum 5, 596 (2021).

[128] Yutaka Hirano, Tomohiro Itogawa, and Keisuke Fujii, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 843 (2024) ISBN:979-8-3315-4137-8.

[129] Haipeng Xie, Nobuyuki Yoshioka, Kento Tsubouchi, and Ying Li, "Noise-Agnostic Unbiased Quantum Error Mitigation for Logical Qubits", Physical Review Letters 136 1, 010603 (2026).

[130] Jiahan Chen, Chenghong Zhu, Ge Bai, and Xin Wang, 2026 ACM/IEEE 53rd Annual International Symposium on Computer Architecture (ISCA) 842 (2026) ISBN:979-8-3315-5065-3.

[131] Héctor Bombín, Mihir Pant, Sam Roberts, and Karthik I. Seetharam, "Fault-Tolerant Postselection for Low-Overhead Magic State Preparation", PRX Quantum 5 1, 010302 (2024).

[132] Andreas Bauer and Julio C. Magdalena de la Fuente, "Planar Fault-Tolerant Circuits for Non-Clifford Gates on the 2D Color Code", PRX Quantum 7 2, 020367 (2026).

[133] F. Orts, E. Filatovas, G. Ortega, J. F. SanJuan-Estrada, and E. M. Garzón, "Improving the number of T gates and their spread in integer multipliers on quantum computing", Physical Review A 107 4, 042621 (2023).

[134] Craig Gidney and Martin Ekerå, "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits", Quantum 5, 433 (2021).

[135] Seok-Hyung Lee, Felix Thomsen, Nicholas Fazio, Benjamin J. Brown, and Stephen D. Bartlett, "Low-Overhead Magic State Distillation with Color Codes", PRX Quantum 6 3, 030317 (2025).

[136] Eloi Descamps, Astghik Saharyan, Adrien Chivet, Arne Keller, and Pérola Milman, "Unified framework for bosonic quantum information encoding, resources, and universality from superselection rules", Optica Quantum 4 2, 148 (2026).

[137] Linsen Li, Lorenzo De Santis, Isaac B. W. Harris, Kevin C. Chen, Yihuai Gao, Ian Christen, Hyeongrak Choi, Matthew Trusheim, Yixuan Song, Carlos Errando-Herranz, Jiahui Du, Yong Hu, Genevieve Clark, Mohamed I. Ibrahim, Gerald Gilbert, Ruonan Han, and Dirk Englund, "Heterogeneous integration of spin–photon interfaces with a CMOS platform", Nature 630 8015, 70 (2024).

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

[139] Noah Shutty and Christopher Chamberland, "Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories", Physical Review Applied 18 1, 014072 (2022).

[140] Meng Wang, Chenxu Liu, Samuel Stein, Yufei Ding, Poulami Das, Prashant J. Nair, and Ang Li, 2026 ACM/IEEE 53rd Annual International Symposium on Computer Architecture (ISCA) 889 (2026) ISBN:979-8-3315-5065-3.

[141] Simon Martiel and Timothée Goubault de Brugière, "Architecture aware compilation of quantum circuits via lazy synthesis", Quantum 6, 729 (2022).

[142] Christopher Chamberland and Earl T. Campbell, "Universal Quantum Computing with Twist-Free and Temporally Encoded Lattice Surgery", PRX Quantum 3 1, 010331 (2022).

[143] Joonho Lee, Dominic W. Berry, Craig Gidney, William J. Huggins, Jarrod R. McClean, Nathan Wiebe, and Ryan Babbush, "Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction", PRX Quantum 2 3, 030305 (2021).

[144] Jason Gavriel, Daniel Herr, Alexis Shaw, Michael J. Bremner, Alexandru Paler, and Simon J. Devitt, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 910 (2023) ISBN:979-8-3503-4323-6.

[145] Hao Dai, Shuangshuang Fu, and Shunlong Luo, "Detecting Magic States via Characteristic Functions", International Journal of Theoretical Physics 61 2, 35 (2022).

[146] Santeri Huhtanen, Yousef Mafi, Ali G. Moghaddam, and Teemu Ojanen, "Many-body entanglement swapping protocol: Opportunities for distributed quantum computing", Physical Review Research 8 1, 013152 (2026).

[147] Kento Oonishi and Noboru Kunihiro, "An Evaluation of Computational Complexity of Shor’s Algorithm on Surface Codes for Factorization", IEEE Access 14, 27264 (2026).

[148] Masahiro Hoshino, Masaki Oshikawa, and Yuto Ashida, "Stabilizer Rényi Entropy and Conformal Field Theory", Physical Review X 16 1, 011037 (2026).

[149] Jixuan Ruan, Xiang Fang, Hezi Zhang, Ang Li, Travis Humble, and Yufei Ding, Proceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3 163 (2025) ISBN:9798400710803.

[150] Michael E. Beverland, Aleksander Kubica, and Krysta M. Svore, "Cost of Universality: A Comparative Study of the Overhead of State Distillation and Code Switching with Color Codes", PRX Quantum 2 2, 020341 (2021).

[151] Joshua Viszlai, Sophia Lin, Siddharth Dangwal, Conor Bradley, Vikram Ramesh, Jonathan Baker, Hannes Bernien, and Frederic T. Chong, 2025 IEEE International Symposium on High Performance Computer Architecture (HPCA) 261 (2025) ISBN:979-8-3315-0647-6.

[152] Aleksei V. Ivanov, Andrew Patterson, Marius Bothe, Christoph Sünderhauf, Bjorn K. Berntson, Jens Jørgen Mortensen, Mikael Kuisma, Earl Campbell, and Róbert Izsák, "Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set", Journal of Chemical Theory and Computation 21 15, 7360 (2025).

[153] Linghang Kong, Fang Zhang, and Jianxin Chen, "Benchmarking fault-tolerant quantum computing hardware via QLOPS", ACM Transactions on Quantum Computing 7 2, 1 (2026).

[154] Bernard Ousmane Sane, Praveen Balaji, Michal Hajdusek, Liang Jiang, and Rodney Van Meter, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1284 (2024) ISBN:979-8-3315-4137-8.

[155] Keming He, Chengkai Zhu, Hongshun Yao, Jinguo Liu, Yinan Li, and Xin Wang, "No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations", Physical Review Letters 136 9, 090204 (2026).

[156] Laura M. Donaire, Gloria Ortega, Francisco Orts, and Ester M. Garzón, Lecture Notes in Computer Science 15385, 64 (2025) ISBN:978-3-031-90199-7.

[157] Yaniv Kurman, Lior Ella, Ramon Szmuk, Oded Wertheim, Benedikt Dorschner, Sam Stanwyck, and Yonatan Cohen, "Benchmarking the Ability of a Controller to Execute Quantum Error Corrected Non-Clifford Circuits", IEEE Transactions on Quantum Engineering 6, 1 (2025).

[158] Hugo Jacinto, Élie Gouzien, and Nicolas Sangouard, "Network requirements for distributed quantum computation", Physical Review Research 8 1, 013205 (2026).

[159] Julio Carlos Magdalena de la Fuente, Nicolas Tarantino, and Jens Eisert, "Non-Pauli topological stabilizer codes from twisted quantum doubles", Quantum 5, 398 (2021).

[160] Zhi-Cheng He and Zheng-Yuan Xue, "Error-mitigated initialization of surface codes with non-Pauli stabilizers", Physical Review A 110 5, 052441 (2024).

[161] Shraddha Singh, Andrew S. Darmawan, Benjamin J. Brown, and Shruti Puri, "High-fidelity magic-state preparation with a biased-noise architecture", Physical Review A 105 5, 052410 (2022).

[162] Yiting Liu, Zhi Ma, Lan Luo, Chao Du, Yangyang Fei, Hong Wang, Qianheng Duan, and Jing Yang, "Magic state distillation and cost analysis in fault-tolerant universal quantum computation", Quantum Science and Technology 8 4, 043001 (2023).

[163] Zhi-Cheng He and Zheng-Yuan Xue, "High-fidelity initialization of a logical qubit with multiple injections", Physical Review A 111 5, 052419 (2025).

[164] David Gosset, Robin Kothari, and Kewen Wu, "Quantum state preparation with optimal T-count", Quantum 10, 2168 (2026).

[165] Ryuji Takagi and Hiroyasu Tajima, "Universal limitations on implementing resourceful unitary evolutions", Physical Review A 101 2, 022315 (2020).

[166] Mamtha Prajapati and Kalyan Babu Killana, 2025 3rd International Conference on Device Intelligence, Computing and Communication Technologies (DICCT) 230 (2025) ISBN:979-8-3315-4335-8.

[167] Koki Shiraishi, Hayata Yamasaki, and Mio Murao, "Efficient local operations and classical communication extraction of quantum information encoded in stabilizer codes", Physical Review A 110 5, 052617 (2024).

[168] Mark L. Turner, Earl T. Campbell, Ophelia Crawford, Neil I. Gillespie, and Joan Camps, "Scalable Decoding Protocols for Fast Transversal Logic in the Surface Code", PRX Quantum 7 1, 010320 (2026).

[169] Shinichi Sunami, Shiro Tamiya, Ryotaro Inoue, Hayata Yamasaki, and Akihisa Goban, "Scalable Networking of Neutral-Atom Qubits: Nanofiber-Based Approach for Multiprocessor Fault-Tolerant Quantum Computers", PRX Quantum 6 1, 010101 (2025).

[170] Casey Duckering, Jonathan M. Baker, David I. Schuster, and Frederic T. Chong, 2020 53rd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO) 173 (2020) ISBN:978-1-7281-7383-2.

[171] Siddharth Dangwal, Suhas Vittal, Lennart Maximilian Seifert, Frederic T. Chong, and Gokul Subramanian Ravi, Proceedings of the 52nd Annual International Symposium on Computer Architecture 1417 (2025) ISBN:9798400712616.

[172] Zhaoyi Li, Isaac Kim, and Patrick Hayden, "Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction", Quantum 7, 1089 (2023).

[173] Pedro Parrado-Rodríguez, Manuel Rispler, and Markus Müller, "Rescaling decoder for two-dimensional topological quantum color codes on 4.8.8 lattices", Physical Review A 106 3, 032431 (2022).

[174] Laura María Donaire, Gloria Ortega, Ester M. Garzón, Francisco Orts, Remigijus Paulavičius, and Ernestas Filatovas, Lecture Notes in Computer Science 15580, 290 (2025) ISBN:978-3-031-85699-0.

[175] Jiaxuan Zhang, Tian-Hao Wei, Xi-Ning Zhuang, Zhao-Yun Chen, Wei-Cheng Kong, Yu-Chun Wu, and Guo-Ping Guo, "Low-Overhead and High-Fidelity Preparation of Logical Non-Clifford States with Multilevel Transversal Injection", Physical Review Letters 136 8, 080603 (2026).

[176] Shayan Srinivasa Garani, Priya J. Nadkarni, and Ankur Raina, "Theory Behind Quantum Error Correcting Codes: An Overview", Journal of the Indian Institute of Science 103 2, 449 (2023).

[177] Samuel J. Elman, Jason Gavriel, and Ryan L. Mann, "Optimal scheduling of graph states via path decompositions", Physical Review A 111 1, 012627 (2025).

[178] Yaniv Kurman, Lior Ella, Nir Halay, Oded Wertheim, and Yonatan Cohen, "Controller-decoder system requirements derived by implementing Shor's algorithm with surface code", Quantum 10, 2170 (2026).

[179] Timothy Proctor, Kevin Young, Andrew D. Baczewski, and Robin Blume-Kohout, "Benchmarking quantum computers", Nature Reviews Physics 7 2, 105 (2025).

[180] Thomas Häner, Damian S. Steiger, Torsten Hoefler, and Matthias Troyer, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2021) ISBN:9781450384421.

[181] Sepehr Nezami and Jeongwan Haah, "Classification of small triorthogonal codes", Physical Review A 106 1, 012437 (2022).

[182] Yujin Kang, Youshin Chung, and Jun Heo, "Space‐Efficient Logical Qubit Architecture with a Bus for Magic State Consumption", Advanced Quantum Technologies 9 4, e00505 (2026).

[183] Filipa C R Peres, Rafael Wagner, and Ernesto F Galvão, "Non-stabilizerness and entanglement from cat-state injection", New Journal of Physics 26 1, 013051 (2024).

[184] Eromanga Adermann, Haiyue Kang, Martin Sevior, and Muhammad Usman, Quantum Science and Technology 413 (2026) ISBN:978-3-032-11152-4.

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

[186] Laura M. Donaire, Gloria Ortega, Ester M. Garzón, and Francisco Orts, "Lowering the cost of quantum comparator circuits", The Journal of Supercomputing 80 10, 13900 (2024).

[187] Tobias Haug and Poetri Sonya Tarabunga, "Efficient witnessing and testing of magic in mixed quantum states", npj Quantum Information 12 1, 40 (2026).

[188] Stefano Veroni, Alexandru Paler, and Giacomo Giudice, "Universal Quantum Computation via Scalable Measurement-Free Error Correction", PRX Quantum 6 4, 040337 (2025).

[189] Evan T. Hockings, Andrew C. Doherty, and Robin Harper, "Scalable Noise Characterization of Syndrome-Extraction Circuits with Averaged Circuit Eigenvalue Sampling", PRX Quantum 6 1, 010334 (2025).

[190] Ilya Besedin, Michael Kerschbaum, Jonathan Knoll, Ian Hesner, Lukas Bödeker, Luis Colmenarez, Luca Hofele, Nathan Lacroix, Christoph Hellings, François Swiadek, Alexander Flasby, Mohsen Bahrami Panah, Dante Colao Zanuz, Markus Müller, and Andreas Wallraff, "Lattice surgery realized on two distance-three repetition codes with superconducting qubits", Nature Physics 22 2, 189 (2026).

[191] Filipa C. R. Peres and Ernesto F. Galvão, "Quantum circuit compilation and hybrid computation using Pauli-based computation", Quantum 7, 1126 (2023).

[192] Andrew Hardy, Priyanka Mukhopadhyay, M. Sohaib Alam, Robert Konik, Layla Hormozi, Eleanor Rieffel, Stuart Hadfield, João Barata, Raju Venugopalan, Dmitri E. Kharzeev, and Nathan Wiebe, "Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories", PRX Quantum 7 1, 010343 (2026).

[193] Andrew Patterson and Leigh Lapworth, "Measurement schemes for quantum linear equation solvers", Quantum Science and Technology 10 2, 025037 (2025).

[194] Cameron Calcluth, Nicolas Reichel, Alessandro Ferraro, and Giulia Ferrini, "Sufficient Condition for Universal Quantum Computation Using Bosonic Circuits", PRX Quantum 5 2, 020337 (2024).

[195] Rhea Alexander, Si Gvirtz-Chen, Nikolaos Koukoulekidis, and David Jennings, "General Entropic Constraints on Calderbank-Shor-Steane Codes within Magic Distillation Protocols", PRX Quantum 4 2, 020359 (2023).

[196] Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime", AVS Quantum Science 4 1, 013801 (2022).

[197] Yangsen Ye, Tan He, He-Liang Huang, Zuolin Wei, Yiming Zhang, Youwei Zhao, Dachao Wu, Qingling Zhu, Huijie Guan, Sirui Cao, Fusheng Chen, Tung-Hsun Chung, Hui Deng, Daojin Fan, Ming Gong, Cheng Guo, Shaojun Guo, Lianchen Han, Na Li, Shaowei Li, Yuan Li, Futian Liang, Jin Lin, Haoran Qian, Hao Rong, Hong Su, Shiyu Wang, Yulin Wu, Yu Xu, Chong Ying, Jiale Yu, Chen Zha, Kaili Zhang, Yong-Heng Huo, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, and Jian-Wei Pan, "Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor", Physical Review Letters 131 21, 210603 (2023).

[198] Eric Kubischta and Ian Teixeira, "Family of Quantum Codes with Exotic Transversal Gates", Physical Review Letters 131 24, 240601 (2023).

[199] Nick S. Blunt, György P. Gehér, and Alexandra E. Moylett, "Compilation of a simple chemistry application to quantum error correction primitives", Physical Review Research 6 1, 013325 (2024).

[200] Yutaka Hirano and Keisuke Fujii, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 670 (2025) ISBN:979-8-3315-5736-2.

[201] Rafael Wagner, Filipa C R Peres, Emmanuel Zambrini Cruzeiro, and Ernesto F Galvão, "Unitary-invariant method for witnessing nonstabilizerness in quantum processors", Journal of Physics A: Mathematical and Theoretical 58 28, 285302 (2025).

[202] Joao F. Doriguello, George Giapitzakis, Alessandro Luongo, and Aditya Morolia, Lecture Notes in Computer Science 16491, 3 (2026) ISBN:978-3-032-22694-5.

[203] Archisman Ghosh, Avimita Chatterjee, and Swaroop Ghosh, 2026 31st Asia and South Pacific Design Automation Conference (ASP-DAC) 198 (2026) ISBN:979-8-3315-9123-6.

[204] Lingxuan Feng and Shunlong Luo, "Clifford orbits and stabilizer states", Journal of Physics A: Mathematical and Theoretical 57 39, 395304 (2024).

[205] Ashutosh Goswami, Mehdi Mhalla, and Valentin Savin, "Fault-tolerant preparation of quantum polar codes encoding one logical qubit", Physical Review A 108 4, 042605 (2023).

[206] Francisco Orts, Remigijus Paulavičius, and Ernestas Filatovas, "Quantum circuit optimization of an integer divider", Journal of Systems and Software 215, 112091 (2024).

[207] Shoham Jacoby, Yotam Vaknin, Alex Retzker, and Arne L. Grimsmo, "Magic State Injection with Erasure Qubits", PRX Quantum 6 4, 040323 (2025).

[208] Sayam Sethi and Jonathan Mark Baker, Proceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 1028 (2025) ISBN:9798400710797.

[209] Lewis W. Anderson, Martin Kiffner, Tom O'Leary, Jason Crain, and Dieter Jaksch, "Solving lattice gauge theories using the quantum Krylov algorithm and qubitization", arXiv:2403.08859, (2024).

[210] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

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

[212] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402, (2018).

[213] Daniel Bochen Tan, Murphy Yuezhen Niu, and Craig Gidney, "A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing", arXiv:2404.18369, (2024).

[214] Casey Duckering, Jonathan M. Baker, David I. Schuster, and Frederic T. Chong, "Virtualized Logical Qubits: A 2.5D Architecture for Error-Corrected Quantum Computing", arXiv:2009.01982, (2020).

[215] Benjamin J. Brown, "A fault-tolerant non-Clifford gate for the surface code in two dimensions", Science Advances 6 21, eaay4929 (2020).

[216] Travis L. Scholten, Carl J. Williams, Dustin Moody, Michele Mosca, William Hurley, William J. Zeng, Matthias Troyer, and Jay M. Gambetta, "Assessing the Benefits and Risks of Quantum Computers", arXiv:2401.16317, (2024).

[217] Andreas Bauer, "Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases", arXiv:2403.12119, (2024).

[218] Satvik Maurya, Abtin Molavi, Aws Albarghouthi, and Swamit Tannu, "Managing Classical Processing Requirements for Quantum Error Correction", arXiv:2406.17995, (2024).

[219] David Gosset, Robin Kothari, and Kewen Wu, "Quantum state preparation with optimal T-count", arXiv:2411.04790, (2024).

[220] Dominic W. Berry, Craig Gidney, Mario Motta, Jarrod R. McClean, and Ryan Babbush, "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization", Quantum 3, 208 (2019).

[221] Allyson Silva, Xiangyi Zhang, Zak Webb, Mia Kramer, Chan Woo Yang, Xiao Liu, Jessica Lemieux, Ka-Wai Chen, Artur Scherer, and Pooya Ronagh, "Multi-qubit Lattice Surgery Scheduling", arXiv:2405.17688, (2024).

[222] Korbinian Staudacher, Tobias Guggemos, Sophia Grundner-Culemann, and Wolfgang Gehrke, "Reducing 2-QuBit Gate Count for ZX-Calculus based Quantum Circuit Optimization", arXiv:2311.08881, (2023).

[223] Aleksei V. Ivanov, Andrew Patterson, Marius Bothe, Christoph Sünderhauf, Bjorn K. Berntson, Jens Jørgen Mortensen, Mikael Kuisma, Earl Campbell, and Róbert Izsák, "Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set", arXiv:2408.03159, (2024).

[224] Craig Gidney, "Cleaner magic states with hook injection", arXiv:2302.12292, (2023).

[225] Jason D. Chadwick, Christopher Kang, Joshua Viszlai, Sophia Fuhui Lin, and Frederic T. Chong, "Averting multi-qubit burst errors in surface code magic state factories", arXiv:2405.00146, (2024).

[226] Yutaka Hirano, Tomohiro Itogawa, and Keisuke Fujii, "Leveraging Zero-Level Distillation to Generate High-Fidelity Magic States", arXiv:2404.09740, (2024).

[227] Ming Lai Chan, Aliki Anna Capatos, Peter Lodahl, Anders Søndberg Sørensen, and Stefano Paesani, "Practical blueprint for low-depth photonic quantum computing with quantum dots", arXiv:2507.16152, (2025).

[228] Paul Webster, Lucas Berent, Omprakash Chandra, Evan T. Hockings, Nouédyn Baspin, Felix Thomsen, Samuel C. Smith, and Lawrence Z. Cohen, "The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes", arXiv:2602.11457, (2026).

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

[230] Theodore J. Yoder, Eddie Schoute, Patrick Rall, Emily Pritchett, Jay M. Gambetta, Andrew W. Cross, Malcolm Carroll, and Michael E. Beverland, "Tour de gross: A modular quantum computer based on bivariate bicycle codes", arXiv:2506.03094, (2025).

[231] Daan Camps, Ermal Rrapaj, Katherine Klymko, Hyeongjin Kim, Kevin Gott, Siva Darbha, Jan Balewski, Brian Austin, and Nicholas J. Wright, "Quantum Computing Technology Roadmaps and Capability Assessment for Scientific Computing -- An analysis of use cases from the NERSC workload", arXiv:2509.09882, (2025).

[232] Sam McArdle, Alexander M. Dalzell, Aleksander Kubica, and Fernando G. S. L. Brandão, "The Fast for the Curious: How to accelerate fault-tolerant quantum applications", arXiv:2510.26078, (2025).

[233] Jahan Claes, "Cultivating T states on the surface code with only two-qubit gates", arXiv:2509.05232, (2025).

[234] Xi-Ning Zhuang, Zhao-Yun Chen, Ming-Yang Tan, Jiaxuan Zhang, Chuang-Chao Ye, Tian-Hao Wei, Teng-Yang Ma, Cheng Xue, Huan-Yu Liu, Qing-Song Li, Tai-Ping Sun, Xiao-Fan Xu, Yun-Jie Wang, Yu-Chun Wu, and Guo-Ping Guo, "A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations", arXiv:2509.08807, (2025).

[235] Archisman Ghosh, Avimita Chatterjee, and Swaroop Ghosh, "Design Automation in Quantum Error Correction", arXiv:2507.12253, (2025).

[236] Dmitry Filippov, Peter Yang, and Prakash Murali, "Architecting Distributed Quantum Computers: Design Insights from Resource Estimation", arXiv:2508.19160, (2025).

[237] Alexander M. Dalzell, András Gilyén, Connor T. Hann, Sam McArdle, Grant Salton, Quynh T. Nguyen, Aleksander Kubica, and Fernando G. S. L. Brandão, "A distillation-teleportation protocol for fault-tolerant QRAM", arXiv:2505.20265, (2025).

[238] Kwok Ho Wan and Zhenghao Zhong, "Cutting stabiliser decompositions of magic state cultivation with ZX-calculus", arXiv:2509.01224, (2025).

[239] Brandon Rodenburg, "Estimating the Power of a Quantum Computer", arXiv:2502.00113, (2025).

[240] Sayam Sethi, Sahil Khan, Aditi Awasthi, Abhinav Anand, and Jonathan Mark Baker, "INJEQT: Improved Magic-State Injection Protocol for Fault-Tolerant Quantum Extractor Architectures", arXiv:2604.25094, (2026).

[241] Riling Li, Keli Zheng, Yiming Zhang, Huazhe Lou, Shenggang Ying, Ke Liu, and Xiaoming Sun, "SOFT: a high-performance simulator for universal fault-tolerant quantum circuits", arXiv:2512.23037, (2025).

[242] Satvik Maurya and Swamit Tannu, "Synchronization for Fault-Tolerant Quantum Computers", arXiv:2506.10258, (2025).

[243] Yutaka Hirano and Keisuke Fujii, "Locality-aware Pauli-based computation for local magic state preparation", arXiv:2504.12091, (2025).

[244] Shifan Xu, Kun Liu, Patrick Rall, Zhiyang He, and Yongshan Ding, "Distilling Magic States in the Bicycle Architecture", arXiv:2602.20546, (2026).

[245] Cameron Calcluth, "From simulatability to universality of continuous-variable quantum computers", arXiv:2505.21618, (2025).

[246] Chenghong Zhu, Xian Wu, Jiahan Chen, Keming He, Junjie Wu, Xin Wang, and Lingling Lao, "O3LS: Optimizing Lattice Surgery via Automatic Layout Searching and Loose Scheduling", arXiv:2604.15099, (2026).

[247] Kun Liu, Shifan Xu, Tomas Jochym-O'Connor, Zhiyang He, Shraddha Singh, and Yongshan Ding, "In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes", arXiv:2604.05126, (2026).

[248] Pei Zeng, Guo Zheng, Qian Xu, and Liang Jiang, "Error-structure-tailored early fault-tolerant quantum computing", arXiv:2511.19983, (2025).

[249] Richie Yeung, Aleks Kissinger, and Rob Cornish, "Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis", arXiv:2605.10910, (2026).

[250] Zoë Webb-Mack and Natalie Klco, "Deforming the Trail: Baseline Quantum Circuitry for $\text{SU(2)}_k$ Lattice Gauge Theory", arXiv:2605.15076, (2026).

[251] Jason D. Chadwick, Willers Yang, Joshua Viszlai, and Frederic T. Chong, "A manufacturable surface code architecture for spin qubits with fast transversal logic", arXiv:2512.07131, (2025).

[252] Erik Weilandt, Tom Peham, and Robert Wille, "Minimizing the Number of Code Switching Operations in Fault-Tolerant Quantum Circuits", arXiv:2512.04170, (2025).

[253] Aditi Awasthi, Gokul Subramanian Ravi, and Jonathan Mark Baker, "Stalls and Spequlation: Pipelined Execution for Fault Tolerant Quantum Computation", arXiv:2606.19593, (2026).

[254] Srushti Patil and Nina Glaser, "Efficient targeting of arbitrary excited states with quantum inverse power iteration through filtering polynomials", arXiv:2606.28255, (2026).

[255] Siyi Wang, Kyungbae Jang, Hyunji Kim, Anik Basu Bhaumik, Anubhab Baksi, Hwajeong Seo, and Anupam Chattopadhyay, "Quantum Arithmetic Circuits in Public-Key Cryptography", arXiv:2607.11713, (2026).

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