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[4] Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown, "Anyon Condensation and the Color Code", PRX Quantum 5 1, 010342 (2024).

[5] Nirupam Basak and Goutam Paul, "Resource reduction in multiparty quantum secret sharing of both classical and quantum information under noisy scenario", Quantum Information Processing 25 4, 132 (2026).

[6] Andreas Bartschi and Stephan Eidenbenz, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 87 (2022) ISBN:978-1-6654-9113-6.

[7] Shouzhen Gu, Yotam Vaknin, Alex Retzker, and Aleksander Kubica, "Optimizing Quantum Error-Correction Protocols with Erasure Qubits", PRX Quantum 6 4, 040354 (2025).

[8] Thomas G. Kiely and Cenke Xu, "Phase transition of topological index driven by dephasing", Physical Review B 112 20, L201112 (2025).

[9] Basudha Srivastava, Anton Frisk Kockum, and Mats Granath, "The XYZ2 hexagonal stabilizer code", Quantum 6, 698 (2022).

[10] Edward H. Chen, Guo-Yi Zhu, Ruben Verresen, Alireza Seif, Elisa Bäumer, David Layden, Nathanan Tantivasadakarn, Guanyu Zhu, Sarah Sheldon, Ashvin Vishwanath, Simon Trebst, and Abhinav Kandala, "Nishimori transition across the error threshold for constant-depth quantum circuits", Nature Physics 21 1, 161 (2025).

[11] 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).

[12] 尹华磊 Yin Hualei, 卢旭阳 Lu Xuyang, 张庆航 Zhang Qinghang, and 陈增兵 Chen Zengbing, " 基于融合的量子计算研究进展（特邀）", Laser & Optoelectronics Progress 62 11, 1127003 (2025).

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[14] Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen, "Quantum computation from dynamic automorphism codes", Quantum 8, 1448 (2024).

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[16] Hanyan Cao, Shoukuan Zhao, Dongyang Feng, Zisong Shen, Haisheng Yan, Tang Su, Weijie Sun, Huikai Xu, Feng Pan, Haifeng Yu, and Pan Zhang, "Exact Decoding of Quantum Error-Correcting Codes", Physical Review Letters 134 19, 190603 (2025).

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[19] Yinzi Xiao, Basudha Srivastava, and Mats Granath, "Exact results on finite size corrections for surface codes tailored to biased noise", Quantum 8, 1468 (2024).

[20] Campbell McLauchlan, György P. Gehér, and Alexandra E. Moylett, "Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements", Quantum 8, 1562 (2024).

[21] Zijian Liang, Yijia Xu, Joseph T. Iosue, and Yu-An Chen, "Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions", PRX Quantum 5 3, 030328 (2024).

[22] Stefano Paesani and Benjamin J. Brown, "High-Threshold Quantum Computing by Fusing One-Dimensional Cluster States", Physical Review Letters 131 12, 120603 (2023).

[23] Da-Chuan Lu, Zhengdi Sun, and Yi-Zhuang You, "Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems", SciPost Physics 17 5, 136 (2024).

[24] Bence Hetényi and James R. Wootton, "Tailoring quantum error correction to spin qubits", Physical Review A 109 3, 032433 (2024).

[25] Umesh Uttamrao Shinde and Ravikumar Bandaru, "Quantum error-correction using humming sparrow optimization based self-adaptive deep cnn noise correction module", Scientific Reports 14 1, 14289 (2024).

[26] Oscar Higgott and Craig Gidney, "Sparse Blossom: correcting a million errors per core second with minimum-weight matching", Quantum 9, 1600 (2025).

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[28] Joseph Sullivan, Rui Wen, and Andrew C. Potter, "Floquet codes and phases in twist-defect networks", Physical Review B 108 19, 195134 (2023).

[29] F. Setiawan and Campbell McLauchlan, "Tailoring dynamical codes for biased noise: the X3Z3 Floquet code", npj Quantum Information 11 1, 149 (2025).

[30] Marcin Kalinowski, Nishad Maskara, and Mikhail D. Lukin, "Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator", Physical Review X 13 3, 031008 (2023).

[31] Yi-Ting Tu, David M. Long, and Dominic V. Else, "Anomalies of Global Symmetries on the Lattice", Physical Review X 16 1, 011027 (2026).

[32] Xuandong Sun, Longcheng Li, Zhiyi Wu, Zechen Guo, Peisheng Huang, Wenhui Huang, Qixian Li, Yongqi Liang, Yiting Liu, Daxiong Sun, Zilin Wang, Changrong Xie, Yuzhe Xiong, Xiaohan Yang, Jiajian Zhang, Jiawei Zhang, Libo Zhang, Zihao Zhang, Weijie Guo, Ji Jiang, Song Liu, Xiayu Linpeng, Jingjing Niu, Jiawei Qiu, Wenhui Ren, Ziyu Tao, Yuefeng Yuan, Yuxuan Zhou, Ji Chu, Youpeng Zhong, Xiaoming Sun, and Dapeng Yu, "Logical Operations with a Dynamical Qubit in Floquet-Bacon-Shor Code", Physical Review Letters 135 22, 220601 (2025).

[33] Jan Behrends, Florian Venn, and Benjamin Béri, "Surface codes, quantum circuits, and entanglement phases", Physical Review Research 6 1, 013137 (2024).

[34] Zhiyuan Wang and Kaden R. A. Hazzard, "Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition", Physical Review Research 5 1, 013086 (2023).

[35] Oskar Novak and Narayanan Rengaswamy, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 109 (2024) ISBN:979-8-3315-4137-8.

[36] Martin Ritter, David M. Long, Qianao Yue, Anushya Chandran, and Alicia J. Kollár, "Autonomous Stabilization of Floquet States Using Static Dissipation", Physical Review X 15 3, 031028 (2025).

[37] David Aasen, Zhenghan Wang, and Matthew B. Hastings, "Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes", Physical Review B 106 8, 085122 (2022).

[38] 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).

[39] Takuya Okuda, Aswin Parayil Mana, and Hiroki Sukeno, "Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement", SciPost Physics 17 4, 113 (2024).

[40] Guillaume Dauphinais, David W. Kribs, and Michael Vasmer, "Stabilizer Formalism for Operator Algebra Quantum Error Correction", Quantum 8, 1261 (2024).

[41] 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).

[42] Julio C. Magdalena de la Fuente, Josias Old, Alex Townsend-Teague, Manuel Rispler, Jens Eisert, and Markus Müller, "XYZ Ruby Code: Making a Case for a Three-Colored Graphical Calculus for Quantum Error Correction in Spacetime", PRX Quantum 6 1, 010360 (2025).

[43] Adithya Sriram, Tibor Rakovszky, Vedika Khemani, and Matteo Ippoliti, "Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model", Physical Review B 108 9, 094304 (2023).

[44] Shi Jie Samuel Tan and Lev Stambler, "Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes", Quantum 9, 1897 (2025).

[45] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson, "Pauli topological subsystem codes from Abelian anyon theories", Quantum 7, 1137 (2023).

[46] M. Sohaib Alam and Eleanor Rieffel, "Dynamical logical qubits in the Bacon-Shor code", Physical Review A 112 2, 022436 (2025).

[47] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson, "Pauli Stabilizer Models of Twisted Quantum Doubles", PRX Quantum 3 1, 010353 (2022).

[48] Chunhui Zhang, Chunhui Li, Zhen Tian, Yan Jiang, Feng Xu, Shihang Zhang, Hao Wang, Yu-Ning Zhang, Xuesong Bai, Baolong Zhao, Yi-Fei Zhang, Huan Shu, Jiaze Liu, Kunrong Wu, Chao Huang, Keji Shi, Mingchao Duan, Tao Xin, Peihao Huang, Tianluo Pan, Song Liu, Guanyong Wang, Guangchong Hu, Yu He, and Dapeng Yu, "Quantum error detection in a silicon quantum processor", Nature Electronics 9 3, 295 (2026).

[49] Zhehao Zhang, Yijian Zou, Timothy H. Hsieh, and Sagar Vijay, "Universal Properties of Critical Mixed-States from Measurement and Feedback", PRX Quantum 6 4, 040363 (2025).

[50] Charles Stahl, "Single-shot quantum error correction in intertwined toric codes", Physical Review B 110 7, 075143 (2024).

[51] Benjamin A. Cordier, Nicolas P. D. Sawaya, Gian Giacomo Guerreschi, and Shannon K. McWeeney, "Biology and medicine in the landscape of quantum advantages", Journal of The Royal Society Interface 19 196, 20220541 (2022).

[52] Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Unifying flavors of fault tolerance with the ZX calculus", Quantum 8, 1379 (2024).

[53] Margarita Davydova, Nathanan Tantivasadakarn, and Shankar Balasubramanian, "Floquet Codes without Parent Subsystem Codes", PRX Quantum 4 2, 020341 (2023).

[54] Vaibhav Sharma, Chao-Ming Jian, and Erich J. Mueller, "Subsystem symmetry, spin-glass order, and criticality from random measurements in a two-dimensional Bacon-Shor circuit", Physical Review B 108 2, 024205 (2023).

[55] Ryohei Kobayashi and Guanyu Zhu, "Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code", PRX Quantum 5 2, 020360 (2024).

[56] Umesh Uttamrao Shinde and Ravikumar Bandaru, "Re-locative guided search optimized self-sparse attention enabled deep learning decoder for quantum error correction", Scientific Reports 15 1, 3615 (2025).

[57] Yu Zeng, Alioscia Hamma, Yu-Ran Zhang, Jun-Peng Cao, Heng Fan, and Wu-Ming Liu, "Bounded light cone and robust topological order out of equilibrium", Physical Review A 111 2, 022414 (2025).

[58] Derek Khu, Andrew Tanggara, Chao Jin, and Kishor Bharti, "Contextuality of Quantum Error-Correcting Codes", PRX Quantum 7 1, 010319 (2026).

[59] Ryota Nakai and Hayato Goto, "Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements", Physical Review Applied 25 1, 014032 (2026).

[60] Ying Li, "Low-density parity-check representation of fault-tolerant quantum circuits", Physical Review Research 7 1, 013115 (2025).

[61] Ali Lavasani, Zhu-Xi Luo, and Sagar Vijay, "Monitored quantum dynamics and the Kitaev spin liquid", Physical Review B 108 11, 115135 (2023).

[62] Andreas Bauer, "Topological error correcting processes from fixed-point path integrals", Quantum 8, 1288 (2024).

[63] Robin Harper, Constance Lainé, Evan T. Hockings, Campbell McLauchlan, Georgia M. Nixon, Benjamin J. Brown, and Stephen D. Bartlett, "Characterising the failure mechanisms of error-corrected quantum logic gates", Nature Communications 17 1, 5039 (2026).

[64] Oscar Higgott, "PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[65] Cory T. Aitchison and Benjamin Béri, "Competing automorphisms and disordered Floquet codes", Physical Review B 111 23, 235112 (2025).

[66] Oscar Higgott, Thomas C. Bohdanowicz, Aleksander Kubica, Steven T. Flammia, and Earl T. Campbell, "Improved Decoding of Circuit Noise and Fragile Boundaries of Tailored Surface Codes", Physical Review X 13 3, 031007 (2023).

[67] Grace M. Sommers, David A. Huse, and Michael J. Gullans, "Crystalline Quantum Circuits", PRX Quantum 4 3, 030313 (2023).

[68] Evan Sutcliffe, Bhargavi Jonnadula, Claire Le Gall, Alexandra E. Moylett, and Coral M. Westoby, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 649 (2025) ISBN:979-8-3315-5736-2.

[69] Shouzhen Gu, Alex Retzker, and Aleksander Kubica, "Fault-tolerant quantum architectures based on erasure qubits", Physical Review Research 7 1, 013249 (2025).

[70] Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen, "Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward", PRX Quantum 4 2, 020339 (2023).

[71] Matthew Brooks and Charles Tahan, "Quantum computation by spin-parity measurements with encoded spin qubits", Physical Review B 108 3, 035206 (2023).

[72] Oliver Lunt, Jonas Richter, and Arijeet Pal, Quantum Science and Technology 251 (2022) ISBN:978-3-031-03997-3.

[73] Dripto M. Debroy, Matt McEwen, Craig Gidney, Noah Shutty, and Adam Zalcman, "LUCI in the Surface Code with Dropouts", Quantum 9, 1936 (2025).

[74] Jintae Kim, Jong Yeon Lee, and Jung Hoon Han, "Gauging modulated symmetries via multiple gauge symmetry operators and adaptive quantum circuits", Physical Review B 113 8, 085139 (2026).

[75] Edward H. Chen, Theodore J. Yoder, Youngseok Kim, Neereja Sundaresan, Srikanth Srinivasan, Muyuan Li, Antonio D. Córcoles, Andrew W. Cross, and Maika Takita, "Calibrated Decoders for Experimental Quantum Error Correction", Physical Review Letters 128 11, 110504 (2022).

[76] Ahmed Adel Mahmoud, Kamal Mohamed Ali, and Steven Rayan, "Systematic approach to hyperbolic quantum error correction codes", Physical Review A 113 4, 042426 (2026).

[77] James R Wootton, "Hexagonal matching codes with two-body measurements", Journal of Physics A: Mathematical and Theoretical 55 29, 295302 (2022).

[78] Yuanchen Zhao, Li Rao, and Dong E. Liu, "Noncommutative weak measurements: Entanglement, symmetry breaking, and the role of readout", Physical Review B 113 17, 174312 (2026).

[79] Ian Hesner, Bence Hetényi, and James R. Wootton, "Using detector likelihood for benchmarking quantum error correction", Physical Review A 111 5, 052452 (2025).

[80] David F. Locher, Josias Old, Katharina Brechtelsbauer, Jakob Holschbach, Hans Peter Büchler, Sebastian Weber, and Markus Müller, "Multiqubit Rydberg Gates for Quantum Error Correction", PRX Quantum 7 2, 020354 (2026).

[81] Margarita Davydova, Andreas Bauer, Julio C. Magdalena de la Fuente, Mark Webster, Dominic J. Williamson, and Benjamin J. Brown, "Universal Fault-Tolerant Quantum Computation in 2D without Getting Tied in Knots", Physical Review X 16 3, 031001 (2026).

[82] David T. Stephen, Arpit Dua, Ali Lavasani, and Rahul Nandkishore, "Nonlocal Finite-Depth Circuits for Constructing Symmetry-Protected Topological States and Quantum Cellular Automata", PRX Quantum 5 1, 010304 (2024).

[83] Clay Córdova, Davi Bastos Costa, and Po-Shen Hsin, "Non-invertible symmetries in finite-group gauge theory", SciPost Physics 18 1, 019 (2025).

[84] Yaodong Li, Nicholas O’Dea, and Vedika Khemani, "Perturbative Stability and Error-Correction Thresholds of Quantum Codes", PRX Quantum 6 1, 010327 (2025).

[85] Anthony Ryan O'Rourke and Simon Devitt, "Compare the pair: Rotated versus unrotated surface codes at equal logical error rates", Physical Review Research 7 3, 033074 (2025).

[86] Craig Gidney, "A Pair Measurement Surface Code on Pentagons", Quantum 7, 1156 (2023).

[87] Bowen Yan, Penghua Chen, and Shawn X. Cui, "Generalized Kitaev spin liquid model and emergent twist defect", Annals of Physics 466, 169682 (2024).

[88] Howard M. Wiseman, Eric G. Cavalcanti, and Eleanor G. Rieffel, "A "thoughtful" Local Friendliness no-go theorem: a prospective experiment with new assumptions to suit", Quantum 7, 1112 (2023).

[89] Matthew P.A. Fisher, Vedika Khemani, Adam Nahum, and Sagar Vijay, "Random Quantum Circuits", Annual Review of Condensed Matter Physics 14 1, 335 (2023).

[90] Shankar Balasubramanian, Margarita Davydova, and Ethan Lake, "A local automaton for the 2D toric code", Quantum 10, 2125 (2026).

[91] Linnea Grans-Samuelsson, David Aasen, and Parsa Bonderson, "Fault-tolerant pairwise measurement-based code on eight qubits", Physical Review A 112 4, 042413 (2025).

[92] Po-Shen Hsin and Zhenghan Wang, "On topology of the moduli space of gapped Hamiltonians for topological phases", Journal of Mathematical Physics 64 4, 041901 (2023).

[93] Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring, "Floquetifying the Colour Code", Electronic Proceedings in Theoretical Computer Science 384, 265 (2023).

[94] Linnea Grans-Samuelsson, Ryan V. Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P. da Silva, and Parsa Bonderson, "Improved Pairwise Measurement-Based Surface Code", Quantum 8, 1429 (2024).

[95] Rahul Sahay and Ruben Verresen, "Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements", PRX Quantum 6 1, 010329 (2025).

[96] Guo-Yi Zhu, Nathanan Tantivasadakarn, and Simon Trebst, "Structured volume-law entanglement in an interacting, monitored Majorana spin liquid", Physical Review Research 6 4, L042063 (2024).

[97] Christophe Vuillot, Alessandro Ciani, and Barbara M. Terhal, "Homological Quantum Rotor Codes: Logical Qubits from Torsion", Communications in Mathematical Physics 405 2, 53 (2024).

[98] Yaodong Li, C. W. von Keyserlingk, Guanyu Zhu, and Tomas Jochym-O'Connor, "Phase diagram of the three-dimensional subsystem toric code", Physical Review Research 6 4, 043007 (2024).

[99] Andreas Bauer, "x+y Floquet code: A simple example for topological quantum computation in the path-integral approach", Physical Review A 111 3, 032413 (2025).

[100] Jianxin Chen, Dawei Ding, Cupjin Huang, and Linghang Kong, "Linear cross-entropy benchmarking with Clifford circuits", Physical Review A 108 5, 052613 (2023).

[101] Grégoire de Gliniasty, Paul Hilaire, Pierre-Emmanuel Emeriau, Stephen C. Wein, Alexia Salavrakos, and Shane Mansfield, "A Spin-Optical Quantum Computing Architecture", Quantum 8, 1423 (2024).

[102] Adam Paetznick, Christina Knapp, Nicolas Delfosse, Bela Bauer, Jeongwan Haah, Matthew B. Hastings, and Marcus P. da Silva, "Performance of Planar Floquet Codes with Majorana-Based Qubits", PRX Quantum 4 1, 010310 (2023).

[103] Thiago Lucena de Macedo Guedes, "A Short Introduction to Quantum Error Correction", Brazilian Journal of Physics 56 2, 94 (2026).

[104] Matthew Brooks, Foster Sabatino, Charles Tahan, and Silas Hoffman, "Measurement-based simulation of geometric gates in topological qubits on noisy intermediate-scale quantum devices", Physical Review A 112 3, 032617 (2025).

[105] Dylan Lewis, Roeland Wiersema, Juan Carrasquilla, and Sougato Bose, "Geodesic algorithm for unitary gate design with time-independent Hamiltonians", Physical Review A 111 5, 052618 (2025).

[106] Jeongwan Haah and Matthew B. Hastings, "Boundaries for the Honeycomb Code", Quantum 6, 693 (2022).

[107] Wooyeong Song, Nuri Kang, Yong-Su Kim, and Seung-Woo Lee, "Encoded-Fusion-Based Quantum Computation for High Thresholds with Linear Optics", Physical Review Letters 133 5, 050605 (2024).

[108] Matthew Buican and Rajath Radhakrishnan, "Qudit stabilizer codes, CFTs, and topological surfaces", Physical Review D 110 8, 085021 (2024).

[109] Ilya A. Simakov and Ilya S. Besedin, "Low-overhead quantum error-correction codes with a cyclic topology", Physical Review A 111 1, 012444 (2025).

[110] Lukas Voss, Sim Jian Xian, Tobias Haug, and Kishor Bharti, "Multivariate bicycle codes", Physical Review A 111 6, L060401 (2025).

[111] Mircea Bejan, Campbell McLauchlan, and Benjamin Béri, "Dynamical Magic Transitions in Monitored Clifford+ T Circuits", PRX Quantum 5 3, 030332 (2024).

[112] Oscar Higgott and Nikolas P. Breuckmann, "Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes", PRX Quantum 5 4, 040327 (2024).

[113] Manuel H. Muñoz-Arias, "Statistical complexity and the road to equilibrium in many-body chaotic quantum systems", Physical Review E 106 4, 044103 (2022).

[114] Shahram Babaie, Sean Grzenda, and Chunming Qiao, 2026 24th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt) 1 (2026) ISBN:978-3-903176-80-5.

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The above citations are from Crossref's cited-by service (last updated successfully 2026-07-15 11:46:28) and SAO/NASA ADS (last updated successfully 2026-07-15 11:46:30). The list may be incomplete as not all publishers provide suitable and complete citation data.