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Literature reviews

This is a page where I keep track of all the papers I read. The central theme is "topological quantum information", though I by no means hold myself to that strictly. There are tags on all of the posts to help keep track of things.

Every post contains a brief summary, along with relevant comments. Posts are written to be maximally lucid upon my future re-reading. I make no effort to define, explain, or prove every term/claim. If something is confusing/you want to know more, email me.


By their compressed narrative nature, summaries/stories are much easier to hold on to than primary experiences. I find myself reading lots of papers, and wanting to remember what I read. This often takes the form of an internal summarizing/storytelling.

To help remember things even better I have taken up the task of writing out these stories, along with technical comments, questions, and tidbits that come up along the process.

An additional point is that keeping such a list forces me to get into the habit of crystallizing stories, and it is useful for future reference.


search:
  1. "Anyonic entanglement and topological entanglement entropy", Parsa Bonderson, Christina Knapp, Kaushal Patel, 2017 [reviewed: January 15, 2025]
  2. "More Is Different", Philip Anderson, 1972 [reviewed: January 9, 2025]
  3. "Heegaard splittings of Seifert fibered spaces", Yoav Moriah, 1988 [reviewed: December 11, 2024]
  4. "Effective field theory in condensed matter physics", Ramamurti Shankar, 1999 [reviewed: December 8, 2024]
  5. "Classifying quantum phases using matrix product states and projected entangled pair states", Norbert Schuch, David Perez-Garcia, Ignacio Cira, 2011 [reviewed: December 5, 2024]
  6. "An historical note on the parity of permutation", Thomas Bartlow, 1972 [reviewed: December 2, 2024]
  7. "Third homology of some sporadic finite groups", Theo Johnson-Freyd, David Treumann, 2019 [reviewed: November 27, 2024]
  8. "Computing the center of a fusion category", Fabian Maurer, Ulrich Thiel, 2024 [reviewed: November 27, 2024]
  9. "An index for invertible phases of two-dimensional quantum spin systems", Nikita Sopenko, 2024 [reviewed: November 25, 2024]
  10. "On Ulam stability", Marc Burger, Narutaka Ozawa, Andreas Thom, 2010 [reviewed: November 24, 2024]
  11. "Magic state cultivation: growing T states as cheap as CNOT gates", Craig Gidney, Noah Shutty, Cody Jones, 2024 [reviewed: November 20, 2024]
  12. "Meandering conduction channels and the tunable nature of quantized charge transport", Benoit Doucot, Dmitry Kovrizhin, Roderich Moessner, 2024 [reviewed: November 19, 2024]
  13. "Quantum circuits with mixed states", Dorit Aharonov, Alexei Kitaev, Noam Nisan, 1998 [reviewed: November 18, 2024]
  14. "Quantum theory, the Church-Turing principle and the universal quantum computer", David Deutsch, 1985 [reviewed: November 18, 2024]
  15. "Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits", Yuanjie Ren, Nathanan Tantivasadakarn, Dominic Williamson, 2024 [reviewed: November 17, 2024]
  16. "A degeneracy bound for homogeneous topological order", Jeongwan Haah, 2021 [reviewed: November 15, 2024]
  17. "Stability of frustration-free Hamiltonians", Spyridon Michalakis, Justyna Zwolak, 2013 [reviewed: November 13, 2024]
  18. "Braiding statistics of loop excitations in three dimensions", Chenjie Wang, Michael Levin, 2014 [reviewed: November 13, 2024]
  19. "The 'transition probability' in the state space of a *-algebra", Armin Uhlmann, 1976 [reviewed: November 11, 2024]
  20. "Quantum money from knots", Edward Farhi et al., 2012 [reviewed: November 11, 2024]
  21. "Bicategories for boundary conditions and for surface defects in 3d TFT", Jurgen Fuchs, Christoph Schweigert, Alessandro Valentino, 2013 [reviewed: November 11, 2024]
  22. "Improved one-dimensional area law for frustration-free systems", Itai Arad, Zeph Landau, Umesh Vazirani, 2012 [reviewed: November 4, 2024]
  23. "Quantum Hamiltonian complexity and the detectability lemma", Dorit Aharonov, Itai Arad, Zeph Landau, Umesh Vazirani, 2010 [reviewed: November 4, 2024]
  24. "Anyon quantum dimensions from an arbitrary ground state wave function", Shang Liu, 2024 [reviewed: November 3, 2024]
  25. "Intrinsic mixed-state topological order without quantum memory", Zijian Wang, Zhengzhi Wu, Zhong Wang, 2023 [reviewed: November 2, 2024]
  26. "Local commuting projector Hamiltonians and the quantum Hall effect", Anton Kapustin, Lukasz Fidkowski, 2020 [reviewed: November 2, 2024]
  27. "Response theory for locally gapped systems", Joscha Henheik, Tom Wessel, 2024 [reviewed: November 2, 2024]
  28. "Topological quantum computation is hyperbolic", Eric Samperton, 2023 [reviewed: November 2, 2024]
  29. "How hard is it to approximate the Jones polynomial?", Greg Kuperberg, 2009 [reviewed: November 2, 2024]
  30. "Coloring invariants of knots and links are often intractable", Greg Kuperberg, Eric Samperton, 2021 [reviewed: October 31, 2024]
  31. "Complexity classes as mathematical axioms", Michael Freedman, 2009 [reviewed: October 31, 2024]
  32. "Cups and Gates I", Nikolas Breuckmann, Margarita Davydova, Jens Eberhardt, Nat Tantivasadakarn, 2024 [reviewed: October 31, 2024]
  33. "Almost-idempotent quantum channels and approximate C^*-algebras", Alexei Kitaev, 2024 [reviewed: October 31, 2024]
  34. "Physics, topology, logic and computation: a Rosetta Stone", John Baez, Mike Stay, 2011 [reviewed: October 31, 2024]
  35. "A single quantum cannot be cloned", William Wotters, Wojciech Zurek, 1982 [reviewed: October 30, 2024]
  36. "A generalized approach to the fundamental group", Daniel Biss, 2000 [reviewed: October 27, 2024]
  37. "An algebraic framework for group duality", Alfons Van Daele, 1998 [reviewed: October 27, 2024]
  38. "Dual-isometric Projected Entangled Pair States", Xie-Hang Yu et al., 2024 [reviewed: October 25, 2024]
  39. "Quantum cellular automata and categorical duality of spin chains", Corey Jones, Kylan Schatz, Dominic Williamson, 2024 [reviewed: October 24, 2024]
  40. "On the critical finite-size gap scaling for frustration-free Hamiltonians", Marius Lemm, Angelo Lucia, 2024 [reviewed: October 15, 2024]
  41. "Quantum union bounds for sequential projective measurements", Jingliang Gao, 2015 [reviewed: October 15, 2024]
  42. "Splitting the topological degeneracy of non-abelian anyons", Parsa Bonderson, 2009 [reviewed: October 11, 2024]
  43. "Measurement-only topological quantum computation", Parsa Bonderson, Michael Freedman, Chetan Nayak, 2008 [reviewed: October 11, 2024]
  44. "Universal gates via fusion and measurement operations on SU(2)_4 anyons", Claire Levaillant, et al., 2015 [reviewed: October 11, 2024]
  45. "Quantum algorithm for linear systems of equations", Adam Harrow, Avinatan Hassidim, Seth Lloyd, 2009 [reviewed: October 6, 2024]
  46. "High-threshold and low-overhead fault-tolerant quantum memory", Sergey Bravyi et al., 2024 [reviewed: October 6, 2024]
  47. "The future of quantum computing with superconducting qubits", Sergey Bravy et al., 2022 [reviewed: October 6, 2024]
  48. "Quantum simulations of hadron dynamics in the Schwinger model using 112 qubits", Roland Farrell et al., 2024 [reviewed: October 6, 2024]
  49. "Reliable cellular automata with self-organization", Peter Gacs, 2001 [reviewed: October 6, 2024]
  50. "Synthetic topological qubits in conventional bilayer quantum Hall systems", Maissam Barkeshli, Xiao-Liang Qi, 2014 [reviewed: September 29, 2024]
  51. "Quantum spin systems on infinite lattices", Pieter Naaijkens, 2013 [reviewed: September 26, 2024]
  52. "Anyon condensation and tensor categories", Liang Kong, 2014 [reviewed: September 23, 2024]
  53. "Monoidal 2-structure of bimodule categories", Justin Greenough, 2010 [reviewed: September 22, 2024]
  54. "Broken quantum symmetry and confinement phases in planar physics", Alexander Bais, Bernd Schroers, Joost Slingerland, 2002 [reviewed: September 18, 2024]
  55. "Symmetry defects and their application to topological quantum computing", Colleen Delaney, Zhenghan Wang, 2020 [reviewed: September 12, 2024]
  56. "Classifying 2D topological phases: mapping ground states to string-nets", Isaac Kim, Daniel Ranard, 2024 [reviewed: September 11, 2024]
  57. "Generalized string-net models: A thorough exposition", Chien-Hung Lin, Michael Levin, Fiona Burnell, 2021 [reviewed: September 11, 2024]
  58. "Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices", Jeongwan Haah, 2021 [reviewed: September 11, 2024]
  59. "On enriching the Levin-Wen model with symmetry", Liang Chang et al., 2015 [reviewed: September 11, 2024]
  60. "'Fractional statistics' in arbitrary dimensions: A generalization of the Pauli principle", Duncan Haldane, 1991 [reviewed: September 10, 2024]
  61. "Phase transition in random circuit sampling", Google quantum AI and collaborators, 2023 [reviewed: September 10, 2024]
  62. "Demonstration of quantum computation and error correction with a tesseract code", Ben Reichardt, et al., 2024 [reviewed: September 10, 2024]
  63. "Classification of Cellular Fake Surfaces", Lucas Fagan, Yang Qiu, Zhenghan Wang, 2024 [reviewed: September 10, 2024]
  64. "Quantum error correction below the surface code threshold", Google quantum AI and collaborators, 2024 [reviewed: September 10, 2024]
  65. "Quantum conditional mutual information and approximate Markov chains", Omar Fawzi, Renato Renner, 2015 [reviewed: September 9, 2024]
  66. "Conditional independence in quantum many-body systems", Isaac Kim, 2013 [reviewed: September 9, 2024]
  67. "Ground-state degeneracy of the fractional quantum Hall states", Xiao-Gang Wen, Qian Niu, 1990 [reviewed: September 9, 2024]
  68. "Entanglement bootstrap approach for gapped domain walls", Bowen Shi, Isaac Kim, 2021 [reviewed: September 9, 2024]
  69. "W-state is not the unique ground state of any local Hamiltonian", Lei Gioia, Ryan Thorngren, 2023 [reviewed: September 9, 2024]
  70. "Discontinuity of maximum entropy inference and quantum phase transitions", Jianxin Chen et al., 2015 [reviewed: September 5, 2024]
  71. "Fusion structure from exchange symmetry in (2+ 1)-dimensions", Sachin Valera, 2021 [reviewed: September 5, 2024]
  72. "Information-theoretical analysis of topological entanglement entropy and multipartite correlations", Kohtaro Kato, Fabian Furrer, Mio Murao, 2016 [reviewed: September 5, 2024]
  73. "Extracting Wilson loop operators and fractional statistics from a single bulk ground state", Ze-Pei Cian, Mohammad Hafezi, Maissam Barkeshli, 2022 [reviewed: September 5, 2024]
  74. "Chiral central charge from a single bulk wave function", Isaac Kim, Bowen Shi, Kohtaro Kato, Victor Albert, 2022 [reviewed: September 5, 2024]
  75. "Verlinde formula from entanglement", Bowen Shi, 2020 [reviewed: September 4, 2024]
  76. "Fusion rules from entanglement", Bowen Shi, Kohtaro Kato, Isaac Kim, 2020 [reviewed: September 4, 2024]
  77. "Conformal Field Theory Ground States as Critical Points of an Entropy Function", Ting-Chun Lin, John McGreevy, 2023 [reviewed: September 4, 2024]
  78. "Boundary topological entanglement entropy in two and three dimensions", Jacob Bridgeman, Benjamin Brown, Samuel Elman, 2022 [reviewed: September 4, 2024]
  79. "Structure of states which satisfy strong subadditivity of quantum entropy with equality", Patrick Hayden, Richard Jozsa, Denes Petz, Andreas Winter, 2004 [reviewed: September 3, 2024]
  80. "Quasiparticle statistics and braiding from ground-state entanglement", Yi Zhang, et al., 2012 [reviewed: September 2, 2024]
  81. "Fermionic quantum computation", Sergey Bravyi, Alexei Kitaev, 2002 [reviewed: August 30, 2024]
  82. "Area laws and efficient descriptions of quantum many-body states", Yimin Ge, Jens Eisert, 2016 [reviewed: August 30, 2024]
  83. "The structure of Renyi entropic inequalities", Noah Linden, Milan Mosonyi, Andreas Winter, 2013 [reviewed: August 30, 2024]
  84. "Spectral gap and exponential decay of correlations", Matthew Hastings, Tohru Koma, 2006 [reviewed: August 30, 2024]
  85. "Quantum algorithm for simulating real time evolution of lattice Hamiltonians", Jeongwan Haah, Matthew Hastings, Robin Kothari, Guang Hao Low, 2021 [reviewed: August 30, 2024]
  86. "Random MERA states and the tightness of the Brandao-Horodecki entropy bound", Matthew Hastings, 2015 [reviewed: August 30, 2024]
  87. "Universal lower bound on topological entanglement entropy", Isaac Kim, Michael Levin, Ting-Chun Lin, Daniel Ranard, Bowen Shi, 2023 [reviewed: August 29, 2024]
  88. "A new operator extension of strong subadditivity of quantum entropy", Ting-Chun Lin, Isaac Kim, Min-Hsiu Hsieh, 2023 [reviewed: August 29, 2024]
  89. "On the informational completeness of local observables", Isaac Kim, 2014 [reviewed: August 29, 2024]
  90. "Seeing topological entanglement through the information convex", Bowen Shi, 2019 [reviewed: August 29, 2024]
  91. "Characterizing topological order by the information convex", Bowen Shi, Yuan-Ming Lu, 2019 [reviewed: August 29, 2024]
  92. "Spurious topological entanglement entropy from subsystem symmetries", Dominic Williamson, Arpit Dua, Meng Cheng, 2019 [reviewed: August 28, 2024]
  93. "Spurious long-range entanglement and replica correlation length", Liujun Zou, Jeongwan Haah, 2016 [reviewed: August 28, 2024]
  94. "Efficient magic state factories with a catalyzed |CCZ> -> 2|T> transformation", Craig Gidney, Austin Fowler, 2019 [reviewed: August 23, 2024]
  95. "Interacting anyons in topological quantum liquids: The golden chain", Adrian Feiguin et al., 2007 [reviewed: August 23, 2024]
  96. "Topological entanglement Renyi entropy and reduced density matrix structure", Steven Flammia, Alioscia Hamma, Taylor Hughes, Xiao-Gang Wen, 2009 [reviewed: August 23, 2024]
  97. "Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order", Alioscia Hamma et al., 2008 [reviewed: August 21, 2024]
  98. "Entanglement Spectrum as a Generalization of Entanglement Entropy", Hui Li, Duncan Haldane, 2008 [reviewed: August 21, 2024]
  99. "Detecting topological order in a ground state wave function", Michael Levin, Xiao-Gang Wen, 2006 [reviewed: August 21, 2024]
  100. "Braid topologies for quantum computation", Steve Simon, Nick Bonesteel, Layla Hormozi, Georgios Zikos, 2005 [reviewed: August 21, 2024]
  101. "Categorical Morita equivalence for group-theoretical categories", Deepak Naidu, 2007 [reviewed: August 19, 2024
  102. "Tensor categories", EGNO, 2015 [reviewed: August 19, 2024]
  103. "Models for gapped boundaries and domain walls", Alexei Kitaev, Liang Kong, 2012 [reviewed: August 19, 2024]
  104. "Matrix product states and projected entangled pair states: Concepts, symmetries, theorems", Ignacio Cirac et al., 2021 [reviewed: March 31, 2024]
  105. "Congruence subgroups and super-modular categories", Parsa Bonderson, Eric Rowell, Zhenghan wang, Qing Zhang, 2018 [reviewed: March 31, 2024]
  106. "Weakly group-theoretical and solvable fusion categories", Pavel Etingof, Dmitri Nikshych, Victor Ostrik, 2009 [reviewed: March 23, 2024]
  107. "Higher central charges and topological boundaries in 2+1-dimensional TQFTs", Justin Kaidi et al., 2021 [reviewed: March 23, 2024]
  108. "Microscopic definitions of anyon data", Kyle Kawagoe, Michael Levin, 2019 [reviewed: March 23, 2024]
  109. "Varieties whose finitely generated members are free", Keith Kearnes, Emil Kiss, Agnes Szendrei, 2016 [reviewed: March 23, 2024]
  110. "Quantum measurements without sums", Bob Coecke, Dusko Pavlovic, 2008 [reviewed: March 23, 2024]
  111. "Beyond anyons", Zhenghan Wang, 2017 [reviewed: March 23, 2024]
  112. "Fermionic modular categories and the 16-fold way", Bruillard et al., 2017 [reviewed: March 23, 2024]
  113. "Anyons in an exactly solved model and beyond", Alexei Kitaev, 2006 [reviewed: March 23, 2024]
  114. "Topological Quantum Computation", Zhenghan Wang, 2010 [reviewed: March 23, 2024]
  115. "A categorical perspective on symmetry, topological order, and quantum information", Colleen Delaney, 2019 [reviewed: March 23, 2024]
  116. "The topological theory of defects in ordered media", David Mermin, 1979 [reviewed: March 23, 2024]
  117. "A categorical perspective on symmetry, topological order, and quantum information", Colleen Delaney, 2019 [reviewed: March 23, 2024]
  118. "Module categories, weak hopf algebras, and modular invariants", Viktor Ostrik, 2001 [reviewed: March 23, 2024]
  119. "The rank of G-crossed braided extensions of modular tensor categories", Marcel Bischoff, 2020 [reviewed: March 23, 2024]
  120. "Fusion categories and homotopy theory", Pavel Etingof, Dmitri Nikshych, Victor Ostrik, 2010 [reviewed: March 23, 2024]
  121. "A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules", Nathan Geer et al., 2022 [reviewed: March 22, 2024]
  122. "Quantum Error Correction with the Semion Code", Guillaume Dauphinais et al., 2019 [reviewed: March 22, 2024]
  123. "A class of P, T-invariant topological phases of interacting electrons", Michael Freedman et al., 2004 [reviewed: March 22, 2024]
  124. "Uniqueness of unitary structure for unitarizable fusion categories", David Reutter, 2023 [reviewed: March 21, 2024]
  125. "Building manifolds from quantum codes", Michael Freedman, Matthew Hastings, 2021 [reviewed: March 15, 2024]
  126. "Good quantum error-correcting codes exist", Robert Calderbank, Peter Shor, 1996 [reviewed: March 14, 2024]
  127. "Invariants of piecewise-linear 3-manifolds", John Barrett, Bruce Westbury, 1996 [reviewed: March 13, 2024]
  128. "String-net model of Turaev-Viro invariants", Alexander Kirillov, 2011 [reviewed: March 13, 2024]
  129. "Ground subspaces of topological phases of matter as error correcting codes", Qiu Yang, Zhenghan Wang, 2020 [reviewed: March 13, 2024]
  130. "Straightening out the Frobenius-Schur indicator", Steven Simon, Joost Slingerland, 2022 [reviewed: February 26, 2024]
  131. "The Penrose Tiling is a Quantum Error-Correcting Code", Zhi Li and Latham Boyle, 2023 [reviewed: February 26, 2024]
  132. "Are we quantum computers, or merely clever robots?", Matthew Fisher, 2017 [reviewed: February 25, 2024]
  133. "Generalized symmetries in condensed matter", John McGreevy, 2023 [reviewed: February 24, 2024]
  134. "The fragility of quantum information?", Barbara Terhal, 2012 [reviewed: February 24, 2024]
  135. "Tradeoffs for reliable quantum information storage in 2D systems", Sergey Bravyi, David Poulin, Barbara Terhal, 2010 [reviewed: February 24, 2024]
  136. "Information storage capacity of discrete spin systems", Beni Yoshida, 2013 [reviewed: February 23, 2024]
  137. "Making better sense of quantum mechanics", David Mermin, 2018 [reviewed: February 18, 2024]
  138. "On classification of modular tensor categories", Eric Rowell, Richard Stong, Zhenghan Wang, 2009 [reviewed: February 16, 2024]
  139. "Asymptotically good quantum and locally testable classical LDPC codes", Pavel Panteleev, Gleb Kalachev, 2022 [reviewed: February 16, 2024]
  140. "An analogue of Radford's S4 formula for finite tensor categories", Pavel Etingof, Dmitri Nikshych, Viktor Ostrik, 2004 [reviewed: February 16, 2024]
  141. "From categories to anyons: a travelogue", Kerstin Beer et al., 2018 [reviewed: February 11, 2024]
  142. "Chiral topologically ordered states on a lattice from vertex operator algebras", Nikita Sopenko, 2023 [reviewed: February 10, 2024]
  143. "Symplectic, Quaternionic, Fermionic", John Baez, 2014 [reviewed: February 4, 2024]
  144. "Traced monoidal categories", Andre Joyal, Ross Street, Dominic Verity, 1996 [reviewed: February 4, 2024]
  145. "Non-Abelian anyons and interferometry", Parsa Bonderson, 2012 [reviewed: February 4, 2024]
  146. "Quantum phases of vortices in rotating Bose-Einstein condensates", Nigel Cooper, Nicola Wilkin, Mike Gunn, 2001 [reviewed: February 3, 2024]
  147. "Quasi-topological phases of matter and topological protection", Parsa Bonderson, Cheten Nayak, 2013 [reviewed: February 2, 2024]
  148. "Measuring topological order", Parsa Bonderson, 2021 [reviewed: February 2, 2024]
  149. "Observation of half-integer thermal Hall conductance", Banerjee et al., 2018 [reviewed: February 2, 2024]
  150. "The theory of probability", Andrey Kolomogorov, 1963 [reviewed: February 2, 2024]
  151. "Symmetry protected topological orders and the group cohomology of their symmetry group", Xie Chen et al., 2013 [reviewed: January 28, 2024]
  152. "Statistical mechanics: Rigorous results", David Ruelle, 1969 [reviewed: January 28, 2024]
  153. "Square kagome quantum antiferromagnet and the eight-vertex model", Rahul Siddharthan, Antoine Georges, 2001 [reviewed: January 28, 2024]
  154. "Growth rates of the number of indecomposable summands in tensor powers", Kevin Coulembier, Victor Ostrik, Daniel Tubbenhauer, 2023 [reviewed: January 21, 2024]
  155. "On generalized symmetries and structure of modular categories", Shawn Cui, Modjtaba Zini, Zhenghan Wang, 2019 [reviewed: January 15, 2024]
  156. "Modular categories are not determined by their modular data", Michael Mignard, Peter Schauenburg, 2021 [reviewed: January 15, 2024]
  157. "Finiteness for mapping class group representations from twisted Dijkgraaf-Witten theory", Paul Gustafson, 2018 [reviewed: January 15, 2024]
  158. "The boundaries and twist defects of the color code and their applications to topological quantum computation", Markus Kesselring et al., 2018 [reviewed: January 14, 2024]
  159. "Topological entanglement entropy with a twist", Benjamin Brown et al., 2013 [reviewed: January 14, 2024]
  160. "Topological entanglement entropy", Alexei Kitaev, John Preskill, 2006 [reviewed: January 14, 2024]
  161. "Two-dimensional color-code quantum computation", Austin Fowler, 2011 [reviewed: January 14, 2024]
  162. "The boundaries and twist defects of the color code and their applications to topological quantum computation", Markus Kesselring and others, 2018 [reviewed: January 14, 2024]
  163. "Topological quantum distillation", Hector Bombin, Miguel Angel Martin-Delgado, 2006 [reviewed: January 14, 2024]
  164. "Fault-tolerant quantum computation", Peter Shor, 1996 [reviewed: January 14, 2024]
  165. "Quantum computations: algorithms and error correction", Alexei Kitaev, 1997 [reviewed: January 14, 2024]
  166. "Subfactors from regular graphs induced by association schemes", Radhakrishnan Balu, 2022 [reviewed: January 9, 2024]
  167. "Association schemes and fusion algebras (an introduction)", Eiichi Bannai, 1993 [reviewed: January 9, 2024]
  168. "Twist defects and projective non-Abelian braiding statistics", Maissam Barkeshli, Chao-Ming Jian, Xiao-Liang Qi, 2013 [reviewed: January 2, 2024]
  169. "Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes", David Aasen, Zhenghan Wang, Matthew Hastings, 2022 [reviewed: January 1, 2024]
  170. "The group structure of quantum cellular automata", Michael Freedman, Jeongwan Haah, Matthew Hastings, 2022 [reviewed: January 1, 2024]
  171. "Topological order with a twist: Ising anyons from an Abelian model", Hector Bombin, 2010 [reviewed: December 31, 2023]
  172. "Indistinguishable chargeon-fluxion pairs in the quantum double of finite groups", Salman Beigi, Peter Shor, Daniel Whalen, 2010 [reviewed: December 31, 2023]
  173. "Quasi-quantum groups related to orbifold models", Robbert Dijkgraaf, Vincent Pasquier, Philippe Roche, 1990 [reviewed: December 31, 2023]
  174. "Non-local finite-depth circuits for constructing SPT states and quantum cellular automata", David Stephen et al., 2022 [reviewed: December 29, 2023]
  175. "Mapping between Morita-equivalent string-net states with a constant depth quantum circuit", Laurens Lootens et al., 2022 [reviewed: December 29, 2023]
  176. "Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code", Yuri Lensky, Kostyantyn Kechedzhi, Igor Aleiner, Eun-Ah Kim, 2022 [reviewed: December 29, 2023]
  177. "On topology of the moduli space of gapped Hamiltonians for topological phases", Po-Shen Hsin, Zhenghan Wang, 2023 [reviewed: December 29, 2023]
  178. "Topological quantum order: stability under local perturbations", Sergey Bravyi, Matthew Hastings, Spyridon Michalakis, 2010 [reviewed: December 29, 2023]
  179. "A blueprint for a topologically fault-tolerant quantum computer", Parsa Bonderson Sankar Das Sarma, Michael Freedman, Chetan Nayak, 2010 [reviewed: December 29, 2023]
  180. "Radical chiral Floquet phases in a periodically driven Kitaev model and beyond", Hoi Chun Po et al., 2017 [reviewed: December 29, 2023]
  181. "Dynamically generated logical qubits", Matthew Hastings, Jeongwan Haah, 2021 [reviewed: December 29, 2023]
  182. "Homotopy quantum field theory", Vladimir Turaev, 2010 [reviewed: December 29, 2023]
  183. "Universality of Z3 parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms", Asmae Benhemou et al., 2023 [reviewed: December 29, 2023]
  184. "Boundary conditions, fusion rules and the Verlinde formula", John Cardy, 1989 [reviewed: December 29, 2023]
  185. "Fusion rules and modular transformations in 2D conformal field theory", Erik Verlinde, 1988 [reviewed: December 29, 2023]
  186. "Topological quantum field theories derived from the Kauffman bracket", Christian Blanchet et al., 1995 [reviewed: December 29, 2023]
  187. "Construction of the Reshetikhin-Turaev TQFT from conformal field theory", Jørgen Ellegaard Andersen, Kenji Ueno, 2014 [reviewed: December 28, 2023]
  188. "Lectures on RCFT", Gregory Moore, Nathan Seiberg, 1990 [reviewed: December 28, 2023]
  189. "The geometry of tensor calculus, I", Andre Joyal, Ross Street, 1991 [reviewed: December 27, 2023]
  190. "Classical and quantum conformal field theory", Gregory Moore, Nathan Seiberg, 1989 [reviewed: December 27, 2023]
  191. "Quantum SU(2) faithfully detects mapping class groups modulo center", Michael Freedman, Kevin Walker, Zhenghan Wang, 2002 [reviewed: December 27, 2023]
  192. "Quantum invariants of knots and 3-manifolds", Vladimir Turaev, 1994 [reviewed: December 26, 2023]
  193. "Topological quantum field theory", Michael Atiyah, 1988 [reviewed: December 26, 2023]
  194. "Topological quantum field theory", Edward Witten, 1988 [reviewed: December 26, 2023]
  195. "Braided monoidal categories", Andre Joyal, Ross Street, 1986 [reviewed: December 19, 2023]
  196. "Dawn of the topological age?", Arthur Ramirez, Brian Skinner, 2020 [reviewed: December 17, 2023]
  197. "Large, nonsaturating thermopower in a quantizing magnetic field", Brian Skinner, Liang Fu, 2018 [reviewed: December 17, 2023]
  198. "Majorana bound states in magnetic skyrmions", Guang Yang et al., 2016 [reviewed: December 17, 2023]
  199. "Topological Superconductivity Mediated by Skyrmionic Magnons", Kristian Maeland, Asle Sudbo, 2023 [reviewed: December 16, 2023]
  200. "Manipulating Topological Phases in Magnetic Topological Insulators", Gang Qiu et al., 2023 [reviewed: December 16, 2023]
  201. "Proposal for a negative capacitance topological quantum field-effect transistor", Michael Fuhrer et al., 2021 [reviewed: December 16, 2023]
  202. "Perspective on skyrmion spintronics", Christopher Marrows, Katharina Zeissler, 2021 [reviewed: December 16, 2023]
  203. "Superconducting proximity effect and Majorana fermions at the surface of a topological insulator", Liang Fu, Charles Kane, 2008 [reviewed: December 16, 2023]
  204. "The BQP-hardness of approximating the Jones polynomial", Dorit Aharonov, Itai Arad, 2011 [reviewed: December 16, 2023]
  205. "A model study of present-day Hall-effect circulators", Benedikt Placke et al., 2017 [reviewed: November 30, 2023]
  206. "Majorana fermions in a tunable semiconductor device", Jason Alicea, 2010 [reviewed: November 27, 2023]
  207. "Introduction to topological superconductivity and Majorana fermions", Martin Leijnse, Jarsten Flensberg, 2012 [reviewed: November 17, 2023]
  208. "A silicon-based nuclear spin quantum computer", Bruce Kane, 1998 [reviewed: November 17, 2023]
  209. "The theory of phase transitions", Lev Landau, 1936 [reviewed: November 16, 2023]
  210. "Majorana zero modes and topological quantum computation", Sankar Das Sarma, Michael Freedman, Cheten Nayak, 2015 [reviewed: November 11, 2023]
  211. "2-categories and Zamolodchikov tetrahedra equations", Mikhail Kapranov, Vladimir Voevodsky, 1994 [reviewed: November 10, 2023]
  212. "Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions", Michael Freedman, Zhenghan Wang, Cheten Nayak, et al., 2011 [reviewed: November 7, 2023]
  213. "Majorana fermions and non-Abelian statistics in three dimensions", Jeffrey Teo, Charles Kane, 2010 [reviewed: November 7, 2023]
  214. "Room-temperature manipulation and decoherence of a single spin in diamond", Ronald Hanson et. al, 2006 [reviewed: November 2, 2023]
  215. "Dislocations as single photon sources in two-dimensional semiconductors", Xiaocheng Zhou, Zhuhua Zhang, Wanlin Guo, 2020 [reviewed: October 19, 2023]
  216. "A survey of graphical languages for monoidal categories", Peter Selinger, 2023 [reviewed: October 15, 2023]
  217. "Comments on the classification of the finite subgroups of SU(3)", Patrick Otto Ludl, 2011 [reviewed: October 13, 2023]
  218. "Dilogarithm identities for conformal field theories and cluster algebras: simply laced case", Tomoki Nakanishi, 2011 [reviewed: October 13, 2023]
  219. "Modular categories as representations of the 3-dimensional bordism 2-category", Bruce Bartlett, et. al, 2015 [reviewed: October 10, 2023]
  220. "Rank-finiteness for modular categories", Paul Bruillard, Siu-Hung Ng, Eric Rowell, Zhenghan Wang, 2016 [reviewed: October 8, 2023]
  221. "On Vafa's theorem for tensor categories", Pavel Etingof, 2002 [reviewed: October 8, 2023]
  222. "Wavefunctionology: The special structure of certain fractional quantum Hall wavefunctions", Steven Simon, 2020 [reviewed: October 8, 2023]
  223. "Topological quantum information theory", Louis Kauffman, Samuel Lomonaco, 2009 [reviewed: October 7, 2023]
  224. "Samuel Beckett's Guide to Particles and Antiparticles", Brian Skinner, 2015 [reviewed: October 7, 2023]
  225. "Localization of unitary braid group representations", Eric Rowell, Zhenghan Wang, 2012 [reviewed: October 7, 2023]
  226. "Symmetry fractionalization, defects, and gauging of topological phases", Maissam Barkeshli, Parsa Bonderson, Meng Cheng, Zhenghan Wang, 2019 [reviewed: October 6, 2023]
  227. "Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation", Benoit Doucot, Lev Ioffe, Julien Vidal, 2004 [reviewed: October 6, 2023]
  228. "A short guide to anyons and modular functors", Simon Burton, 2023 [reviewed: October 1, 2023]
  229. "Adaptive constant-depth circuits for manipulating non-abelian anyons", Sergey Bravyi, et al., 2022 [reviewed: October 1, 2023]
  230. "Spin networks in gauge theory", John Baez, 1996 [reviewed: October 1, 2023]
  231. "A statistical mechanics view on Kitaev's proposal for quantum memories", Robert Alicki, Mark Fannes, Michał Horodecki, 2007 [reviewed: October 1, 2023]
  232. "Haag duality and the distal split property for cones in the toric code", Pieter Naaijkens, 2012 [reviewed: October 1, 2023]
  233. "Kitaev's quantum double model as an error correcting code", Shawn Cui, Stanford physics people, 2020 [reviewed: October 1, 2023]
  234. "Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models", Oliver Buerschaper, Miguel Aguado, 2009 [reviewed: October 1, 2023]
  235. "An invitation to topological orders and category theory", Liang Kong, Zhi-Hao Zhang, 2022 [reviewed: September 13, 2023]
  236. "Metaplectic categories, gauging and property F", Paul Gustafson, Eric Rowell, Yuze Ruan, 2020 [reviewed: September 13, 2023]
  237. "Quantum codes, CFTs, and defects", Matthew Buican, Anatoly Dymarsky, Rajath Radhakrishnan, 2023 [reviewed: September 13, 2023]
  238. "Mathematical Aspects of Quantum Field Theories", conference proceeding, 2015 [reviewed: September 13, 2023]
  239. "On the history of the algebraic theory of quadratic forms", Winfried Scharlau, 2000 [reviewed: September 13, 2023]
  240. "Geometric search for Hadamard matrices", Jeffery Kline, 2019 [reviewed: September 12, 2023]
  241. "Higher linear algebra in topology and quantum information theory", David Reutter, 2019 [reviewed: September 12, 2023]
  242. "Qudits and high-dimensional quantum computing", Yuchen Wang, Zixuan Hu, Barry Sanders, Sabre Kais, 2020 [reviewed: September 6, 2023]
  243. "Bulk-edge correspondence in (2+ 1)-dimensional abelian topological phases", Chetan Nayak, et al., 2014 [reviewed: September 6, 2023]
  244. "In and around Abelian anyon models", Zhenghan Wang, Liang Wang, 2020 [reviewed: September 6, 2023]
  245. "Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the ADE Classification", Mayukh Nilay Khan, et al., 2014 [reviewed: September 5, 2023]
  246. "A concise guide to complex Hadamard matrices", Wojciech Tadej, Karol Zyczkowski, 2006 [reviewed: September 5, 2023]
  247. "A hierarchy of anyon models realised by twists in stacked surface codes", Thomas Scruby, Dan Browne, 2020 [reviewed: September 4, 2023]
  248. "Universal fault-tolerant quantum computing with stabilizer codes", Paul Webster et al., 2022 [reviewed: September 4, 2023]
  249. "Introduction to representation theory", Pavel Etingof et al., 2009 [reviewed: September 4, 2023]
  250. "Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs", Nathan Geer, et al., 2022 [reviewed: September 4, 2023]
  251. "Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I", Simon Lentner, et al., 2023 [reviewed: September 4, 2023]
  252. "Origins of the Temperley-Lieb algebra: early history", Stephen Doty, Anthony Giaquinto, 2023 [reviewed: September 1, 2023]
  253. "Index for subfactors", Vaughan Jones, 1983 [reviewed: September 1, 2023]
  254. "Non-binary unitary error bases and quantum codes", Emanuel Knill, 1996 [reviewed: September 1, 2023]
  255. "A polynomial invariant for knots via von Neumann algebras", Vaughn Jones, 1985 [reviewed: August 31, 2023]
  256. "State sum invariants of 3-manifolds and quantum 6j-symbols", Vladimir Turaev, Oleg Viro, 1992 [reviewed: August 31, 2023]
  257. "Invariants of 3-manifolds via link polynomials and quantum groups", Nicolai Reshetikhin, Vladimir Turaev, 1991 [reviewed: August 31, 2023]
  258. "Quantum field theory and the Jones polynomial", Edward Witten, 1989 [reviewed: August 31, 2023]
  259. "Quantum Groups at Roots of Unity and Modularity", Stephen Sawin, 2006 [reviewed: August 31, 2023]
  260. "Lectures on tensor categories and modular functors", Bojko Bakalov, Alexander Kirillov, 2001 [reviewed: August 31, 2023]
  261. "From Quantum Groups to Unitary Modular Tensor Categories", Eric Rowell, 2006 [reviewed: August 31, 2023]
  262. "Subfactors and mathematical physics", David Evans, Yasuyuki Kawahigashi, 2023 [reviewed: August 31, 2023]
  263. "Turaev-Viro invariants as an extended TQFT III", Benjamin Balsam, 2010 [reviewed: August 31, 2023]
  264. "Mixed-state TQFTs", Modjtaba Shokrian Zini, Zhenghan Wang, 2021 [reviewed: August 31, 2023]
  265. "From subfactors to categories and topology II: The quantum double of tensor categories and subfactors", Michael Muger, 2003 [reviewed: August 31, 2023]
  266. "From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories", Michael Muger, 2003 [reviewed: August 31, 2023]
  267. "Quantum advantage of unitary Clifford circuits with magic state inputs", Mithuna Yoganathan, Richard Jozsa, Sergii Strelchuk, 2019 [reviewed: August 25, 2023]
  268. "Quantum double finite group algebras and their representations", Mark Gould, 1993 [reviewed: August 25, 2023]
  269. "Trading classical and quantum computational resources", Sergey Bravyi, Graeme Smith, John Smolin, 2016 [reviewed: August 25, 2023]
  270. "Congruence subgroups and generalized Frobenius-Schur indicators", Siu-Hung Ng, Peter Schauenburg, 2010 [reviewed: August 25, 2023]
  271. "Semi-Clifford operations, structure of C_k hierarchy, and gate complexity for fault-tolerant quantum computation", Bei Zeng, Xie Chen, Isaac Chuang, 2008 [reviewed: August 25, 2023]
  272. "Universal quantum computation with ideal Clifford gates and noisy ancillas", Sergey Bravyi, Alexei Kitaev, 2005 [reviewed: August 25, 2023]
  273. "Quantum Teleportation is a Universal Computational Primitive", Daniel Gottesman, Isaac Chuang, 1999 [reviewed: August 25, 2023]
  274. "Indicators of Tambara-Yamagami categories and Gauss sums", Tathagata Basak, Ryan Johnson, 2015 [reviewed: August 24, 2023]
  275. "Quadratic forms on finite groups, and related topics", Charles Wall, 1963 [reviewed: August 24, 2023]
  276. "Surface code quantum computing by lattice surgery", Dominic Horsman, Austin Fowler, Simon Devitt, Rodney Van Meter, 2012 [reviewed: August 24, 2023]
  277. "Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes", Daniel Litinski, Felix von Oppen, 2018 [reviewed: August 24, 2023]
  278. "Solutions of the hexagon equation for abelian anyons", Cesar Galindo, Nicolas Jaramillo Torres, 2016 [reviewed: August 23, 2023]
  279. "NP-complete Problems and Physical Reality", Scott Aaronson, 2005 [reviewed: August 23, 2023]
  280. "Parafermions in a Kagome lattice of qubits for topological quantum computation", Adrian Hutter, James Wootton, Daniel Loss, 2015 [reviewed: August 22, 2023]
  281. "Quantum Computing with Parafermions", Adrian Hutter, Daniel Loss, 2016 [reviewed: August 22, 2023]
  282. "Universal quantum computation with weakly integral anyons", Shawn Cui, Seung-Moon Hong, Zhenghan Wang, 2015 [reviewed: August 22, 2023]
  283. "The Quantum Double Model with Boundary: Condensations and Symmetries", Salman Beigi, Peter Shor, Daniel Whalen, 2011 [reviewed: August 21, 2023]
  284. "Nested Topological Order", Hector Bombin, Miguel Martin-Delgado, 2011 [reviewed: August 21, 2023]
  285. "Quantum double aspects of surface code models", Alexander Cowtan, Shahn Majid, 2022 [reviewed: August 21, 2023]
  286. "Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras", Bowen Yan, Penghua Chen, Shawn Cui, 2022 [reviewed: August 21, 2023]
  287. "A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation", Hector Bombin, Miguel Martin-Delgado, 2008 [reviewed: August 21, 2023]
  288. "Topological quantum computation with gapped boundaries", Iris Cong, Meng Cheng, Zhenghan Wang, 2015 [reviewed: August 21, 2023]
  289. "Logical Blocks for Fault-Tolerant Topological Quantum Computation", PsiQuantum, 2023 [reviewed: August 21, 2023]
  290. "3-Fermion topological quantum computation", Sam Roberts, Dominic Williamson, 2020 [reviewed: August 21, 2023]
  291. "Universal Quantum Computation with Gapped Boundaries", Iris Cong, Meng Cheng, Zhenghan Wang, 2017 [reviewed: August 18, 2023]
  292. "Fault-tolerant conversion between the steane and reed-muller quantum codes", Jonas Anderson, Guillaume Duclos-Cianci, David Poulin, 2014 [reviewed: August 18,2023]
  293. "Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes", Hector Bombin, 2015 [reviewed: August 18, 2023]
  294. "Quantum Control in the Cs 6S_(1/2) Ground Manifold Using r-f and mu-w Magnetic Fields", Poul Jessen's lab, 2013 [reviewed: August 18, 2023]
  295. "Classification of topologically protected gates for local stabilizer codes", Sergey Bravyi, Robert Konig, 2013 [reviewed: August 18, 2023]
  296. "Qudit color codes and gauge color codes in all spatial dimensions", Fern Watson, Earl Campbell, Hussain Anwar, Dan Browne, 2015 [reviewed: August 18, 2023]
  297. "Qudit surface codes and gauge theory with finite cyclic groups", Stephen Bullock, Gavin Brennen, 2007 [reviewed: August 18, 2023]
  298. "Homological Error Correction: Classical and Quantum Codes", Hector Bombin, Miguel Martin-Delgado, 2007 [reviewed: August 18, 2023]
  299. "Is quantum mechanics useful?", Rolf Landauer, 1995 [reviewed: August 18, 2023]
  300. "Transversal Clifford gates on folded surface codes", Jonathan Moussa, 2016 [reviewed: August 18, 2023]
  301. "Quantum circuits for qubit fusion", Jonathan Moussa, 2015 [reviewed: August 17, 2023]
  302. "Universal quantum computation in the surface code using non-Abelian islands", Katharina Laubscher, Daniel Loss, James Wootton, 2019 [reviewed: August 17, 2023]
  303. "Kitaev's Zd-Codes Threshold Estimates", Guillaume Duclos-Cianci, David Poulin, 2013 [reviewed: August 17, 2023]
  304. "Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code", Benjamin Brown, Katharina Laubscher, Markus Kesselring, James Wootton, 2017 [reviewed: August 17, 2023]
  305. "Fast decoders for qudit topological codes", Hussain Anwar, Benjamin Brown, Earl Campbell, Dan Browne, 2014 [reviewed: August 17, 2023]
  306. "Restrictions on Transversal Encoded Quantum Gate Sets", Bryan Eastin, Emanuel Knill, 2009 [reviewed: August 17, 2023]
  307. "Fault-Tolerant Quantum Computation with Higher-Dimensional Systems", Daniel Gottesman, 1998 [reviewed: August 17, 2023]
  308. "The Heisenberg Representation of Quantum Computers", Daniel Gottesman, 1998 [reviewed: August 17, 2023]
  309. "Abelian Hypergroups and Quantum Computation", Juani Bermejo-Vega and Kevin C. Zatloukal, 2015 [reviewed: August 17, 2023]
  310. "Classical simulations of Abelian-group normalizer circuits with intermediate measurements", Juani Bermejo-Vega, Maarten Van den Nest [reviewed: August 17, 2023]
  311. "Efficient classical simulations of quantum Fourier transforms and normalizer circuits over Abelian groups", Maarten Van den Nest, 2012 [reviewed: August 17, 2023]
  312. "Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic", Erik Hostens, Jeroen Dehaene, and Bart De Moor, 2005 [reviewed: August 17, 2023]
  313. "A linearized stabilizer formalism for systems of finite dimension", Niel de Beaudrap, 2011 [reviewed: August 17, 2023]
  314. "Normalizer Circuits and Quantum Computation", Juani Bermejo-Vega, 2016 [reviewed: August 17, 2023]
  315. "Dissecting Topological Quantum Computation", James Wootton, 2010 [reviewed: August 17, 2023]
  316. "Discrete gauge theories", Mark de Wild Propitius, F. Alexander Bais, 1996 [reviewed: July 28, 2023]
  317. "Topological views on computational complexity", Michael Freedman, 1998 [reviewed: July 27, 2023]
  318. "Anyon computers with smaller groups", Carlos Mochon, 2004 [reviewed: July 26, 2023]
  319. "Anyons from non-solvable groups are sufficient for universal quantum computation", Carlos Mochon, 2003 [reviewed: July 26, 2023]
  320. "Quantum computation with abelian anyons", Seth Lloyd, 2000 [reviewed: July 26, 2023]
  321. "Topological quantum computation", John Preskill, Walter Ogburn, 1998 [reviewed July 26, 2023]
  322. "Fault-tolerant quantum computation", John Preskill, 1997 [reviewed: July 26, 2023]
  323. "Quantum computation and the localization of modular functors", Michael Freedman, 2000 [reviewed: July 26, 2023]
  324. "The two-eigenvalue problem and density of Jones representation of braid groups", Michael Freedman, Michael Larsen, Zhenghan Wang, 2002 [reviewed July 25, 2023]
  325. "Quantum measurements and the Abelian stabilizer problem", Alexei Kitaev, 1995 [reviewed: July 25, 2023]
  326. "Quantum error correction with imperfect gates", Alexei Kitaev, 1997 [reviewed: July 25, 2023]
  327. "Unpaired Majorana Fermions in quantum wires", Alexei Kitaev, 2001 [reviewed: July 25, 2023]
  328. "Topological quantum computation", Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang, 2003 [reviewed: July 22, 2023]
  329. "A modular functor which is universal for quantum computation", Michael Freedman, Michael Larsen, Zhenghan Wang, 2002 [reviewed: July 22, 2023]
  330. "Simulations of topological field theories by quantum computers", Michael Freedman, Alexei Kitaev, Zhenghan Wang, 2002 [reviewed: July 22, 2023]
  331. "P/NP, and the quantum field computer", Michael Freedman, 1998 [reviewed: July 22, 2023]
  332. "Fault tolerant quantum computation by anyons", Alexei Kitaev, 1997 [reviewed: July 21, 2023]