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In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation.
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A. Yu. Kitaev · 1997
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“Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping”
P. T. Cochrane, G. J. Milburn, and W. J. Munro · 1999
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“Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations”
Daniel Gottesman and Isaac L. Chuang · 1999
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“Encoding a qubit in an oscillator”
Daniel Gottesman, Alexei Kitaev, and John Preskill · 2001
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“Topological quantum memory”
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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“Fault-tolerant quantum computation by anyons”
A.Yu. Kitaev · 2003
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“Anyon computers with smaller groups”
Carlos Mochon · 2004
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“Universal quantum computation with ideal clifford gates and noisy ancillas”
Sergey Bravyi and Alexei Kitaev · 2005
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“Correspondences of ribbon categories”
Jürg Fröhlich, Jürgen Fuchs, Ingo Runkel, and Christoph Schweigert · 2006
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“Non-abelian anyons and topological quantum computation”
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma · 2008
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“Topological quantum computation”
Zhenghan Wang · 2008
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“Family of non-abelian kitaev models on a lattice: Topological condensation and confinement”
H. Bombin and M. A. Martin-Delgado · 2008
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“An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation” (2009)
Daniel Gottesman · 2009
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“Restrictions on transversal encoded quantum gate sets”
Bryan Eastin and Emanuel Knill · 2009
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“Condensate-induced transitions between topologically ordered phases”
F. A. Bais and J. K. Slingerland · 2009
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“On braided fusion categories i”
Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik · 2010
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“Surface codes: Towards practical large-scale quantum computation”
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
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“Surface code quantum computing by lattice surgery”
Dominic Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter · 2012
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“Fault-tolerant conversion between the steane and reed-muller quantum codes”
Jonas T. Anderson, Guillaume Duclos-Cianci, and David Poulin · 2014
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“Diagrammatics for bose condensation in anyon theories”
I. S. Eliëns, J. C. Romers, and F. A. Bais · 2014
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“Anyon condensation and tensor categories”
Liang Kong · 2014
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“An ideal characterization of the clifford operators”
J M Farinholt · 2014
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“Error correction for non-abelian topological quantum computation”
James R. Wootton, Jan Burri, Sofyan Iblisdir, and Daniel Loss · 2014
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“Universal transversal gates with color codes: A simplified approach”
Aleksander Kubica and Michael E. Beverland · 2015
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“Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes”
Héctor Bombín · 2015
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“Gauging quantum states: From global to local symmetries in many-body systems”
Jutho Haegeman, Karel Van Acoleyen, Norbert Schuch, J. Ignacio Cirac, and Frank Verstraete · 2015
“A (dummy’s) guide to working with gapped boundaries via (fermion) condensation”
Jiaqi Lou, Ce Shen, Chaoyi Chen, and Ling-Yan Hung · 2021
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“Quantum circuits assisted by local operations and classical communication: Transformations and phases of matter”
Lorenzo Piroli, Georgios Styliaris, and J. Ignacio Cirac · 2021
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Ruben Verresen, Nathanan Tantivasadakarn, and Ashvin Vishwanath · 2021
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“Adaptive constant-depth circuits for manipulating non-abelian anyons” (2022)
Sergey Bravyi, Isaac Kim, Alexander Kliesch, and Robert Koenig · 2022
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Cited alongside, same era.
“Universal quantum computation with weakly integral anyons”
Shawn X. Cui, Seung-Moon Hong, and Zhenghan Wang · 2015
Cited alongside, same era.
“Quantum circuits for qubit fusion”
Jonathan E. Moussa · 2016
Cited alongside, same era.
“Transversal clifford gates on folded surface codes”
Jonathan E. Moussa · 2016
Cited alongside, same era.
“Poking holes and cutting corners to achieve clifford gates with the surface code”
Benjamin J. Brown, Katharina Laubscher, Markus S. Kesselring, and James R. Wootton · 2017
Cited alongside, same era.
“Universal quantum computation with gapped boundaries”
Iris Cong, Meng Cheng, and Zhenghan Wang · 2017
Cited alongside, same era.
“Hamiltonian and algebraic theories of gapped boundaries in topological phases of matter”
Iris Cong, Meng Cheng, and Zhenghan Wang · 2017
Cited alongside, same era.
Alexander Cowtan · 2022
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“Pauli stabilizer models of twisted quantum doubles”
Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J. Williamson · 2022
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“Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward”
Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen · 2023
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“Shortest route to non-abelian topological order on a quantum processor”
Nathanan Tantivasadakarn, Ruben Verresen, and Ashvin Vishwanath · 2023
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“Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements”
Yabo Li, Hiroki Sukeno, Aswin Parayil Mana, Hendrik Poulsen Nautrup, and Tzu-Chieh Wei · 2023
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“Topological quantum computation assisted by phase transitions” (2023)
Yuanjie Ren and Peter Shor · 2023
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“The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries” (2023)
Lakshya Bhardwaj, Lea E. Bottini, Daniel Pajer, and Sakura Schafer-Nameki · 2023
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“Holographic theory for continuous phase transitions: Emergence and symmetry protection of gaplessness”
Arkya Chatterjee and Xiao-Gang Wen · 2023
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“Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases”
Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, and Ruben Verresen · 2024
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“Anyon condensation and the color code”
Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown · 2024
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“Low-overhead fault-tolerant quantum computation by gauging logical operators” (2024)
Dominic J. Williamson and Theodore J. Yoder · 2024
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“Inplace Access to the Surface Code Y Basis”
Craig Gidney · 2024
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“Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries” (2024)
Lakshya Bhardwaj, Daniel Pajer, Sakura Schafer-Nameki, and Alison Warman · 2024
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“Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits” (2024)
Yuanjie Ren, Nathanan Tantivasadakarn, and Dominic J. Williamson · 2024
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“Non-abelian topological order and anyons on a trapped-ion processor”
Mohsin Iqbal, Nathanan Tantivasadakarn, Ruben Verresen, Sara L. Campbell, Joan M. Dreiling, Caroline Figgatt, John P. Gaebler, Jacob Johansen, Michael Mills, Steven A. Moses, Juan M. Pino, Anthony Ransford, Mary Rowe, Peter Siegfried, Russell P. Stutz, Michael Foss-Feig, Ashvin Vishwanath, and Henrik Dreyer · 2024
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“Code switching revisited: Low-overhead magic state preparation using color codes”
Lucas Daguerre and Isaac H. Kim · 2025
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“Universal fault tolerant quantum computation in 2D without getting tied in knots” (2025)
Margarita Davydova, Andreas Bauer, Julio C. Magdalena de la Fuente, Mark Webster, Dominic J. Williamson, and Benjamin J. Brown · 2025
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