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Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object.
Quantum codes on a lattice with boundary, arxiv
S. B. Bravyi and A. Y. Kitaev · 1998
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Recognition of Flat Orbifolds and the Classification of Tilings in R 3 R^{3}
O. Delgado-Friedrichs · 2001
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Quantum orders in an exact soluble model
Xiao-Gang Wen · 2003
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Fault-tolerant quantum computation by anyons
A Yu Kitaev · 2003
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Data structures and algorithms for tilings I
Olaf Delgado-Friedrichs · 2003
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Resource-efficient linear optical quantum computation
Daniel E Browne and Terry Rudolph · 2005
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Efficient quantum computation with probabilistic quantum gates
L-M Duan and R Raussendorf · 2005
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Long-range quantum entanglement in noisy cluster states
Robert Raussendorf, Sergey Bravyi, and Jim Harrington · 2005
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Universal quantum computation with ideal clifford gates and noisy ancillas
Sergey Bravyi and Alexei Kitaev · 2005
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Stabilizer formalism for operator quantum error correction
David Poulin · 2005
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Anyons in an exactly solved model and beyond
Alexei Kitaev · 2006
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A fault-tolerant one-way quantum computer
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2006
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Operator quantum error-correcting subsystems for self-correcting quantum memories
Dave Bacon · 2006
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Topological quantum distillation
Hector Bombin and Miguel Angel Martin-Delgado · 2006
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Topological fault-tolerance in cluster state quantum computation
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2007
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Optimal resources for topological two-dimensional stabilizer codes: Comparative study
Héctor Bombín and Miguel A Martin-Delgado · 2007
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Fault-tolerant quantum computation with high threshold in two dimensions
Robert Raussendorf and Jim Harrington · 2007
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Blossom v: a new implementation of a minimum cost perfect matching algorithm
Vladimir Kolmogorov · 2009
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Quantum measurements and gates by code deformation
Héctor Bombín and Miguel Angel Martin-Delgado · 2009
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Topological order with a twist: Ising anyons from an abelian model
Héctor Bombín · 2010
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Quantum computation with turaev–viro codes
Robert Koenig, Greg Kuperberg, and Ben W Reichardt · 2010
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Surface code quantum computing with error rates over 1%
David S Wang, Austin G Fowler, and Lloyd CL Hollenberg · 2011
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Interacting quantum observables: categorical algebra and diagrammatics
Bob Coecke and Ross Duncan · 2011
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Error and loss tolerances of surface codes with general lattice structures
Keisuke Fujii and Yuuki Tokunaga · 2012
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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
Clare Horsman, Austin G. Fowler, Simon Devitt, and Rodney Van Meter · 2012
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Time-optimal quantum computation
Austin G Fowler · 2012
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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Models for gapped boundaries and domain walls
Alexei Kitaev and Liang Kong · 2012
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Braiding statistics approach to symmetry-protected topological phases
Michael Levin and Zheng-Cheng Gu · 2012
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Homological stabilizer codes
Jonas T Anderson · 2013
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Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength
Jean-Pierre Tillich and Gilles Zémor · 2013
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Twist defects and projective non-abelian braiding statistics
Maissam Barkeshli, Chao-Ming Jian, and Xiao-Liang Qi · 2013
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Universal fault-tolerant quantum computation with only transversal gates and error correction
Adam Paetznick and Ben W Reichardt · 2013
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Tradeoffs for reliable quantum information storage in surface codes and color codes
Nicolas Delfosse · 2013
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The zx-calculus is complete for stabilizer quantum mechanics
Miriam Backens · 2014
Cited alongside, same era.
Homological product codes
Sergey Bravyi and Matthew B Hastings · 2014
Cited alongside, same era.
Reduced space-time and time costs using dislocation codes and arbitrary ancillas
Matthew B Hastings and A Geller · 2014
Cited alongside, same era.
From three-photon greenberger-horne-zeilinger states to ballistic universal quantum computation
Logical majorana fermions for fault-tolerant quantum simulation
Andrew J Landahl and Benjamin CA Morrison · 2021
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Tailoring fusion-based error correction for high thresholds to biased fusion failures
Kaavya Sahay, Jahan Claes, and Shruti Puri · 2022
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High-threshold quantum computing by fusing one-dimensional cluster states
Stefano Paesani and Benjamin J Brown · 2022
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Building a fault-tolerant quantum computer using concatenated cat codes
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, et al · 2022
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Boundaries for the honeycomb code
Jeongwan Haah and Matthew B Hastings · 2022
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Mercedes Gimeno-Segovia, Pete Shadbolt, Dan E Browne, and Terry Rudolph · 2015
Cited alongside, same era.
Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
Antonio D Córcoles, Easwar Magesan, Srikanth J Srinivasan, Andrew W Cross, Matthias Steffen, Jay M Gambetta, and Jerry M Chow · 2015
Cited alongside, same era.
A magic state’s fidelity can be superior to the operations that created it
Ying Li · 2015
Cited alongside, same era.
Gapped domain walls, gapped boundaries, and topological degeneracy
Tian Lan, Juven C Wang, and Xiao-Gang Wen · 2015
Cited alongside, same era.
Single-shot fault-tolerant quantum error correction
Héctor Bombín · 2015
Cited alongside, same era.
Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes
Héctor Bombín · 2015
Cited alongside, same era.
Unfolding the color code
Aleksander Kubica, Beni Yoshida, and Fernando Pastawski · 2015
Cited alongside, same era.
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A pair measurement surface code on pentagons
Craig Gidney · 2022
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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 · 2022
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Adiabatic paths of hamiltonians, symmetries of topological order, and automorphism codes
David Aasen, Zhenghan Wang, and Matthew B Hastings · 2022
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Pymatching: A python package for decoding quantum codes with minimum-weight perfect matching
Oscar Higgott · 2022
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Fault-tolerant post-selection for low overhead magic state preparation
Héctor Bombín, Mihir Pant, Sam Roberts, and Karthik I Seetharam · 2022
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Circuit-level protocol and analysis for twist-based lattice surgery
Christopher Chamberland and Earl T Campbell · 2022
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Single-shot quantum error correction with the three-dimensional subsystem toric code
Aleksander Kubica and Michael Vasmer · 2022
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Pauli topological subsystem codes from abelian anyon theories
Tyler D Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, and Dominic J Williamson · 2022
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Fusion-based quantum computation
Sara Bartolucci, Patrick Birchall, Hector Bombin, Hugo Cable, Chris Dawson, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Naomi Nickerson, Mihir Pant, et al · 2023
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Parity-encoding-based quantum computing with bayesian error tracking
Seok-Hyung Lee, Srikrishna Omkar, Yong Siah Teo, and Hyunseok Jeong · 2023
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High photon-loss threshold quantum computing using ghz-state measurements
Brendan Pankovich, Angus Kan, Kwok Ho Wan, Maike Ostmann, Alex Neville, Srikrishna Omkar, Adel Sohbi, and Kamil Brádler · 2023
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Suppressing quantum errors by scaling a surface code logical qubit
Google Quantum AI · 2023
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Relaxing hardware requirements for surface code circuits using time-dynamics
Matt McEwen, Dave Bacon, and Craig Gidney · 2023
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Tangling schedules eases hardware connectivity requirements for quantum error correction
Gyorgy P Geher, Ophelia Crawford, and Earl T Campbell · 2023
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Performance of planar floquet codes with majorana-based qubits
Adam Paetznick, Christina Knapp, Nicolas Delfosse, Bela Bauer, Jeongwan Haah, Matthew B Hastings, and Marcus P da Silva · 2023
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Floquet codes without parent subsystem codes
Margarita Davydova, Nathanan Tantivasadakarn, and Shankar Balasubramanian · 2023
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Unifying flavors of fault tolerance with the zx calculus
Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts · 2023
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Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring · 2023
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Engineering floquet codes by rewinding
Arpit Dua, Nathanan Tantivasadakarn, Joseph Sullivan, and Tyler D Ellison · 2023
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Logical blocks for fault-tolerant topological quantum computation
Hector Bombin, Chris Dawson, Ryan V Mishmash, Naomi Nickerson, Fernando Pastawski, and Sam Roberts · 2023
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Fusion blossom: Fast mwpm decoders for qec
Yue Wu and Lin Zhong · 2023
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Optimizing graph codes for measurement-based loss tolerance
Thomas J Bell, Love A Pettersson, and Stefano Paesani · 2023
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Increasing error tolerance in quantum computers with dynamic bias arrangement
Hector Bombín, Chris Dawson, Naomi Nickerson, Mihir Pant, and Jordan Sullivan · 2023
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Hierarchical memories: Simulating quantum ldpc codes with local gates
Christopher A Pattison, Anirudh Krishna, and John Preskill · 2023
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Modular decoding: parallelizable real-time decoding for quantum computers
Héctor Bombín, Chris Dawson, Ye-Hua Liu, Naomi Nickerson, Fernando Pastawski, and Sam Roberts · 2023
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Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
Jacob C Bridgeman, Aleksander Kubica, and Michael Vasmer · 2023
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Single-shot quantum error correction in intertwined toric codes
Charles Stahl · 2023
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Topological error correcting processes from fixed-point path integrals
Andreas Bauer · 2023
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Constructions and performance of hyperbolic and semi-hyperbolic floquet codes
Oscar Higgott and Nikolas P Breuckmann · 2023
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