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Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy.
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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. Kitaev · 2003
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“Confinement-Higgs Transition in a Disordered Gauge Theory and the Accuracy Threshold for Quantum Memory”
Chenyang Wang, Jim Harrington and John Preskill · 2003
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“Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory”
Takuya Ohno, Gaku Arakawa, Ikuo Ichinose and Tetsuo Matsui · 2004
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“Improved Simulation of Stabilizer Circuits”
Scott Aaronson and Daniel Gottesman · 2004
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“Topological Quantum Distillation”
H. Bombin and M.. Martin-Delgado · 2006
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“Magnetic-Glassy Multicritical Behavior of the Three-Dimensional ± J Ising Model”
M. Hasenbusch, F. Toldin, A. Pelissetto and E. Vicari · 2007
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“Variational Study of Hard-Core Bosons in a 2-D Optical Lattice Using Projected Entangled Pair States (PEPS)”
V. Murg, F. Verstraete and J.. Cirac · 2007
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“Accurate Determination of Tensor Network State of Quantum Lattice Models in Two Dimensions”
H.. Jiang, Z.. Weng and T. Xiang · 2008
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“Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions”
J. Jordan et al · 2008
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“Logical Operators of Quantum Codes”
Mark. Wilde · 2009
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“Simulation of Strongly Correlated Fermions in Two Spatial Dimensions with Fermionic Projected Entangled-Pair States”
Philippe Corboz, Roman Orus, Bela Bauer and Guifre Vidal · 2010
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“An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation”
Daniel Gottesman · 2010
Cited alongside, same era.
“Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code”
Sergey Bravyi, Martin Suchara and Alexander Vargo · 2014
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“Tensor Networks and Quantum Error Correction”
Andrew. Ferris and David Poulin · 2014
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“A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States”
Román Orús · 2014
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“Fault-Tolerant Renormalization Group Decoder for Abelian Topological Codes”
Guillaume Duclos-Cianci and David Poulin · 2014
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“Algorithms for Finite Projected Entangled Pair States”
Michael Lubasch, J. Cirac and Mari-Carmen Bañuls · 2014
“General Tensor Network Decoding of 2D Pauli Codes”, 2021
Christopher. Chubb · 2021
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“Single-Shot Error Correction of Three-Dimensional Homological Product Codes”
Armanda. Quintavalle, Michael Vasmer, Joschka Roffe and Earl. Campbell · 2021
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“Stim: A Fast Stabilizer Circuit Simulator”
Craig Gidney · 2021
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“Cellular automaton decoders for topological quantum codes with noisy measurements and beyond”
Michael Vasmer, Dan. Browne and Aleksander Kubica · 2021
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Andrew. Darmawan, Yoshifumi Nakata, Shiro Tamiya and Hayata Yamasaki · 2022
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Cited alongside, same era.
“Infinite Projected Entangled Pair States Algorithm Improved: Fast Full Update and Gauge Fixing”
Ho. Phien et al · 2015
Cited alongside, same era.
“A Linear-Time Benchmarking Tool for Generalized Surface Codes”, 2016
Nicolas Delfosse, Pavithran Iyer and David Poulin · 2016
Cited alongside, same era.
“The ABCs of the Color Code: A Study of Topological Quantum Codes as Toy Models for Fault-Tolerant Quantum Computation and Quantum Phases Of Matter”, 2017
Aleksander Kubica · 2017
Cited alongside, same era.
“Hand-Waving and Interpretive Dance: An Introductory Course on Tensor Networks”
Jacob. Bridgeman and Christopher. Chubb · 2017
Cited alongside, same era.
“Renormalization Group Decoder for a Four-Dimensional Toric Code”
K. Duivenvoorden, N.. Breuckmann and B.. Terhal · 2018
Cited alongside, same era.
“Scalable Neural Network Decoders for Higher Dimensional Quantum Codes”
Nikolas. Breuckmann and Xiaotong Ni · 2018
Cited alongside, same era.
Eric Huang et al · 2022
Later among the works it cites.
“PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching”
Oscar Higgott · 2022
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“Quantum Constructions on Hamiltonians, Codes, and Circuits”, 2022
Thomas Bohdanowicz · 2022
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“LDPC: Python Tools for Low Density Parity Check Codes”, 2022
Joschka Roffe · 2022
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“Suppressing quantum errors by scaling a surface code logical qubit”
Rajeev Acharya et al · 2023
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“Efficient tensor network simulation of IBM’s largest quantum processors”, 2023
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