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In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators.
Low-density parity-check codes
R. Gallager · 1962
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A separator theorem for planar graphs
Richard J Lipton and Robert Endre Tarjan · 1979
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Applications of a planar separator theorem
Richard J Lipton and Robert Endre Tarjan · 1980
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Good quantum error-correcting codes exist
A. R. Calderbank and Peter W. Shor · 1996
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Expander codes
M. Sipser and D. A. Spielman · 1996
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Simple quantum error-correcting codes
A. M. Steane · 1996
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Quantum teleportation is a universal computational primitive
Daniel Gottesman and Isaac L Chuang · 1999
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A simple algorithm for edge-coloring bipartite multigraphs
Noga Alon · 2003
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Combining hard and soft decoders for hypergraph product codes
Antoine Grospellier, Lucien Grouès, Anirudh Krishna, and Anthony Leverrier · 2004
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Sparse-graph codes for quantum error correction
D.J.C. MacKay, G. Mitchison, and P.L. McFadden · 2004
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On the iterative decoding of sparse quantum codes
David Poulin and Yeojin Chung · 2008
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Introduction to algorithms
Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, and Clifford Stein · 2009
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On cayley graphs, surface codes, and the limits of homological coding for quantum error correction
Gilles Zémor · 2009
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Tradeoffs for Reliable Quantum Information Storage in 2D Systems
Sergey Bravyi, David Poulin, and Barbara Terhal · 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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Decoding in hyperbolic spaces: Ldpc codes with linear rate and efficient error correction
Matthew B Hastings · 2013
Cited alongside, same era.
Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength
J. Tillich and G. Zémor · 2013
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Quantum supremacy using a programmable superconducting processor
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al · 2019
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Numerical study of hypergraph product codes
Antoine Grospellier and Anirudh Krishna · 2019
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A spacetime area law bound on quantum correlations
Ilya Kull, Philippe Allard Guérin, and Časlav Brukner · 2019
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Degenerate quantum ldpc codes with good finite length performance
Pavel Panteleev and Gleb Kalachev · 2019
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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 · 2020
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Daniel Gottesman · 2014
Cited alongside, same era.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Larry Guth and Alexander Lubotzky · 2014
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Quantum Expander Codes
A. Leverrier, J. Tillich, and G. Zémor · 2015
Cited alongside, same era.
Entanglement rates and the stability of the area law for the entanglement entropy
Michaël Mariën, Koenraad MR Audenaert, Karel Van Acoleyen, and Frank Verstraete · 2016
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Scalable designs for quasiparticle-poisoning-protected topological quantum computation with majorana zero modes
Torsten Karzig, Christina Knapp, Roman M Lutchyn, Parsa Bonderson, Matthew B Hastings, Chetan Nayak, Jason Alicea, Karsten Flensberg, Stephan Plugge, Yuval Oreg, et al · 2017
Cited alongside, same era.
Constant Overhead Quantum Fault-Tolerance with Quantum Expander Codes
Omar Fawzi, Antoine Grospellier, and Anthony Leverrier · 2018
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Numerical and analytical bounds on threshold error rates for hypergraph-product codes
Alexey A Kovalev, Sanjay Prabhakar, Ilya Dumer, and Leonid P Pryadko · 2018
Cited alongside, same era.
Later among the works it cites.
Quantum ldpc codes with almost linear minimum distance
Pavel Panteleev and Gleb Kalachev · 2020
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Decoding across the quantum low-density parity-check code landscape
Joschka Roffe, David R White, Simon Burton, and Earl Campbell · 2020
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Connectivity constrains quantum codes
Nouédyn Baspin and Anirudh Krishna · 2021
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Toward a union-find decoder for quantum ldpc codes
Nicolas Delfosse, Vivien Londe, and Michael Beverland · 2021
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Fiber bundle codes: breaking the n 1/2 polylog (n) barrier for quantum ldpc codes
Matthew B Hastings, Jeongwan Haah, and Ryan O’Donnell · 2021
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Constant-overhead quantum error correction with thin planar connectivity
Maxime A. Tremblay, Nicolas Delfosse, Michael E. Beverland · 2021
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