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Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes.
A separator theorem for planar graphs
R. J. Lipton and R. E. Tarjan · 1979
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A separator theorem for graphs of bounded genus
J. R. Gilbert, J. P. Hutchinson, and R. E. Tarjan · 1984
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Fast algorithms for shortest paths in planar graphs, with applications
G. N. Federickson · 1987
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Points, Spheres, and Separators, A Unified Geometric Approach to Graph Partitioning
S. Teng · 1991
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A unified geometric approach to graph separators
S. Teng, G. Miller, and S. Vavasis · 1991
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On sparse spanners of weighted graphs
I. Althöfer, G. Das, D. Dobkin, D. Joseph, and J. Soares · 1993
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Planarization of graphs embedded on surfaces
H. N. Djidjev and S. M. Venkatesan · 1995
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Linear algorithms for partitioning embedded graphs of bounded genus
L. Aleksandrov and H. Djidjev · 1996
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Class of quantum error-correcting codes saturating the quantum Hamming bound
D. Gottesman · 1996
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Fault-tolerant quantum computation
P. W. Shor · 1996
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Expander codes
M. Sipser and D. Spielman · 1996
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Spectral partitioning works: planar graphs and finite element meshes
D. A. Spielman and S.-H. Teng · 1996
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Fault-tolerant quantum computation with constant error
D. Aharonov and M. Ben-Or · 1997
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Stabilizer codes and quantum error correction
D. Gottesman · 1997
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Faster shortest-path algorithms for planar graphs
M. R. Henzinger, P. Klein, S. Rao, and S. Subramanian · 1997
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Quantum computations: algorithms and error correction
A. Y. Kitaev · 1997
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Theory of quantum error-correcting codes
E. Knill and R. Laflamme · 1997
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Separators for sphere-packings and nearest neighbor graphs
G. L. Miller, S.-H. Teng, W. Thurston, and S. A. Vavasis · 1997
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Quantum codes on a lattice with boundary
S. Bravyi and A. Y. Kitaev · 1998
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Resilient quantum computation: error models and thresholds
E. Knill, R. Laflamme, and W. H. Zurek · 1998
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Combinatorial aspects of geometric graphs
S.-H. Teng · 1998
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Upper bounds on the size of quantum codes
A. Ashikhmin and S. Litsyn · 1999
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
D. Gottesman and I. L. Chuang · 1999
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Single-shot decoding of linear rate ldpc quantum codes with high performance
N. P. Breuckmann and V. Londe · 2001
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On expander codes
G. Zémor · 2001
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Z2-systolic freedom and quantum codes
M. H. Freedman, D. A. Meyer, and F. Luo · 2002
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Quantum computation and quantum information
M. A. Nielsen and I. Chuang · 2002
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Fault-tolerant quantum computation by anyons
A. Kitaev · 2003
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Improved simulation of stabilizer circuits
S. Aaronson and D. Gottesman · 2004
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Metric embeddings with relaxed guarantees
I. Abraham, Y. Bartal, T.-H. Chan, K. Dhamdhere, A. Gupta, J. Kleinberg, O. Neiman, and A. Slivkins · 2005
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Quantum accuracy threshold for concatenated distance-3 codes
P. Aliferis, D. Gottesman, and J. Preskill · 2005
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Bounded-degree graphs have arbitrarily large geometric thickness
J. Barát, J. Matoušek, and D. R. Wood · 2006
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Topological quantum distillation
H. Bombin and M. A. Martin-Delgado · 2006
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Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus
J. A. Kelner · 2006
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Spectral graph theory and its applications
D. A. Spielman · 2007
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Degree-3 treewidth sparsifiers
C. Chekuri and J. Chuzhoy · 2014
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Fault-tolerant quantum computation with constant overhead
D. Gottesman · 2014
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Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
L. Guth and A. Lubotzky · 2014
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Ramanujan complexes and bounded degree topological expanders
T. Kaufman, D. Kazhdan, and A. Lubotzky · 2014
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Separator-based graph embedding into multidimensional grids with small edge-congestion
A. Matsubayashi · 2014
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Genus, treewidth, and local crossing number
V. Dujmović, D. Eppstein, and D. R. Wood · 2015
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Nearly tight low stretch spanning trees
I. Abraham, Y. Bartal, and O. Neiman · 2008
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On tree width, bramble size, and expansion
M. Grohe and D. Marx · 2008
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On low dimensional local embeddings
I. Abraham, Y. Bartal, and O. Neiman · 2009
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Bandwidth, expansion, treewidth, separators and universality for bounded-degree graphs
J. Böttcher, K. P. Pruessmann, A. Taraz, and A. Würfl · 2009
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A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
S. Bravyi and B. Terhal · 2009
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Topological order with a twist: Ising anyons from an abelian model
H. Bombin · 2010
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Fault-tolerant logical gates in quantum error-correcting codes
F. Pastawski and B. Yoshida · 2015
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Constructions and noise threshold of hyperbolic surface codes
N. P. Breuckmann and B. M. Terhal · 2016
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Layouts of expander graphs
V. Dujmovic, A. Sidiropoulos, and D. R. Wood · 2016
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A continuum of expanders
D. Hume · 2016
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Efficient decoding of random errors for quantum expander codes
O. Fawzi, A. Grospellier, and A. Leverrier · 2017
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Metric embeddings with outliers
A. Sidiropoulos, D. Wang, and Y. Wang · 2017
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Metric embedding via shortest path decompositions
I. Abraham, A. Filtser, A. Gupta, and O. Neiman · 2018
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The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration
H. Dell, C. Komusiewicz, N. Talmon, and M. Weller · 2018
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Treewidth of graphs with balanced separations
Z. Dvořák and S. Norin · 2018
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Constant overhead quantum fault-tolerance with quantum expander codes
O. Fawzi, A. Grospellier, and A. Leverrier · 2018
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The need for structure in quantum LDPC codes
L. Eldar, M. Ozols, and K. Thompson · 2019
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Golden codes: quantum LDPC codes from regular tessellations of hyperbolic 4-manifolds
V. Londe and A. Leverrier · 2019
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Higher-dimensional quantum hypergraph-product codes with finite rates
W. Zeng and L. P. Pryadko · 2019
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Decodable quantum LDPC codes beyond the square root distance barrier using high dimensional expanders
S. Evra, T. Kaufman, and G. Zémor · 2020
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Separation profiles of graphs of fractals
V. Gladkova and V. Shum · 2020
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Poincaré profiles of groups and spaces
D. Hume, J. Mackay, and R. Tessera · 2020
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Hyperbolic intersection graphs and (quasi)-polynomial time
S. Kisfaludi-Bak · 2020
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Separation and Poincaré profiles
C. Le Coz · 2020
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Balanced product quantum codes
N. P. Breuckmann and J. N. Eberhardt · 2021
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Fiber bundle codes: Breaking the n 1 / 2 n^{1/2} poly log ( n ) \log(n) barrier for quantum LDPC codes
M. B. Hastings, J. Haah, and R. O’Donnell · 2021
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Mathematica, Version 12.3.1
W. R. Inc · 2021
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New cosystolic expanders from tensors imply explicit quantum LDPC codes with Ω ( n log k n ) \Omega(\sqrt{n}\log^{k}n) distance
T. Kaufman and R. J. Tessler · 2021
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Quantum LDPC codes with almost linear minimum distance
P. Panteleev and G. Kalachev · 2021
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