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We present a quantum LDPC code family that has distance $\Omega(N^{3/5}/\operatorname{polylog}(N))$ and $\tilde\Theta(N^{3/5})$ logical qubits.
On concentrators, superconcentrators, generalizers, and nonblocking networks
Fan R. K. Chung · 1979
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Asymptotically optimal switching circuits
Leonid Bassalygo · 1981
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Explicit construction of linear sized tolerant networks
Noga Alon and Fan R. K. Chung · 1988
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Random Cayley graphs and expanders
Noga Alon and Yuval Roichman · 1994
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Expander codes
Michael Sipser and Daniel A. Spielman · 1996
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Derandomizing approximation algorithms based on semidefinite programming
Sanjeev Mahajan and H. Ramesh · 1999
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Projective plane and planar quantum codes
Michael H. Freedman and David A. Meyer · 2001
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Z 2 Z_{2} -systolic freedom and quantum codes
Michael H. Freedman, David A. Meyer, and Feng Luo · 2002
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Fault-tolerant quantum computation by anyons
Alexei Yu. Kitaev · 2003
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Stabilizer formalism for operator quantum error correction
David Poulin · 2005
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Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
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Modern Coding Theory
Tom Richardson and Rüdiger Urbanke · 2008
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Pseudorandomness
Salil P. Vadhan · 2012
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Homological product codes
Sergey Bravyi and Matthew B. Hastings · 2014
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Quantum systems on non- k k -hyperfinite complexes: a generalization of classical statistical mechanics on expander graphs
Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength
Jean-Pierre Tillich and Gilles Zémor · 2014
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Quantum expander codes
Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor · 2015
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Sparse quantum codes from quantum circuits
Dave Bacon, Steven T. Flammia, Aram W. Harrow, and Jonathan Shi · 2017
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Quantum codes from high-dimensional manifolds
Matthew B. Hastings · 2017
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Weight reduction for quantum codes
Matthew B. Hastings · 2017
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Decodable quantum LDPC codes beyond the n \sqrt{n} distance barrier using high dimensional expanders
Shai Evra, Tali Kaufman, and Gilles Zémor · 2020
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Michael H. Freedman and Matthew B. Hastings · 2014
Cited alongside, same era.
https://ncatlab.org/nlab/show/chain+homotopy
Cited in the paper.
Quantum LDPC codes with Ω ( n log k n ) \Omega(\sqrt{n}\log^{k}n) distance, for any k k
Tali Kaufman and Ran J. Tessler · 2020
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