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We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC).
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Good quantum error-correcting codes exist
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Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Turbo codes are low density parity check codes
David J. C. MacKay · 2002
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The Monte Carlo method in the physical sciences: Celebrating the 50th anniversary of the Metropolis algorithm
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Information Theory, Inference, and Learning Algorithms
D. J. C. MacKay · 2003
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An introduction to factor graphs
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Sparse graph codes for quantum error-correction
David J.C. MacKay, Graeme Mitchison, and Paul L. McFadden · 2004
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High threshold universal quantum computation on the surface code
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Interacting quantum observables: categorical algebra and diagrammatics
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Quantum picturalism for topological cluster-state computing
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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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D. Horsman, A. Fowler, S. Devitt, and R. Van Meter · 2012
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Simon J Devitt, William J Munro, and Kae Nemoto · 2013
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Jean-Pierre Tillich and Gilles Zémor · 2013
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Ashley M. Stephens · 2014
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T. P. Harty, D. T. C. Allcock, C. J. Ballance, L. Guidoni, H. A. Janacek, N. M. Linke, D. N. Stacey, and D. M. Lucas · 2014
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W. Wang, J. Machta, and H. G. Katzgraber · 2015
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Maximum-entropy inference with a programmable annealer
Nicholas Chancellor, Szilard Szoke, Walter Vinci, Gabreil Aeppli, and Paul A. Warburton · 2016
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Completeness of the zx-calculus
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Single-shot error mitigation by coherent pauli checks
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Good quantum LDPC codes with linear time decoders
Irit Dinur, Min-Hsiu Hsieh, Ting-Chun Lin, and Thomas Vidick · 2023
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Unifying flavors of fault tolerance with the zx calculus
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http://www.dwavesys.com/. Accessed: 2023-01-06
2023
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