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We study parallel fault-tolerant quantum computing for families of homological quantum low-density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant encoding rate.
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L. Guth and A. Lubotzky, Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds, Journal of Mathematical Physics 55
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A. Kubica, B. Yoshida, and F. Pastawski, Unfolding the color code, New Journal of Physics 17
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H. Bombin, Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes, New Journal of Physics 17
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2022
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2017
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N. P. Breuckmann, C. Vuillot, E. Campbell, A. Krishna, and B. M. Terhal, Hyperbolic and semi-hyperbolic surface codes for quantum storage, Quantum Science and Technology 2
2017
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P. Webster and S. D. Bartlett, Locality-preserving logical operators in topological stabilizer codes, Phys. Rev. A 97
2018
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S. Kojima and G. McShane, Normalized entropy versus volume for pseudo-anosovs, Geom. Topol. 22
2018
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2018
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2019
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2019
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2022
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2022
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2022
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2022
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2022
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2022
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2022
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2022
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2022
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2022
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G. Zhu, T. Jochym-O’Connor, and A. Dua, Topological order, quantum codes, and quantum computation on fractal geometries, PRX Quantum 3
2022
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I. Dinur, M. Hsieh, T. Lin, and T. Vidick, Good quantum ldpc codes with linear time decoders, in Proc. ACM STOC (Association for Computing Machinery, New York, NY, USA, 2023) pp. 905–918
2023
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