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We introduce quantum pin codes: a class of quantum CSS codes.
1905
Earlier work this paper cites.
R. Gallager, “Low-density parity-check codes,” IRE Transactions on information theory , vol. 8, no. 1, pp. 21–28, 1962
1962
Earlier work this paper cites.
H. S. M. Coxeter, Regular polytopes . Courier Corporation, 1973
1973
Earlier work this paper cites.
——, Regular polytopes , 3rd ed. New York: Dover Publications, 1973, open Library ID: OL5436086M
1973
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Physical Review A , vol. 54, no. 2, pp. 1098–1105, Aug. 1996. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.54.1098
1996
Earlier work this paper cites.
Steane Andrew, “Multiple-particle interference and quantum error correction,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences , vol. 452, no. 1954, pp. 2551–2577, Nov. 1996. [Online]. Available: https://royalsocietypublishing.org/doi/10.1098/rspa.1996.0136
1996
Earlier work this paper cites.
E. Knill, R. Laflamme, and W. Zurek, “Threshold Accuracy for Quantum Computation,” arXiv:quant-ph/9610011 , Oct. 1996
1996
Earlier work this paper cites.
D. Gottesman, “Stabilizer codes and quantum error correction,” PhD Thesis, California Institute of Technology, Jan. 1997
1997
Earlier work this paper cites.
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, “Quantum error correction via codes over GF(4),” in Proceedings of IEEE International Symposium on Information Theory , Jun. 1997, pp. 292–
1997
Earlier work this paper cites.
M. Grassl, T. Beth, and T. Pellizzari, “Codes for the quantum erasure channel,” Physical Review A , vol. 56, no. 1, pp. 33–38, Jul. 1997. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.56.33
1997
Earlier work this paper cites.
L. Zhang and I. Fuss, “Quantum Reed-Muller Codes,” arXiv:quant-ph/9703045 , Mar. 1997
1997
Earlier work this paper cites.
A. Steane, “Quantum Reed-Muller codes,” IEEE Transactions on Information Theory , vol. 45, no. 5, pp. 1701–1703, Jul. 1999
1999
Earlier work this paper cites.
M. H. Freedman and D. A. Meyer, “Projective Plane and Planar Quantum Codes,” Foundations of Computational Mathematics , vol. 1, no. 3, pp. 325–332, Jul. 2001. [Online]. Available: https://doi.org/10.1007/s102080010013
2001
Earlier work this paper cites.
M. H. Freedman, D. A. Meyer, and F. Luo, “$Z_2$-systolic freedom and quantum codes,” in Mathematics of quantum computation , ser. Computational Mathematics, R. K. Brylinski and G. Chen, Eds. Boca Raton, FL: Chapman & Hall/CRC, 2002, no. 3, pp. 287–320
2002
Earlier work this paper cites.
P. McMullen and E. Schulte, Abstract Regular Polytopes , ser. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2002
2002
Earlier work this paper cites.
A. Y. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics , vol. 303, no. 1, pp. 2–30, Jan. 2003. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0003491602000180
2003
Earlier work this paper cites.
S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas,” Physical Review A , vol. 71, no. 2, p. 022316, Feb. 2005. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.71.022316
2005
Earlier work this paper cites.
P. Sarvepalli and A. Klappenecker, “Nonbinary quantum Reed-Muller codes,” in Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. , Sep. 2005, pp. 1023–1027
2005
Earlier work this paper cites.
D. Poulin, “Stabilizer Formalism for Operator Quantum Error Correction,” Physical Review Letters , vol. 95, no. 23, p. 230504, Dec. 2005. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.95.230504
2005
Earlier work this paper cites.
D. Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories,” Physical Review A , vol. 73, no. 1, p. 012340, Jan. 2006. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.73.012340
2006
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, “Topological Quantum Distillation,” Physical Review Letters , vol. 97, no. 18, p. 180501, Oct. 2006. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.97.180501
2006
Cited alongside, same era.
H. Bombin and M. A. Martin-Delgado, “Exact topological quantum order in {$d=3$} and beyond: Branyons and brane-net condensates,” Physical Review B , vol. 75, no. 7, p. 075103, Feb. 2007. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevB.75.075103
2007
Cited alongside, same era.
M. W. Davis, The Geometry and Topology of Coxeter Groups. (LMS-32) (London Mathematical Society Monographs) . Princeton University Press, Oct. 2007, open Library ID: OL11182953M
2007
Cited alongside, same era.
J. J. Rotman, An introduction to homological algebra . Springer Science & Business Media, 2008
2008
Cited alongside, same era.
A. Bhagoji and P. Sarvepalli, “Equivalence of 2d color codes (without translational symmetry) to surface codes,” in 2015 IEEE International Symposium on Information Theory (ISIT) , Jun. 2015, pp. 1109–1113
2015
Later among the works it cites.
H. Bombín, “Single-Shot Fault-Tolerant Quantum Error Correction,” Physical Review X , vol. 5, no. 3, p. 031043, Sep. 2015. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevX.5.031043
2015
Later among the works it cites.
N. P. Breuckmann and B. M. Terhal, “Constructions and Noise Threshold of Hyperbolic Surface Codes,” IEEE Transactions on Information Theory , vol. 62, no. 6, pp. 3731–3744, Jun. 2016
2016
Later among the works it cites.
E. T. Campbell, B. M. Terhal, and C. Vuillot, “Roads towards fault-tolerant universal quantum computation,” Nature , vol. 549, no. 7671, pp. 172–179, Sep. 2017. [Online]. Available: https://www.nature.com/articles/nature23460
2017
Later among the works it cites.
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S. Bravyi and J. Haah, “Magic-state distillation with low overhead,” Physical Review A , vol. 86, no. 5, p. 052329, Nov. 2012. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.86.052329
2012
Cited alongside, same era.
E. T. Campbell, H. Anwar, and D. E. Browne, “Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes,” Physical Review X , vol. 2, no. 4, p. 041021, Dec. 2012
2012
Cited alongside, same era.
A. A. Kovalev and L. P. Pryadko, “Quantum Kronecker sum-product low-density parity-check codes with finite rate,” Physical Review A , vol. 88, no. 1, p. 012311, Jul. 2013. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.88.012311
2013
Cited alongside, same era.
A. Couvreur, N. Delfosse, and G. Zémor, “A Construction of Quantum LDPC Codes From Cayley Graphs,” IEEE Transactions on Information Theory , vol. 59, no. 9, pp. 6087–6098, Sep. 2013
2013
Cited alongside, same era.
2013
Cited alongside, same era.
C. Jones, “Multilevel distillation of magic states for quantum computing,” Physical Review A , vol. 87, no. 4, p. 042305, Apr. 2013. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.87.042305
2013
Cited alongside, same era.
N. Delfosse, “Tradeoffs for reliable quantum information storage in surface codes and color codes,” in 2013 IEEE International Symposium on Information Theory , Jul. 2013, pp. 917–921
2013
Cited alongside, same era.
L. Guth and A. Lubotzky, “Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds,” Journal of Mathematical Physics , vol. 55, no. 8, p. 082202, Aug. 2014. [Online]. Available: https://aip.scitation.org/doi/10.1063/1.4891487
2014
Cited alongside, same era.
E. T. Campbell and M. Howard, “Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost,” Physical Review A , vol. 95, no. 2, p. 022316, Feb. 2017. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.95.022316
2017
Later among the works it cites.
S. X. Cui, D. Gottesman, and A. Krishna, “Diagonal gates in the Clifford hierarchy,” Physical Review A , vol. 95, no. 1, Jan. 2017. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.95.012329
2017
Later among the works it cites.
E. T. Campbell and M. Howard, “Unifying Gate Synthesis and Magic State Distillation,” Physical Review Letters , vol. 118, no. 6, p. 060501, Feb. 2017. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.118.060501
2017
Later among the works it cites.
J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, “Magic state distillation with low space overhead and optimal asymptotic input count,” Quantum , vol. 1, p. 31, Oct. 2017. [Online]. Available: https://quantum-journal.org/papers/q-2017-10-03-31/
2017
Later among the works it cites.
2017
Later among the works it cites.
J. Haah and M. B. Hastings, “Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates,” Quantum , vol. 2, p. 71, Jun. 2018. [Online]. Available: https://quantum-journal.org/papers/q-2018-06-07-71/
2018
Later among the works it cites.
M. B. Hastings and J. Haah, “Distillation with Sublogarithmic Overhead,” Physical Review Letters , vol. 120, no. 5, p. 050504, Jan. 2018. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.120.050504
2018
Later among the works it cites.
A. B. Aloshious and P. K. Sarvepalli, “Projecting three-dimensional color codes onto three-dimensional toric codes,” Physical Review A , vol. 98, no. 1, p. 012302, Jul. 2018. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.98.012302
2018
Later among the works it cites.
A. Kubica, M. E. Beverland, F. Brandão, J. Preskill, and K. M. Svore, “Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping,” Physical Review Letters , vol. 120, no. 18, p. 180501, May 2018. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.120.180501
2018
Later among the works it cites.
B. Audoux and A. Couvreur, “On tensor products of CSS codes,” Annales de l’Institut Henri Poincaré D , vol. 6, no. 2, pp. 239–287, Mar. 2019. [Online]. Available: https://www.ems-ph.org/journals/show_abstract.php?issn=2308-5827&vol=6&iss=2&rank=4
2019
Closest in time.
E. T. Campbell, “A theory of single-shot error correction for adversarial noise,” Quantum Science and Technology , vol. 4, no. 2, p. 025006, Feb. 2019. [Online]. Available: https://doi.org/10.1088%2F2058-9565%2Faafc8f
2019
Closest in time.
W. Zeng and L. P. Pryadko, “Higher-Dimensional Quantum Hypergraph-Product Codes with Finite Rates,” Physical Review Letters , vol. 122, no. 23, p. 230501, Jun. 2019
2019
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N. Rengaswamy, R. Calderbank, M. Newman, and H. D. Pfister, “On optimality of css codes for transversal T,” IEEE Journal on Selected Areas in Information Theory , vol. 1, no. 2, pp. 499–514, 2020
2020
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M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes,” Online available at http://www.codetables.de , 2007, accessed on 2021-04-26
2021
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M. S. Kesselring, F. Pastawski, J. Eisert, and B. J. Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation,” Quantum , vol. 2, p. 101, Oct. 2018. [Online]. Available: https://quantum-journal.org/papers/q-2018-10-19-101/
2021
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