×

Construction of polygonal color codes from hyperbolic tesselations. (English) Zbl 1525.81018

MSC:

81P70 Quantum coding (general)
51M09 Elementary problems in hyperbolic and elliptic geometries
94B60 Other types of codes
Full Text: DOI

References:

[1] C.D. Albuquerque, R. Palazzo & E.B. Silva. Topological quantum codes on compact surfaces with genus g¿2. Journal of Mathematical Physics, 50(2) (2009), 023513-023513. doi:10.1063/1.3081056. · doi:10.1063/1.3081056
[2] H. Bombin & M.A. Martin-Delgado. Topological Quantum Error Correction with Optimal Encod-ing Rate. Physical Review A, 73(6) (2006). doi:10.1103/physreva.73.062303. URL http://dx.doi. org/10.1103/physreva.73.062303. · doi:10.1103/physreva.73.062303
[3] H. Bombin & M.A. Martin-Delgado. Computacion Cuantica topologica y sistemas fuertemente correlacionados. Revista espanola de fisica, 21(2) (2007), 31-45.
[4] H. Bombin & M.A. Martin-Delgado. Topological Quantum Distillation. Physical Review Letters, 97(18) (2007), 180501+. doi:10.1103/physrevlett.97.180501. URL http://dx.doi.org/10.1103/ physrevlett.97.180501. · doi:10.1103/physrevlett.97.180501
[5] N.P. Breuckmann & B.M. Terhal. Constructions and Noise Threshold of Hyperbolic Surface Codes. IEEE Transactions on Information Theory, 62(6) (2016), 3731-3744. doi:10.1109/TIT.2016. 2555700. · Zbl 1359.94882 · doi:10.1109/TIT.2016.2555700
[6] A.R. Calderbank & P.W. Shor. Good Quantum Error-Correcting Codes Exist. Physical Review A, 54(2) (1996), 1098-1105. doi:10.1103/physreva.54.1098. URL http://dx.doi.org/10.1103/ physreva.54.1098. · doi:10.1103/physreva.54.1098
[7] C.D. de Albuquerque, R.P. Junior & E.B. da Silva. On toric quantum codes. Int. J. Pure Appl. Math, 50 (2009), 221-226. · Zbl 1213.94197
[8] N. Delfosse. “Tradeoffs for reliable quantum information storage in surface codes and color codes”. IEEE (2013), 917-921 pp. doi:10.1109/isit.2013.6620360. URL http://dx.doi.org/10.1109/ isit.2013.6620360. · doi:10.1109/isit.2013.6620360
[9] D. Gottesman. A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound. Physical Review A, 54(3) (1996), 1862-1868. doi:10.1103/physreva.54.1862. URL http://dx.doi. org/10.1103/physreva.54.1862. · doi:10.1103/physreva.54.1862
[10] D. Gottesman & I.L. Chuang. Quantum Teleportation is a Universal Computational Primitive. Nature, 402(6760) (1999), 390-393. doi:10.1038/46503. URL http://dx.doi.org/10.1038/46503. · doi:10.1038/46503
[11] S. Katok. “Fuchsian Groups”. Chicago Lectures in Mathematics. University of Chicago Press (1992). URL https://books.google.com.br/books?id=pJ2Se3tCr-cC. · Zbl 0753.30001
[12] A. Kitaev. Fault-tolerant quantum computation by anyons. Annals of Physics, 303(1) (2003), 2-30. doi:http://dx.doi.org/10.1016/S0003-4916(02)00018-0. URL http://www.sciencedirect. com/science/article/pii/S0003491602000180. · Zbl 1012.81006
[13] D. Lidar & T. Brun. “Quantum Error Correction”. Cambridge University Press (2013). URL https: //books.google.com.br/books?id=XV9sAAAAQBAJ.
[14] A. Ramsay & R.D. Richtmyer. “Constructions by Straightedge and Compass in the Hyperbolic Plane”. Springer New York, New York, NY (1995), pp. 254-282. doi:10.1007/978-1-4757-5585-5 12. URL https://doi.org/10.1007/978-1-4757-5585-5_12. · doi:10.1007/978-1-4757-5585-512
[15] C.E. Shannon. A Mathematical Theory of Communication. SIGMOBILE Mob. Comput. Com-mun. Rev., 5(1) (2001), 3-55. doi:10.1145/584091.584093. URL http://doi.acm.org/10.1145/ 584091.584093. · doi:10.1145/584091.584093
[16] P.W. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 52 (1995), R2493-R2496. doi:10.1103/PhysRevA.52.R2493. URL http://link.aps.org/doi/10. 1103/PhysRevA.52.R2493. · doi:10.1103/PhysRevA.52.R2493
[17] W.S. Soares Jr & E.B. Silva. Construction of color codes from polygons. Journal of Physics Communications, 2(9) (2018), 095011. URL http://stacks.iop.org/2399-6528/2/i=9/a= 095011.
[18] W.S. Soares Jr & E.B. Silva. Hyperbolic Quantum Color Codes. Quantum Information and Computation, 18(3 and 4) (2018), 308-320.
[19] A. Steane. Simple Quantum Error Correcting Codes. Physical Review A, 54(6) (1996), 4741-4751. doi:10.1103/physreva.54.4741. URL http://dx.doi.org/10.1103/physreva.54.4741. · doi:10.1103/physreva.54.4741
[20] W.G. Unruh. Maintaining coherence in Quantum Computers. Physical Review A, 51(2) (1994), 992-997. doi:10.1103/physreva.51.992. URL http://dx.doi.org/10.1103/physreva.51.992. · doi:10.1103/physreva.51.992
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.