Abstract
As seen in previous chapters, in 1996 a new class of codes, now known as CSS codes, was proposed by Robert Calderbank, Peter Shor, and Andrew Steane. These codes were generalized into a rich code structure, which is the stabilizer quantum codes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.D. Albuquerque, R. Palazzo Jr., and E.B. Silva. Topological quantum codes on compact surfaces with genus g ≥ 2. J. Mathematical Physics, 50:023513-1-20, 2009.
C.D. Albuquerque, R. Palazzo Jr., and E.B. Silva. On toric quantum codes. International Journal of Pure and Applied Mathematics, 50(2):221–226, 2009.
A.F. Beardon. The Geometry of Discrete Groups. Springer-Verlag, 1983.
H. Bombin, and M. A. Martin-Delgado. Topological quantum distillation. Phys. Rev. Letters, 97:180501, 2006.
H. Bombin, and M.A. Martin-Delgado. Topological Quantum Error Correction with Optimal Encoding Rate. Phys. Rev. A, 73(6):062303, 2007.
H. Bombin. An Introduction to Topological Quantum Codes. ar**v:1311.0277, 2013.
N.P. Breuckmann, and B.M. Terhal. Constructions and noise threshold of hyperbolic surface codes. IEEE Trans. Inform. Theory, 62(6):3731–3744, 2016.
A. R. Calderbank, and P. W. Shor. Good quantum error-correcting codes exist. Phys. Rev. A, 54:1098–1105, 1996.
N. Delfosse. Tradeoffs for reliable quantum information storage in surface codes and color codes. IEEE International Symposium on Information Theory, pp. 917, 2013.
D. Gottesman. Class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A, 54:1862, 1996.
A.Yu Kitaev. Fault-tolerant quantum computation by anyons. Ann. Phys., 303(1):2–30, 2003.
W.S. Soares Jr., and E.B. Silva. Construction of color codes from polygons. J. Phys. Communications, 2(9):095011, 2018.
A.M. Steane. Simple quantum error correcting codes. Phys. Rev. Lett., 77:793–797, 1996.
A.M. Steane. Error correcting codes in quantum theory. Phys. Rev. Letters, 77:793, 1996.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Albuquerque, C.D.d., Silva, E.B.d., Soares Jr., W.S. (2022). Color Codes. In: Quantum Codes for Topological Quantum Computation. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-06833-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-06833-1_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-06832-4
Online ISBN: 978-3-031-06833-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)