Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-20T16:29:10.364Z Has data issue: false hasContentIssue false
  • English
  • Français

An inducing construction of quantum codes from classical error correcting codes

Published online by Cambridge University Press:  14 July 2016

K. R. Parthasarathy
K. R. Parthasarathy*
Affiliation:
Indian Statistical Institute
*
1Postal address: Indian Statistical Institute, Delhi Centre, 7 S. J. S. Sansanwal Marg, New Delhi 110 016, India. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The aim of the present paper is to construct error correcting quantum codes from classical error correcting group codes by using the Schur orthogonality relations for characters of a finite abelian group and the Knill–Laflamme criterion for a quantum code to correct a pre-assigned family of errors. This is an abstraction and generalization of Shor's example of a nine qubit single error correcting quantum code.

Keywords

Error correcting group codequantum codeWeyl commutation relationscharacters of an abelian group

MSC classification

Primary: 81P15: Quantum measurement theory
Type
Probability theory
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 27 - 32
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Knill, E. and Laflamme, R. (1997). Theory of quantum error correcting codes. Phys. Rev. Ser. A 55(2), 900–911.Google Scholar
Macwilliams, F. J. and Sloane, N. J. A. (1977). The Theory of Error-correcting Codes. North Holland, Amsterdam.Google Scholar
Parthasarathy, K. R. (1992). An Introduction to Quantum Stochastic Calculus. Birkhauser, Basel.Google Scholar
Parthasarathy, K. R. (2000). Quantum codes arising from Weyl commutation relations on finite abelian groups. Preprint, Indian Statistical Institute, Delhi Centre.Google Scholar
Pittenger, A. O. (1999). An Introduction to Quantum Computing Algorithms (Progress in Computer Science and Applied Logic 19). Birkhauser, Basel.Google Scholar
Shor, P. (1995). Scheme for reducing decoherence in quantum computer memory. Phys. Rev. Ser. A 52(4), R2493–R2496.Google Scholar
Steane, A. M. (1996). Error correcting codes in quantum theory. Phys. Rev. Lett. 77(5), 793–797.Google Scholar