A combinatorial approach to quantum error correcting codes

@article{Luna2013ACA,
  title={A combinatorial approach to quantum error correcting codes},
  author={German Luna and Samuel Reid and Bianca De Sanctis and Vlad Gheorghiu},
  journal={ArXiv},
  year={2013},
  volume={abs/1304.6743}
}
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric n-vertices colorable graph and a group of operations (coloring rules) on the graph: find the minimum sequence of operations that maps between two given graph colorings. We provide an explicit algorithm for computing the solution of our problem, which in turn is directly related to computing the distance (performance) of an underlying quantum error correcting code… 
View PDF on arXiv

Figures from this paper

References

SHOWING 1-10 OF 14 REFERENCES

Quantum-error-correcting codes using qudit graph states

The concept of a stabilizer is extended to general $D$, and shown to provide a dual representation of an additive graph code.

Graphical Quantum Error-Correcting Codes

A purely graph-theoretical object, namely the coding clique, is introduced to construct quantum error-correcting codes and the optimal ((10,24,3)) code and a family of 1-error detect-ing nonadditive codes with the highest encoding rate so far are constructed.

Stabilizer Codes and Quantum Error Correction

An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed.

Quantum computation and quantum information

  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…

Good quantum error-correcting codes exist.

  • CalderbankShor
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1996
The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.

Stabilizer codes can be realized as graph codes

We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized…

Entanglement in Graph States and its Applications

This review gives a tutorial introduction into the theory of graph states, and discusses the basic notions and properties of these states, including aspects of non-locality, bi-partite and multi- partite entanglement and its classification in terms of the Schmidt measure.

Theory of Error-correcting Codes

This course expounds the principles of coded modulations for the Gaussian channel and, if time permits, for Rician and Rayleigh fading channels (fully interleaved), and reminds students of the basics of the theory of linear codes for conventional memoryless ergodic channels.

Scheme for reducing decoherence in quantum computer memory.

  • Shor
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1995
In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits\char22{}techniques that may become the key to practical quantum computing on a large scale.

The theory of error-correcting codes (north-holland