Research Projects

The main approach for constructing quantum codes from the classical linear codes is by the stabilizer formalism. However, the need of dual containing condition in the stabilizer formalism puts a severe restriction on the supporting linear code. Entanglement-assisted quantum error-correcting (EAQEC) codes show a way to lift this restriction. In EAQEC codes, a quantum code can be constructed from any classical linear code provided the sender and receiver share some specified pairs of maximally entangled states (ebits). EAQEC codes are an evolving area and require more exploration. There are many families of classical codes that are not well suited for the standard stabilizer formalism, but they can be used as supporting linear codes for EAQEC codes. Many of these codes can provide quantum codes with good parameters. Through this project we propose to construct EAQEC codes from some classes of linear codes like cyclic codes, constacyclic codes, quasi-cyclic codes and quasi-twisted codes. We also propose to obtain some efficient methods for computing the required number of shared ebits. Further, we propose to get some EAQEC codes with good parameters from the above classes of codes using computer search.

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