Codes over GF(4)Codes over GF(4)

Polynomials can be used and their transformations as shown here

Codes Codes over over GF(4) GF(4)

and Pauli and Pauli MatricesMatrices

From Symplectic Form to GF(4)

Self Orthogonal & Self Dual

Toric Codes of Kitaev 1997Toric Codes of Kitaev 1997

Toric Code

Example

Homological Codes Homological Codes

Conclusions

• Reliable quantum computation can not be achieved without error control.

• Quantum error correcting codes were discovered in 1995 by breaking the barrier of quantum no-cloning theorem.

• Quantum error correction is a challenging, interesting, and rich field for research.

• References• References