Asymmetric Quantum Cyclic Codes

It is recently conjectured that phase-shift errors occur with high probability than qubitflip errors, hence phase-shift errors are more disturbing to quantum information than qubit-flip errors. This leads to construct asymmetric quantum error-correcting codes (AQEC) to protect quantum information over asymmetric channels, PrZ ≥ PrX. In this paper we present two generic methods to derive asymmetric quantum cyclic codes using the generator polynomials and defining sets of classical cyclic codes. Consequently, the methods allow us to construct several families of asymmetric quantum BCH, RS, and RM codes. Finally, the methods are used to construct families of asymmetric subsystem codes. Construction of AQEC (Main Results). The following theorem shows the CSS construction of asymmetric quantum error control codes over Fq. Theorem 1 (CSS AQEC) Let C1 and C2 be two classical codes with parameters [n, k1, d1]q and [n, k2, d2]q respectively, and dx = min { wt(C1\C ⊥ 2 ),wt(C2\C ⊥ 1 ) }