Asymmetric Quantum Codes: Constructions, Bounds, and Performance

Recently, quantum error-correcting codes were proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit flip and phase flip errors. An example for a channel which exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit flips and phase flips can be related to relaxation and dephasing time, respectively. We study asymmetric quantum codes that are obtained from the CSS construction. For such codes we derive upper bounds on the code parameters using linear programming. A central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes. For instance, we derive asymmetric codes using a combination of BCH and finite geometry LDPC codes. We show that asymmetric quantum codes offer two advantages, namely to allow a higher rate without sacrificing performance when compared to symmetric codes and vice versa to allow a higher performance when compared to symmetric codes of comparable rates. Our approach is based on a CSS construction that combines BCH and finite geometry LDPC codes.