  By taking into account the physical nature of quantum errors it is possible
to improve the efficiency of quantum error correction. Here we consider an
optimisation to conventional quantum error correction which involves exploiting
asymmetries in the rates of X and Z errors by reducing the rate of X
correction. As an example, we apply this optimisation to the [[7,1,3]] code and
make a comparison with conventional quantum error correction. After two levels
of concatenated error correction we demonstrate a circuit depth reduction of at
least 43% and reduction in failure rate of at least 67%. This improvement
requires no additional resources and the required error asymmetry is likely to
be present in most physical quantum computer architectures.
