  The theory of quantum error correction was established more than a decade ago
as the primary tool for fighting decoherence in quantum information processing.
Although great progress has already been made in this field, limited methods
are available in constructing new quantum error correction codes from old
codes. Here we exhibit a simple and general method to construct new quantum
error correction codes by nesting certain quantum codes together. The problem
of finding long quantum error correction codes is reduced to that of searching
several short length quantum codes with certain properties. Our method works
for all length and all distance codes, and is quite efficient to construct
optimal or near optimal codes. Two main known methods in constructing new codes
from old codes in quantum error-correction theory, the concatenating and
pasting, can be understood in the framework of nested quantum error correction
codes.
