  Quantum error correction is an important building block for reliable quantum
information processing. A challenging hurdle in the theory of quantum error
correction is that it is significantly more difficult to design
error-correcting codes with desirable properties for quantum information
processing than for traditional digital communications and computation. A
typical obstacle to constructing a variety of strong quantum error-correcting
codes is the complicated restrictions imposed on the structure of a code.
Recently, promising solutions to this problem have been proposed in quantum
information science, where in principle any binary linear code can be turned
into a quantum error-correcting code by assuming a small number of reliable
quantum bits. This paper studies how best to take advantage of these latest
ideas to construct desirable quantum error-correcting codes of very high
information rate. Our methods exploit structured high-rate low-density
parity-check codes available in the classical domain and provide quantum
analogues that inherit their characteristic low decoding complexity and high
error correction performance even at moderate code lengths. Our approach to
designing high-rate quantum error-correcting codes also allows for making
direct use of other major syndrome decoding methods for linear codes, making it
possible to deal with a situation where promising quantum analogues of
low-density parity-check codes are difficult to find.
