  We explore the design of quantum error-correcting codes for cases where the
decoherence events of qubits are correlated. In particular, we consider the
case where only spatially contiguous qubits decohere, which is analogous to the
case of burst errors in classical coding theory. We present several different
efficient schemes for constructing families of such codes. For example, one can
find one-dimensional quantum codes of length n=13 and 15 that correct burst
errors of width b < 4; as a comparison, a random-error correcting quantum code
that corrects t=3 errors must have length n > 18. In general, we show that it
is possible to build quantum burst-correcting codes that have near optimal
dimension. For example, we show that for any constant b, there exist
b-burst-correcting quantum codes with length n, and dimension k=n-log n -O(b);
as a comparison, the Hamming bound for the case with t (constant) random errors
yields k < n - t log n - O(1) .
