Spatially correlated qubit errors and burst-correcting quantum codes

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, we construct a one–dimensional quantum code of length n = 15 that corrects burst errors of length b ≤ 3; as a comparison, a randomerror correcting quantum code that corrects t = 3 errors must have length n ≥ 17. 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).