4 Conclusions

A practical advantage of EAQEC codes over standard QEC codes is that they are much easier to construct from classical codes because self-orthogonality is not required. This allows us to import the classical theory of error correction wholesale, including capacity-achieving modern codes. The appeal of these modern codes comes from the existence of efficient decoding algorithms that provide an excellent trade-off between decoding complexity and decoding performance. In fact, these decoding algorithms, such as sum-product algorithm, can be modified to decode the error syndromes effectively [13]. The only problem of using these iterative decoding algorithms on quantum LDPC actually comes from those shortest 4 cycles that were introduced inevitably because of the self-orthogonality constraint. However, by allowing assisted entanglement, those 4 cycles can be eliminated completely, and the performance of the iterative decoding improves substantially in our numerical simulations [11]. This finding further confirms the contribution of our EA formalism. We plan to further examine the performance of classical LDPC codes and turbo codes in the context of the catalyst size for EAQEC codes.

Acknowledgements TAB received financial support from NSF Grant No. CCF-0448658, and TAB and MHH both received support from NSF Grant No. ECS-0507270. ID and MHH received financial support from NSF Grant No. CCF-0524811 and NSF Grant No. CCF-0545845.

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