What are the general direction and target question in the field of quantum error correction?
One big open question is the existence of &quot;good&quot; quantum LDPC codes. These are stabilizer quantum error correcting codes with constant check weight, constant rate and linear distance. Most recently there was a series of breakthroughs on this front by Hastings, Haah and O'Donnell (arXiv:2009.03921), Breuckmann and Eberhardt (arXiv:2012.09271) and Panteleev and Kalachev (arXiv:2012.04068).