Open Problems

During the QCDA kickoff meeting in November 2018 the following list of open problems was compiled. This list will be updated with news and relevant publications as the QCDA project progresses.

  1. Given an LDPC code with check weights and degree upper bounded by w, what are the trade-offs between [[n,k,d]] and w?  That is, what are the known constructions and can be prove any bounds?
  2. Is there an efficient decoder that works (e.g. corrects all errors upto code distance) for all hypergraph product codes.
  3. What are the necessary conditions for single shot error correction?
  4. What is the unifying notion of single-shot error correction that also encompasses the quantum expander codes?
  5. What is the statistical mechanics phases diagram for concatenation of any CV code with a topological code?
  6. Can we achieve not just constant multiplicative space overhead ( al a Gottesman ) but also constant time space overhead?
  7. Is magic state distillation possible in the continuous variable setting?
  8. Can we develop a general theory of magic state distillation beyond triorthogonal codes?
  9. What are the transversal gates for continuous variable codes?