Quantum List Recovery and Decoding: Achievability and Limitations
The research explores Quantum List Recovery (QLR) and Decoding (QLD), which aim to find short lists of Pauli corrections consistent with error syndromes. The study establishes tight combinatorial bounds for folded Reed-Solomon codes and random CSS codes, showing that the optimal list sizes scale predictably as the code radius approaches its quantum limit. Achievability is proven using pairing lemmas and quotient-aware bounds.