Quantum List Decoding from Quantumly Corrupted Codewords for Classical Block Codes of Polynomially Small Rate

d Abstract) Tomoyuki Yamakami Department of Computer Software, University of Aizu 90 Kami-Iawase, Tsuruga, Ikki-machi, Fukushima 965-8580, Japan Our task of quantum list decoding for a classical block code is to recover from a given quantumly corrupted codeword a short list containing all messages whose codewords have high “presence” in this quantumly corrupted codeword. All known families of efficiently quantum list decodable codes, nonetheless, have exponentially-small message rate. We show that certain generalized Reed-Solomon codes concatenated with Hadamard codes of polynomially-small rate and constant codeword alphabet size have efficient quantum list decoding algorithms, provided that target codewords should have relatively high presence in a given quantumly corrupted codeword.

• Type: Conference
• Year: 2007
• Where: CATS
• Authors: Tomoyuki Yamakami
• Keywords: Applied Computing, CATS 2007, Constant Codeword Alphabet, Quantum List, Quantumly Corrupted Codeword