Provided is an apparatus for designing a quantum code, which includes an analyzing unit for analyzing at least one quantum error generated in a quantum error channel as at least one binary error by using a standard form codeword stabilized quantum (CWS) code, a code generating unit for generating a binary error-correcting code which corrects the at least one binary error, a word operator generating unit for generating at least one word operator of the CWS code by using the at least one binary error-correcting code, and a codeword generating unit for generating at least one codeword including at least one entangled qubit (ebit) by using the at least one word operator.

A method of encoding a set of information bits to produce a codeword that encodes the set of information bits for reliable communication is provided. The set of information bits is received. The set of information bits are provided to a plurality of permutation layers separated by neural network processing layers. Each permutation layer accepts an input vector and generates a reordered output vector that is a reordering of the input vector. Each neural network processing layer accepts a vector of input values and generates a vector of output values based on a non-linear function of the vector of input values. The reordered output vector of a final permutation layer of the plurality of permutation layers is provided as the codeword. In some embodiments, a corresponding method of decoding a codeword to retrieve a set of information bits is provided.