Systems and methods herein provide for error correction via Low Density Parity Check (LDPC) coding. In one embodiment, a system includes a data buffer operable to receive a block of Low Density Parity Check (LDPC) encoded data. The system also includes a processor operable to reduce a belief propagation algorithm used to encode the LDPC encoded data into a quadratic polynomial, to embed the quadratic polynomial onto a plurality of quantum bits (qubits), and to decode the block of LDPC encoded data via the qubits.