  Motivated by the recent advancement of quantum processors, we investigate
quantum approximate optimization algorithm (QAOA) to employ
quasi-maximum-likelihood (ML) decoding of classical channel codes. QAOA is a
hybrid quantum-classical variational algorithm, which is advantageous for the
near-term noisy intermediate-scale quantum (NISQ) devices, where the fidelity
of quantum gates is limited by noise and decoherence. We first describe how to
construct Ising Hamiltonian model to realize quasi-ML decoding with QAOA. For
level-1 QAOA, we derive the systematic way to generate theoretical expressions
of cost expectation for arbitrary binary linear codes. Focusing on (7, 4)
Hamming code as an example, we analyze the impact of the degree distribution in
associated generator matrix on the quantum decoding performance. The excellent
performance of higher-level QAOA decoding is verified when Pauli rotation
angles are optimized through meta-heuristic variational quantum eigensolver
(VQE). Furthermore, we demonstrate the QAOA decoding performance in a real
quantum device.
