Channel Decoding with Quantum Approximate Optimization Algorithm

TL;DR

This paper explores using the quantum approximate optimization algorithm (QAOA) for decoding classical channel codes, demonstrating its potential on near-term quantum devices through theoretical analysis and real-device experiments.

Contribution

It introduces a method to implement quasi-ML decoding with QAOA, including theoretical expressions and performance analysis for specific codes like the (7,4) Hamming code.

Findings

Higher-level QAOA improves decoding accuracy with optimized angles.

QAOA decoding shows promising results on real quantum hardware.

The impact of generator matrix degree distribution on performance is analyzed.

Abstract

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.