Quantum Approximation Optimization Algorithm for the Trellis Based Viterbi Decoding of Classical Error Correcting Codes

We construct a hybrid quantum-classical Viterbi decoder for the classical error-correcting codes. Viterbi decoding is a trellis-based procedure for maximum likelihood decoding of classical error-correcting codes. In this article, we demonstrate that the quantum approximate optimization algorithm can find any path on the trellis with the minimum Hamming distance relative to the received erroneous vector. We construct a generalized method to map the Viterbi decoding problem into optimization of a parameterized quantum circuit for any classical linear block code. Also, we propose a uniform parameter optimization strategy to optimize the parameterized quantum circuit using a classical optimizer. We observe that the proposed method efficiently generates low-depth trainable parameterized quantum circuits. Our approach makes the hybrid decoder more efficient than previous attempts at making quantum Viterbi algorithm. We show that using uniform parameter optimization, we obtain parameters more efficiently for the parameterized quantum circuit than previously used methods such as random sampling and fixing the parameters.