Vieterbi decoder algorithm using quantum computing

Quantum computing promises a leap in performance over classical computing. Its computational power was revealed after the introduction of some quantum algorithms such as Grover´s search algorithm. Many classical algorithms especially that deal with Error Correcting Codes are introduced to solve an exhaustive search problem. The quantum techniques promise an optimal search speed that is of special importance when the size of the searched domain is quite large. In this paper we devise the use of quantum search algorithm introduced by Grover to implement the viterbi algorithm (VA). Due to lack of resources and the nature of implementing quantum algorithms, only theoretical results are obtained. The use of quantum search algorithm showed that we can reduce the number of search computations exponentially. For example if the classical VA requires 262144 searching operations for a signalling length of 1024 intervals, the quantum algorithm will need only 512 searching operations when single search quantum viterbi algorithm (SSQVA) is used. And for the multi search quantum viterbi algorithm (MSQVA) it needs 16384 searching operations for the same signalling length.