Application of Quantum Walk for Signal Processing

Signal processing is important for modern technologies such as digital communication systems and sensor networks, and is used to enhance and optimize the quality of transmitted signals. However, traditional methods and design frameworks are insufficient for the demands of future communication networks, which are expected to be highly complex and constantly changing. Our research focuses on a mathematical model known as a Markov model, which represents a system as a series of states linked by transitions. This model can be applied to various signal processing challenges in telecommunications, such as the modeling of communication channels, sources of information, and the correction of distortion and noise in transmitted signals. We examine the random walk algorithm, a simple and efficient way to simulate the behavior of a Markov chain, as it can provide valuable insights into the performance of communication systems and help to optimize their design. However, it may not be able to accurately model systems with complex transitions or systems that exhibit long-term correlations. In order to address the challenges and limitations of classical random walk, we propose the use of quantum random walk, which is a quantum mechanical version of classical random walk. It describes the motion of particles in a probabilistic way, similar to classical random walk, but with the added complexity of quantum mechanics. We also provide quantum walk algorithm with Hadamard gate implementation for coin operator.