This paper presents a quantum search algorithm based on quantum random walks, which achieves a speed-up of $ O(\sqrt{N}) $ for searching a database of $ N = 2^n $ items. The algorithm uses a quantum random walk on the n-cube (hypercube) graph, where each node corresponds to an n-bit binary string. The algorithm involves initializing the system in an equal superposition of all states, applying a perturbed evolution operator $ U' $, and then measuring the state. The key idea is that the quantum random walk provides a way to efficiently search for a marked node in the graph, with the marked node corresponding to the target state. The algorithm is shown to have a similar performance to Grover's search algorithm, achieving a speed-up of $ O(\sqrt{N}) $. However, there are important differences between the two algorithms. The random walk search algorithm operates on a two-dimensional subspace spanned by the equal superposition state and a second state, while Grover's algorithm operates on a subspace spanned by the equal superposition state and the marked state. The random walk search algorithm also retains some of the underlying structure of the hypercube graph in its final state, with small contributions from neighboring nodes. The paper also discusses the connection between quantum random walks and Grover's algorithm, highlighting that both algorithms can be viewed as rotations in a two-dimensional subspace. However, the random walk search algorithm is not exactly equivalent to Grover's algorithm, as it does not yield a pure marked state in the final result. Instead, it provides a linear combination of states that includes the marked state and small contributions from neighboring states. The paper concludes that the random walk search algorithm is optimal up to a constant factor, as it achieves the known lower bound for quantum search algorithms. The results suggest that quantum random walks provide a promising framework for developing new quantum algorithms. The paper also notes that further research is needed to explore the potential of quantum random walks for other types of search problems and to determine whether different marking strategies can lead to improved performance.This paper presents a quantum search algorithm based on quantum random walks, which achieves a speed-up of $ O(\sqrt{N}) $ for searching a database of $ N = 2^n $ items. The algorithm uses a quantum random walk on the n-cube (hypercube) graph, where each node corresponds to an n-bit binary string. The algorithm involves initializing the system in an equal superposition of all states, applying a perturbed evolution operator $ U' $, and then measuring the state. The key idea is that the quantum random walk provides a way to efficiently search for a marked node in the graph, with the marked node corresponding to the target state. The algorithm is shown to have a similar performance to Grover's search algorithm, achieving a speed-up of $ O(\sqrt{N}) $. However, there are important differences between the two algorithms. The random walk search algorithm operates on a two-dimensional subspace spanned by the equal superposition state and a second state, while Grover's algorithm operates on a subspace spanned by the equal superposition state and the marked state. The random walk search algorithm also retains some of the underlying structure of the hypercube graph in its final state, with small contributions from neighboring nodes. The paper also discusses the connection between quantum random walks and Grover's algorithm, highlighting that both algorithms can be viewed as rotations in a two-dimensional subspace. However, the random walk search algorithm is not exactly equivalent to Grover's algorithm, as it does not yield a pure marked state in the final result. Instead, it provides a linear combination of states that includes the marked state and small contributions from neighboring states. The paper concludes that the random walk search algorithm is optimal up to a constant factor, as it achieves the known lower bound for quantum search algorithms. The results suggest that quantum random walks provide a promising framework for developing new quantum algorithms. The paper also notes that further research is needed to explore the potential of quantum random walks for other types of search problems and to determine whether different marking strategies can lead to improved performance.