This article presents an experimental realization of a one-way quantum computer using a four-qubit cluster state encoded in the polarization of four photons. The one-way quantum computer differs from traditional quantum computing models by relying on a highly-entangled cluster state and single-qubit measurements with classical feedforward, rather than unitary quantum logic gates. The cluster state is prepared using nonlinear optics and characterized through quantum state tomography, revealing its entanglement properties. The experiment demonstrates the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations, and implements Grover's search algorithm, showcasing the potential of this approach for efficient quantum computation. The one-way quantum computer is based on the entanglement of the cluster state, where the order and choices of measurements determine the algorithm. The cluster state is prepared by entangling four photons in a specific polarization state, and the quantum computation proceeds through a sequence of single-qubit measurements. The results of these measurements are used for classical feedforward, which compensates for errors and ensures deterministic computation. The experiment demonstrates that the cluster state can be used to implement a wide range of quantum circuits, including single-qubit rotations and two-qubit gates, and that the cluster state is universal for quantum computation. The article also discusses the entanglement properties of the cluster state, showing that it can be used to generate entanglement between encoded qubits. The experiment demonstrates that the cluster state can be used to implement a two-qubit search algorithm, which is significantly more efficient than classical algorithms. The results show that the cluster state is a promising approach for quantum computation, with potential applications in quantum information processing and quantum communication. The article concludes with a discussion of the challenges and future directions for one-way quantum computing, including the need for efficient cluster state preparation and the implementation of fast feedforward.This article presents an experimental realization of a one-way quantum computer using a four-qubit cluster state encoded in the polarization of four photons. The one-way quantum computer differs from traditional quantum computing models by relying on a highly-entangled cluster state and single-qubit measurements with classical feedforward, rather than unitary quantum logic gates. The cluster state is prepared using nonlinear optics and characterized through quantum state tomography, revealing its entanglement properties. The experiment demonstrates the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations, and implements Grover's search algorithm, showcasing the potential of this approach for efficient quantum computation. The one-way quantum computer is based on the entanglement of the cluster state, where the order and choices of measurements determine the algorithm. The cluster state is prepared by entangling four photons in a specific polarization state, and the quantum computation proceeds through a sequence of single-qubit measurements. The results of these measurements are used for classical feedforward, which compensates for errors and ensures deterministic computation. The experiment demonstrates that the cluster state can be used to implement a wide range of quantum circuits, including single-qubit rotations and two-qubit gates, and that the cluster state is universal for quantum computation. The article also discusses the entanglement properties of the cluster state, showing that it can be used to generate entanglement between encoded qubits. The experiment demonstrates that the cluster state can be used to implement a two-qubit search algorithm, which is significantly more efficient than classical algorithms. The results show that the cluster state is a promising approach for quantum computation, with potential applications in quantum information processing and quantum communication. The article concludes with a discussion of the challenges and future directions for one-way quantum computing, including the need for efficient cluster state preparation and the implementation of fast feedforward.