Measurement-based quantum computation is a form of quantum computing that operates on a prepared entangled graph state, typically a cluster state. In this dissertation, we will detail the creation of graph states across various physical platforms using different entangling gates. We will then benchmark the quality of graph states created with error-prone interactions through quantum wire teleportation experiments. By leveraging underlying symmetry, we will design graph states as measurement-based quantum error correction codes to protect against perturbations, such as ZZ crosstalk in quantum wire teleportation. Additionally, we will explore other measurement-based algorithms used for the quantum simulation of time evolution in fermionic systems, using the Kitaev model and the Hubbard model as examples. / Doctor of Philosophy / A quantum computer refers to a device that performs general computational functions relying on logic gates using units dominated by microscopic quantum properties. The fundamental difference between quantum computers and classical computers lies in the distinction be- tween the basic quantum unit, the qubit, and the classical computational unit, the bit. Both qubits and bits can exist in states 0 and 1. However, qubits possess two characteristics that classical computational units do not: superposition and entanglement. Superposition allows a qubit to exist in a combination of both states 0 and 1 simultaneously. Entanglement refers to the phenomenon where qubits interact and form an inseparable unified state. The effec- tive utilization of these unique properties enables quantum computers to exhibit capabilities far surpassing those of classical computers. Analogous to classical computers, qubits can be interconnected in a circuit-like manner sim- ilar to classical bits, forming an architecture known as circuit-based quantum computation (CBQC). However, given the unique properties of quantum systems, particularly entan- glement, a novel architecture called measurement-based quantum computing (MBQC) can also be designed. MBQC relies on pre-entangled graph states, usually cluster states, and only requires single-qubit measurements to implement quantum algorithms. The MBQC framework also includes a universal gate set, similar to other quantum computing architec- tures like CBQC. In this dissertation, we will introduce the creation of graph states and the implementation of measurement-based quantum algorithms.