The measurement-based techniques consist of entangling a cluster of qubits and performing a set of measurements. Thanks to the correlation between the entangled qubits, the flow of information (from left to right) is carried on by the measurements on the physical qubits in the cluster.
The one-way quantum computer, also known as measurement-based quantum computer (MBQC), is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is “one-way” because the resource state is destroyed by the measurements.
The outcome of each individual measurement is random, but they are related in such a way that the computation always succeeds. In general, the choices of basis for later measurements need to depend on the results of earlier measurements, and hence the measurements cannot all be performed at the same time.
The hardware implementation of MBQC mainly relies on photonic devices, due to the difficulty of entangling photons without measurements, and the relative simplicity of creating and measuring them. However, MBQC is also possible with matter-based qubits. The process of entanglement and measurement can be described with the help of graph tools and group theory, in particular by the elements from the stabilizer group.