Among measurement-based models two slightly different approaches might be identified: the teleportation-based model, which is based on Bell-pairs and two-qubit measurements, and the one-way model which consists of single-qubit measurements on graph states. Both models are equivalent and are closely related to the teleportation primitive where, thanks to adaptive measurements performed on multipartite entangled states, arbitrary unitaries can be executed.

Instead of implementing a logic operation via unitary transformations, the same operation is executed measuring a set of

The order and basis in which the qubits are measured dictates the implemented computation. Therefore, as measurements produce non-deterministic outcomes, every basis depends on the previous results and need to be adapted.

In the Bloch sphere picture, any transformation single-qubit unitary can be seen as a rotation of an angle *Euler angles*^{1}

a sequence of rotations along the

After the state generation, the computation proceeds with the measurement of the first 4 qubits in the basis described by the following operator^{2}

Qubit | Basis | Result |
---|---|---|

1 | ||

2 | ||

3 | ||

4 |

defined as

After all the measurements, the state of the qubit reads