Figure 2: Graph code.
From: Experimental demonstration of a graph state quantum error-correction code
(a) Encoding logical states. In order to encode the state of the ancilla qubit into the graph it should be measured in the X basis. This propagates the information into the graph code while at the same time applying a Hadamard operation. Thus, the ancilla state is encoded in the Hadamard basis. The background shading represents the quantum state nonlocally encoded into the qubits in the graph resource. (b) Logical density matrices for the four different probe states |0›, |1›, |+› and |+y› once propagated into the code. These are calculated from the expectation values of the joint four-qubit logical operators 
, 
and 
. (c) Encoding as a channel. Here, the Bloch sphere transformation is shown for the encoding of arbitrary ancilla qubits (points on the surface of the sphere) into the code. Note that a Hadamard operation has been performed on the qubit, corresponding to a rotation of 180 degrees about the X–Z plane.
