Glossary: Difference between revisions

The cylinder brickwork state <math>G^{C}_{n*m}</math> is a modification of the brickwork state of size <math>n*m</math>, for even n, where the first and the last rows are connected such that the regular brickwork structure is preserved while introducing rotational symmetry. A tape <math>T_i</math>, shown in Fig.1.3, present in a cylinder brickwork graph is the subgraph which includes all the states in the random rows <math>i</math> and <math>i + 1</math>.

If all the nodes in <math>T_i</math> of the graph <math>G^{C}_{n*m}</math> are prepared in the dummy qubit state, <math>|z\rangle</math> where <math>z \in {0,1}</math> and the rest of the nodes are prepared in the state <math>|+_{\thetha_i}\rangle</math>, then after entangling according to the cylinder brickwork state, the nodes are completely disentangled from the rest of the graph. The final obtained graph would be <math>G^{C}_{(n-1)*m} \bigotimes^{m}_{i=1} |z\rangle</math>.

• A random qubit is chosen to be the trap qubit (red node in Fig.1.1)

• All other vertices in the tape containing the trap qubit (solid black nodes

in Fig.1.2), are set to be dummy qubits

• This results in an isolated trap qubit in the state <math>|+_{\thetha_i}\rangle</math> together with many dummy qubits after entanglement operations (Fig 1.3)

• The net result, after discarding the dummy qubits, is a disentangled trap qubit in a product state with a brickwork state (Fig 1.4)