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→Cylinder Brickwork States
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====Cylinder Brickwork States==== | ====Cylinder Brickwork States==== | ||
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\langle</math> where <math>z \in {0,1}</math> and the rest of the nodes are prepared in the state |+θi⟩, 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 GC(n−1)×m mi=1|zi⟩. | |||
The steps to perform single trap verifiable universal blind quantum comput- ing are: | |||
• 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 |θi⟩ 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) | |||
====Flow Construction-Determinism==== | ====Flow Construction-Determinism==== | ||