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→Cylinder Brickwork States
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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>. | 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\ | |||
The steps to perform single trap verifiable universal blind quantum | 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>. | ||
The steps to perform single trap verifiable universal blind quantum computing are: | |||
• A random qubit is chosen to be the trap qubit (red node in Fig.1.1) | • 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 | • All other vertices in the tape containing the trap qubit (solid black nodes | ||
in Fig.1.2), are set to be dummy qubits | in Fig.1.2), are set to be dummy qubits | ||
• This results in an isolated trap qubit in the state | | • 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) | • The net result, after discarding the dummy qubits, is a disentangled trap qubit in a product state with a brickwork state (Fig 1.4) | ||