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X4s3Z4s2Z1s2M3xM2xE13E234{equation missing} <br/> | X4s3Z4s2Z1s2M3xM2xE13E234{equation missing} <br/> | ||
Hence, we obtain a measurement pattern to implement C-NOT gate with a T-shaped graph state with three qubits entangled chain {2,3,4} and 1 entangled to 3. X dependency sets for qubit 1:{s3}, 2:φ, 3:φ, 4:φ. Z dependency sets for qubit 1:{s2}, 2:φ, 3:φ, 4:{s2}. The measurements are independent of any outcome so they can all be performed in parallel. In the end, Pauli corrections are performed as such. Parity (modulo 2 sum) of all the previous outcomes in the dependency set is calculated for each qubit{equation missing} (i), for X (sXi = s1 ⊕ s2 ⊕ ...) and Z (sZi = s1 ⊕ s2 ⊕ ...), separately. Thus, is operated on qubit i.{equation missing} <br/> | Hence, we obtain a measurement pattern to implement C-NOT gate with a T-shaped graph state with three qubits entangled chain {2,3,4} and 1 entangled to 3. X dependency sets for qubit 1:{s3}, 2:φ, 3:φ, 4:φ. Z dependency sets for qubit 1:{s2}, 2:φ, 3:φ, 4:{s2}. The measurements are independent of any outcome so they can all be performed in parallel. In the end, Pauli corrections are performed as such. Parity (modulo 2 sum) of all the previous outcomes in the dependency set is calculated for each qubit{equation missing} (i), for X (sXi = s1 ⊕ s2 ⊕ ...) and Z (sZi = s1 ⊕ s2 ⊕ ...), separately. Thus, is operated on qubit i.{equation missing} <br/> | ||
==Fault Tolerance== | |||
===Quantum Error Correction=== | |||
===Quantum Error Correcting Codes (QECCs)=== | |||
===Stabilizer Codes=== | |||
===Topological Error Correction=== | |||
==Classical Methods== | ==Classical Methods== | ||
===Learning with errors=== | ===Learning with errors=== | ||
===Trapdoor Claw-free function pair=== | ===Trapdoor Claw-free function pair=== | ||
===Homomorphic Encryption=== | ===Homomorphic Encryption=== | ||