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If C(1)=P, C(2)=C, C(3)=T, then | If C(1)=P, C(2)=C, C(3)=T, then | ||
C(n)={U:UQU\dagger=C(n-1),Q\epsilon C(1)} | C(n)={U:UQU\dagger=C(n-1),Q\epsilon C(1)} | ||
==Classical Quantum State | |||
== | ==Density Matrices== | ||
== Quantum One Time Pad == | == Quantum One Time Pad == | ||
===Pauli Gates=== | |||
===Clifford Gates=== | |||
===T Gates=== | |||
==Discrete Variables and Continuous Variables== | |||
== Measurement Based Quantum Computation (MBQC)== | == Measurement Based Quantum Computation (MBQC)== | ||
| Line 118: | Line 120: | ||
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/> | ||
==Classical Methods== | |||
===Learning with errors=== | |||
===Trapdoor Claw-free function pair For Quantum Verification=== | |||
===Homomorphic Encryption=== | |||