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== Hierarchy of Quantum Gates == | == Hierarchy of Quantum Gates == | ||
There are different class of quantum gates as follows, | |||
*'''Pauli Gates(U):''' Single Qubit Gates I (Identity), X, Y, Z. All the gates in this set follow U2 = I | |||
*'''Clifford Gates(C):''' Pauli Gates, Phase Gate, C-NOT. This set of gates can be simulated on classical computer. All the gates in this set follow CU=U’C, where U and U’ are two different Pauli gates depending on C | |||
*'''Universal Set of gates:''' This set consists of all Clifford gates and one Non-Clifford gate (T gate). If a model can realise Universal Set of gates, it can imlement any quantum computation efficiently. T gates follow UT = PaU0T, where P is the phase gate and U, U’ are any two Pauli gates depending on C. Parameter 1 is obtained from U, such that P0 = I, P1 = P. | |||
To summarize, the hierarchy of quantum can be defined as such.<br/> | |||
If C(1)=P, C(2)=C, C(3)=T, then | |||
C(n)={U:UQU\dagger=C(n-1),Q\epsilon C(1)} | |||
== Homomorphic Encryption == | == Homomorphic Encryption == | ||