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→Hierarchy of Quantum Gates
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*'''Pauli Gates(U):''' Single Qubit Gates I (Identity), X, Y, Z. All the gates in this set follow U2 = I | *'''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 | *'''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 | ||
*'''Toffoli Gate | *'''Toffoli Gate:''' A three qubit gate that does not belong to Clifford Group | ||
*'''T Gates:''' \sqrt{Z} Although a member of Clifford Gate, its eigen states can be used as acillas to make quantum gate sthat are not! | |||
*'''Universal Set of gates:''' This set consists of all Clifford gates and one Non-Clifford gate (T gate). One can also say one Toffoli gate and Hadamard gate constitute the set of Universal Gates. If a model can realise Universal Set of gates, it can imlpement 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. | *'''Universal Set of gates:''' This set consists of all Clifford gates and one Non-Clifford gate (T gate). One can also say one Toffoli gate and Hadamard gate constitute the set of Universal Gates. If a model can realise Universal Set of gates, it can imlpement 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. | ||
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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)} | ||
===Magic States=== | ===Magic States=== | ||
===Universal Resource=== | ===Universal Resource=== | ||