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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 | ||
*'''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. | *'''T Gate:''' This set contains all single qubit gates that do not belong to the set of Clifford Gates | ||
*'''Toffoli Gate:''' This set contains three qubit gates (e.g. CCNOT) | |||
*'''Universal Set of gates:''' This set consists of all Clifford gates and one Non-Clifford gate (T or Toffoli 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/> | To summarize, the hierarchy of quantum can be defined as such.<br/> | ||