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→Hierarchy of Quantum Gates
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=== Hierarchy of Quantum Gates === | === Hierarchy of Quantum Gates === | ||
There are different class of quantum gates as follows, | 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 <math>U^2=I</math> | ||
* | *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 <math>UT=P^aU'T</math>, where P is the phase gate and U, U' are any two Pauli gates depending on C. Parameter <math>a\epsilon{0,1}</math> is obtained from U, such that <math>P^0=I</math>, <math>P^1=P</math>.</br> | ||
To summarize, if <math>C^1=</math>P, <math>C^2=</math>C, <math>C^3=</math>T, then <math>C^{k}=\{U:UQU=C^{k-1}|Q\epsilon C^1\}</math> | |||
To summarize, | |||
C | |||
===Magic States=== | ===Magic States=== | ||