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Basic Quantum Logic Gates


 Classic NOT Gate:

The NOT gate converts bit 0 to bit 1 and bit 1 to bit 0.


 

Sigma X Gate:

The X gate, also known as the Pauli X matrix, also refers to the NOT gate.
The X matrix and the expressions |0> and |1> are as follows.

 

If we make the X gate act on the qubits |0> and |1>;

 

In general, if we write;

For example, let's draw a 2-qubit circuit;

Sigma Z Gate: 

The Pauli Z gate does not change the result when it acts on the |0> qubit. However, when it acts on the |1> qubit, it changes phase, that is, it introduces a minus sign.

If we make the Z gate act on the qubits |0> and |1>;

Sigma Y Gate: 


If we make the Y gate act on the qubits |0> and |1>;

Hadamard Gate: 

The Hadamard gate [H] is used to superposition our qubit.

If we make the H gate act on the qubits |0> and |1>;


The gates you've read so far were single qubit gates. However, the CNOT gate we will see now is used for multiple qubits.

 

CNOT (Controlled NOT) Gate:

Notation of CNOT; 


There are two states at the CNOT gate:

Case 1: If the first qubit is |0> it does nothing to the second qubit.

Case 2: If the first qubit is |1>, it modifies the second qubit. That is if the second qubit is |0> it makes |1>, if |1> makes |0>.





Reference

https://learn.qiskit.org/course/ch-states/single-qubit-gates

 

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