What are the Reversible gates in quantum computing

In quantum computing, there are several commonly used reversible gates that form the building blocks for constructing quantum circuits. Here are nine important reversible gates:

1. Identity Gate (I): The identity gate does not change the state of the qubit. It maps |0⟩ to |0⟩ and |1⟩ to |1⟩.

2. Pauli-X Gate (X): The Pauli-X gate, also known as the NOT gate, flips the state of the qubit. It maps |0⟩ to |1⟩ and |1⟩ to |0⟩.

3. Pauli-Y Gate (Y): The Pauli-Y gate is similar to the Pauli-X gate but also introduces a phase change. It maps |0⟩ to i|1⟩ and |1⟩ to -i|0⟩, where i is the imaginary unit.

4. Pauli-Z Gate (Z): The Pauli-Z gate introduces a phase change. It maps |0⟩ to |0⟩ and |1⟩ to -|1⟩.

5. Hadamard Gate (H): The Hadamard gate creates superposition by transforming |0⟩ to (|0⟩ + |1⟩)/√2 and |1⟩ to (|0⟩ - |1⟩)/√2.

6. CNOT Gate (CX): The controlled-NOT gate applies the Pauli-X gate to the target qubit if the control qubit is in the state |1⟩. It leaves the target qubit unchanged if the control qubit is in the state |0⟩.

7. Toffoli Gate (CCX): The Toffoli gate is a three-qubit gate that applies the Pauli-X gate to the target qubit if both control qubits are in the state |1⟩. Otherwise, it leaves the target qubit unchanged.

8. Controlled Phase (CZ) Gate: The controlled phase gate introduces a phase change of -1 to the target qubit if the control qubit is in the state |1⟩. Otherwise, it leaves the target qubit unchanged.

9. SWAP Gate: The SWAP gate swaps the states of two qubits. It exchanges the state of the first qubit with the state of the second qubit.

10. CSWAP Gate /Fredking gate 

These gates are fundamental to quantum computing and are used in various combinations to perform quantum operations and construct quantum algorithms.