The effect of CNOT gate on the control qubit

[quantumadmin]

The CNOT gate, also known as the Controlled-NOT gate or CX gate, is a fundamental two-qubit gate in quantum computing. It performs an operation on a target qubit based on the state of a control qubit. The effect of the CNOT gate on the control qubit depends on the state of the control qubit itself.

The CNOT gate can be represented by the following matrix:

Code: Select all

CNOT = [[1, 0, 0, 0],
             [0, 1, 0, 0],
             [0, 0, 0, 1],
            [0, 0, 1, 0]]

Here's how the CNOT gate affects the control qubit based on its initial state:

Control qubit in state |0⟩:

If the target qubit is initially |0⟩, the CNOT gate does not change the state of the control qubit. The resulting state is still |0⟩ for the control qubit.
If the target qubit is initially |1⟩, the CNOT gate flips the state of the control qubit. The resulting state is |1⟩ for the control qubit.

Control qubit in state |1⟩:

If the target qubit is initially |0⟩, the CNOT gate flips the state of the target qubit. The resulting state is |1⟩ for the target qubit.
If the target qubit is initially |1⟩, the CNOT gate flips the state of both the control and target qubits. The resulting state is |0⟩ for the control qubit and |0⟩ for the target qubit.

In summary, the CNOT gate flips the state of the control qubit if the target qubit is initially |1⟩. If the target qubit is initially |0⟩, the CNOT gate does not affect the state of the control qubit. The specific outcome depends on the initial states of the control and target qubits and determines the entanglement and correlation between them.