The CNOT Gate

The controlled-NOT (CNOT, or CX) is the workhorse two-qubit gate. It flips a target qubit if and only if the control qubit is $|1\rangle$:

| input | output | | --- | --- | | $\lvert 00\rangle$ | $\lvert 00\rangle$ | | $\lvert 01\rangle$ | $\lvert 01\rangle$ | | $\lvert 10\rangle$ | $\lvert 11\rangle$ | | $\lvert 11\rangle$ | $\lvert 10\rangle$ |

(Here the left bit is qubit 0, the control.) On a superposed control, CNOT does something with no classical analogue: it correlates the two qubits, which is the seed of entanglement — the subject of the next module.

Try it

Put the control in $|1\rangle$ and use CNOT to flip the target, reaching $|11\rangle$.

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