CNOT Gate

The CNOT gate is two-qubit operation, where the first qubit is usually referred to as the control qubit and the second qubit as the target qubit. Expressed in basis states, the CNOT gate:

leaves the control qubit unchanged and performs a Pauli-X gate on the target qubit when the control qubit is in state $|1\rangle$ ;
leaves the target qubit unchanged when the control qubit is in state $|0\rangle$ .

$\ CNOT = \begin{pmatrix} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 1 \ 0 & 0 & 1 & 0 \end{pmatrix}$

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          version 1.0
qubits 2
H q[0] # execute Hadamard gate on qubit 0 to create a superposition state
CNOT q[0], q[1] # entangle both qubits using CNOT gate


q[0]
q[1]

Note: For multi-qubit gates, it must always be checked whether the topology (connectivity) allows for a direct implementation of the operation. A compilation step may be required in order to map an operation.

As an example, on the Starmon-5 backend q[0] and q[1] are not connected. An operation such as cnot q[0],q[1] should therefore be rewritten as cnot q[0],q[2] or compiled by inserting swap gates, when the intended operation is indeed a a cnot between q[0] and q[1].