Implementing the CNOT gate
Learn how we can implement the CNOT‐gate with multiple control qubits.
Applying the CNOT gate with |0> as the control qubit
from math import sqrtfrom qiskit import QuantumCircuit, Aer, executefrom qiskit.visualization import plot_histogram# Redefine the quantum circuitqc = QuantumCircuit(2)# Initialise the qubitsqc.initialize([1,0], 0)qc.initialize([1,0], 1)# Apply the CNOT-gateqc.cx(0,1)# Tell Qiskit how to simulate our circuitbackend = Aer.get_backend('statevector_simulator')# execute the qcresults = execute(qc,backend).result().get_counts()# plot the resultsplot_histogram(results)
In lines 9 to 10, when we initialize both qubits with before applying the CNOT-gate in line 13, we always measure 00, and nothing happens.
When we initialize the control qubit with and the target qubit with , we always measure 11.
Applying the CNOT gate with |1> as the control qubit
qc = QuantumCircuit(2)# Initialise the 0th qubit in the state `initial_state`qc.initialize([0,1], 0)qc.initialize([1,0], 1)# Apply the CNOT-gateqc.cx(0,1)# Tell Qiskit how to simulate our circuitbackend = Aer.get_backend('statevector_simulator')# execute the qcresults = execute(qc,backend).result().get_counts()# plot the resultsplot_histogram(results)
When we only look at the basis states, there is still nothing special going on here. The result equals the result that a classical circuit produces.
It becomes interesting when the control qubit is in a state of superposition. We initialize both qubits in the state , again. Then, the Hadamard gate puts the qubit into the state . When measured, a qubit in this state is either 0 or 1, with a probability of 50% each. The following figure depicts the quantum circuit diagram.