Hands-On Quantum Machine Learning with Python/

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Implementing the CNOT gate

Implementing the CNOT gate

Learn how we can implement the CNOT‐gate with multiple control qubits.

We'll cover the following...

Applying the CNOT gate with |0> as the control qubit

Javascript (babel-node)
from math import sqrt
from qiskit import QuantumCircuit, Aer, execute
from qiskit.visualization import plot_histogram
# Redefine the quantum circuit
qc = QuantumCircuit(2)
# Initialise the qubits
qc.initialize([1,0], 0) 
qc.initialize([1,0], 1)
# Apply the CNOT-gate
qc.cx(0,1)
# Tell Qiskit how to simulate our circuit
backend = Aer.get_backend('statevector_simulator')
# execute the qc
results = execute(qc,backend).result().get_counts()
# plot the results
plot_histogram(results)

In lines 9 to 10, when we initialize both qubits with ∣0⟩|0\rangle before applying the CNOT-gate in line 13, we always measure 00, and nothing happens.

When we initialize the control qubit with ∣1⟩|1\rangle and the target qubit with ∣0⟩|0\rangle, we always measure 11.

Applying the CNOT gate with |1> as the control qubit

Javascript (babel-node)
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-gate
qc.cx(0,1)
# Tell Qiskit how to simulate our circuit
backend = Aer.get_backend('statevector_simulator')
# execute the qc
results = execute(qc,backend).result().get_counts()
# plot the results
plot_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 ∣0⟩|0\rangle, again. Then, the Hadamard gate puts the qubit QQ into the state ∣+⟩|+\rangle. 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.

Applying

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