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Hands-On Quantum Machine Learning with Python

Probabilities and the Qubit States

Explore the relationship between qubit states and measurement probabilities, focusing on how the Ry gate rotates qubits and alters probabilities. Gain practical skills in computing qubit measurement likelihoods and translating them into rotation angles, essential for quantum circuit design and quantum machine learning.

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Let’s look at our transformation in action.

Rotating the qubit state

Javascript (babel-node)
from math import pi
# Define state |0>
initial_state = [1, 0] 
# Redefine the quantum circuit
qc = QuantumCircuit(1)
# Initialise the 0th qubit in the state `initial_state`
qc.initialize(initial_state, 0) 
# Rotate the state by a quarter of a half circle.
qc.ry(pi/4,0)
# 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)

The Qiskit QuantumCircuit object provides the ry function in line 13. The ry function is for RyR_y gate. Since it rotates the qubit around the y-axis of the quantum system, this function takes the angle θ\theta, in radians, as the first parameter. The value of 2*pi denotes a full rotation of 360°. The second parameter of the function is the position of the qubit to apply the gate to.

However, we should be cautious. The angle θ\theta does not stop when it “reaches” the state ∣1⟩|1\rangle. We can rotate our qubit state beyond it. Then, rather than increasing the probability of measuring 1, you decrease it.

The RyR_y gate is easily reversible. We apply another RyR_y gate with −θ-\theta as the parameter.

We started with the goal to increase the casino’s chance to win by 10%. What is 10% in terms of the angle θ\theta?

θ\theta denotes the angle between the basis state ∣0⟩|0\rangle and ∣ψ⟩ ...