Exercise 1.6.3 - Plot and matrix form mismatch

Codebook
1

Hi there,

after completing exercise 1.6.3 I tried to deduce the matrix form of RY from the resulting plot with the actual matrix form of RY, given in the theory. See both here:

image
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It seems that either the rows should be interchanged or something is wrong when producing the plot.

This is the full code is used for producing the plot for reference:

dev = qml.device("default.qubit", wires=1)


@qml.qnode(dev)
def apply_ry(theta, state):
    """Apply an RY gate with an angle of theta to a particular basis state.

    Args:
        theta (float): A rotation angle.
        state (int): Either 0 or 1. If 1, initialize the qubit to state |1>
            before applying other operations.

    Returns:
        np.array[complex]: The state of the qubit after the operations.
    """
    if state == 1:
        qml.PauliX(wires=0)

    ##################
    # YOUR CODE HERE #
    ##################

    # APPLY RY(theta) AND RETURN THE STATE
    qml.RY(theta, wires=0)

    return qml.state()


# Code for plotting
angles = np.linspace(0, 4 * np.pi, 200)
output_states = np.array([apply_ry(t, 0) for t in angles])

plot = plotter(angles, output_states)

Could someone help me spot the mistake or how the plot and the given matrix form of RY match?
In the exercise before (1.6.2), I was able to successfully deduce the matrix form of RX from the plot.

Thanks in advance!

3

Hi @NoName , welcome to the Forum!

The graph and the matrix are indeed correct.

If you look at the solution of ex I.6.3 (on the right) you’ll notice a cosine (orange line) and a sine (tiel line). The graph and the first column of the matrix are indeed alike!

image
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5

Thanks, you are absolutely right!

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