Is Y equivalent to( S X Sdg)?

Codebook
1

I have this code here to solve " I.14 Multi-qubit gate challenge" of the codebook here .

https://codebook.xanadu.ai/I.14
I could not figure out why state|11> is wrong, any idea

dev = qml.device("default.qubit", wires=3)

# State of first 2 qubits
state = [0, 1]

@qml.qnode(device=dev)
def apply_control_sequence(state):
    # Set up initial state of the first two qubits
    if state[0] == 1:
        qml.PauliX(wires=0)
    if state[1] == 1:
        qml.PauliX(wires=1) 

    # Set up initial state of the third qubit - use |->
    # so we can see the effect on the output
    qml.PauliX(wires=2)
    qml.Hadamard(wires=2)
    
    ##################
    # YOUR CODE HERE #
    ##################
    
    # IMPLEMENT THE MULTIPLEXER
    # IF STATE OF FIRST TWO QUBITS IS 01, 
    #APPLY X TO THIRD QUBIT
    qml.PauliX(wires=0)
    qml.Toffoli(wires=[0,1,2])
    qml.PauliX(wires=0)

    # IF STATE OF FIRST TWO QUBITS IS 10,
    #APPLY Z TO THIRD QUBIT

    qml.PauliX(wires=1)
    qml.Hadamard(2)
    qml.Toffoli(wires=[0,1,2])
    qml.Hadamard(2)
    qml.PauliX(wires=1)

    # IF STATE OF FIRST TWO QUBITS IS 11, 
    #APPLY Y TO THIRD QUBIT
    qml.S(2)
    qml.Toffoli(wires=[0,1,2])
    qml.adjoint(qml.S(2))
  
    return qml.state()
    

print(apply_control_sequence(state))

I got this error:

Incorrect: your circuit does not have the correct action on |11>.

2

Hi @Afrah, you’re almost there!

Take a close look at the ordering of the gates in the last part of your code. Is it the same to apply S first or adjoint(S) first?
I hope this hint helps you!