Stuck on Codercise I.5.4

Codebook
1

Hello,
I was able to simplify the circuit as follows:

image
image719×419 6.35 KB

However, I received the following error:
Incorrect: Your resulting output doesn’t look quite right.
Incorrect: more than 1 T gates are needed.
Incorrect: the optimal depth of the circuit is not 4.
Incorrect: the optimal T-count of the circuit is not 1.
Incorrect: the optimal T-depth of the circuit is not 1.

In wire 0: the pairs of H-gates, T-gates, and adjoint T-gates cancel each other, and one H-gate remains
In wire 1: the pair of H-gates cancel each other and the 2 pairs of T-gates become S-gates, one T-gate, and H-gate remain
In wire 2: the pair of H-gates cancel each other, the 2 pairs of adjoint T-gates become adjoint S-gates, and one H-gate remains

I am not sure where the simplification went wrong.

2

The simplification went wrong because you can only cancel out the pairs of gates when they are right next to each other. For example H T H cannot be simplified to T, but H H T can be. This is because the operators do not commute: you cannot generally swap the ordering of matrix transformations around.

Now with this I’m sure your simplification will be very different.

1 Like
3

Yes, my updated simplification is now different. I forgot about the non-commutativity, looks like I need to revise the basics. Thank you for your explanation.

1 Like
4

Hey @Sfdq! Welcome to the forum :slight_smile:

If you have any further questions or concerns, write back!

5

Hi,

I am also stuck with the error:

“Error: Hadamard: wrong number of wires. 3 wires given, 1 expected.”
I guess it is something related to the optimisation and the reduction of the number of Hadamard gates, but I really don’t see it. Any advice?

Thanks,

Gian

Here is my circuit:

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

@qml.qnode(dev)
def too_many_ts():
    """You can implement the original circuit here as well, it may help you with
    testing to ensure that the circuits have the same effect.

    Returns:
        array[float]: The measurement outcome probabilities.
    """
    qml.Hadamard(wires=[0,1,2])
    
    qml.T(wires=[0,1])
    qml.adjoint(qml.T(wires=2))
    
    qml.T(wires=0)
    
    qml.Hadamard(wires=[0,1,2])
    
    qml.adjoint(qml.T(wires=[0,2]))
    qml.T(wires=1)
    
    qml.adjoint(qml.T(wires=[0,2]))
    qml.T(wires=1)
    
    qml.T(wires=1)
    qml.adjoint(qml.T(wires=2))
    
    qml.T(wires=1)
    qml.Hadamard(wires=[0,1,2])
    
    return qml.probs(wires=[0, 1, 2])

@qml.qnode(dev)
def just_enough_ts():
    """Implement an equivalent circuit as the above with the minimum number of 
    T and T^\dagger gates required.

    Returns:
        array[float]: The measurement outcome probabilities.
    """

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

    # IMPLEMENT THE CIRCUIT, BUT COMBINE AND OPTIMIZE THE GATES
    # TO MINIMIZE THE NUMBER OF TS
    
    qml.Hadamard(wires=[0,1,2])
    
    qml.S(wires=0)
    qml.T(wires=1)
    qml.adjoint(qml.T(wires=2))
    
    qml.Hadamard(wires=[0,1,2])
    
    qml.adjoint(qml.S(wires=[0, 2]))
    qml.S(wires=1)
    
    
    qml.S(wires=1)
    qml.adjoint(qml.T(wires=2))
    
    qml.Hadamard(wires = [0, 1, 2])

    return qml.probs(wires=[0, 1, 2])

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

# FILL IN THE CORRECT VALUES FOR THE ORIGINAL CIRCUIT
original_depth = 8
original_t_count = 13
original_t_depth = 6

# FILL IN THE CORRECT VALUES FOR THE NEW, OPTIMIZED CIRCUIT
optimal_depth = 6
optimal_t_count = 3
optimal_t_depth = 2
6

Hi @GianAsara,

What the error is saying is that you’re trying to apply the Hadamard to 3 qubits at the same time but it can only be applied to one at a time. So qml.Hadamard(wires=[0,1,2]) should actually be split into three lines if you want to apply it to the three wires.

I hope this helps!