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!