In Quantum Computing --> Information --> Quiz 3: Gates Galore --> Problem 10, three quantum gates are applied, in the following order: "first X, then Z, and then H".

I tried to solve this by turning HZX into a single operation using matrix multiplication. However, I seem to have ordered my multiplication incorrectly. I thought that the order would be (X times Z) times H, which works out to the correct answer of \(\frac{1}{\sqrt2}\begin{bmatrix} -1 & 1\\ 1 & 1 \end{bmatrix} \)

However, the order shown in the explanation (which gives the same answer) is H times (Z times X).

Which is correct, and why?

P.S. Quantum Computing does not show up as a Topic when making a post, so I labelled this "Computer Science".

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## Comments

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TopNewestInterestingly, the next problem is, "Would the resulting state always be the same if we had applied the gates in a different order?"

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In general, matrix multiplication is non-commutative (meaning that the order is important). Try out the order shown in the problem and see if it works out to your answer. If it doesn't, there is probably a typo in the quiz.

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As I understand, we usually understand \(\ket{0}\) to be the vector \(\begin{bmatrix}0\\ 1\end{bmatrix}\). So, in order to apply the function (or linear transformation) \(X\) on \(\ket{0}\), one says \(X\ket{0}\). Seen this way, we need to figure out \(HZX\ket{0}\)

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