Help: Applying Quantum Gates in Order

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".

#ComputerScience

Easy Math Editor

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Comments

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

Adrian Self - 2 years, 4 months ago

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.

Steven Chase - 2 years, 4 months ago

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 $HZX\ket{0}$

Agnishom Chattopadhyay - 2 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$