B What is the significance of 'i' in quantum computation notation?

[Quark Effect]

TL;DR Summary

The meaning of notation 'i'?

Hi guys, I am currently having some difficulties with this quantum state. I don't entirely understand what that letter 'i' means, where it comes from and why it appears in brackets [1, i]. Shouldn't there be a '0' instead?

I am an absolute beginner in quantum computation. I've been following a tutorial for beginners while this quantum state appeared with the letter 'i' and there's no further explanation where it comes from and what it means.

 

[PeterDonis]

I don't entirely understand what that letter 'i' means

It's the square root of $-1$.

 

[PeterDonis]

I am an absolute beginner

Thread level changed to "B" accordingly.

 

[mfb]

You'll need to know complex numbers for everything in quantum mechanics.

 

[Quark Effect]

It's the square root of $-1$.

You'll need to know complex numbers for everything in quantum mechanics.

Thanks a lot!

 

[PeterDonis]

why it appears in brackets [1, i]. Shouldn't there be a '0' instead?

No. What you have shown is column vector notation. You have a vector space with two basis vectors, $|0\rangle$ and $|1\rangle$. The upper number in the column vector is the $|0\rangle$ component of the vector and the lower number is the $|1\rangle$ component. The image you showed has factored out the common $1 / \sqrt{2}$ factor, so that leaves $\begin{bmatrix} 1 \\ i \end{bmatrix}$ since the coefficient in front of $|0\rangle$ is $1$ and the coefficient in front of $|1\rangle$ is $i$.

 

[Quark Effect]

No. What you have shown is column vector notation. You have a vector space with two basis vectors, $|0\rangle$ and $|1\rangle$. The upper number in the column vector is the $|0\rangle$ component of the vector and the lower number is the $|1\rangle$ component. The image you showed has factored out the common $1 / \sqrt{2}$ factor, so that leaves $\begin{bmatrix} 1 \\ i \end{bmatrix}$ since the coefficient in front of $|0\rangle$ is $1$ and the coefficient in front of $|1\rangle$ is $i$.

Finally understood it. Thanks a lot man!

 

[PeterDonis]

Thanks a lot man!

You're welcome!