17 questions linked to/from How does bra-ket notation work?
1 vote
459 views

### Magnitudes and phases of coefficients of a qubit [duplicate]

Quantum mechanics is based on the idea of waves, and waves have both a magnitude and a phase? $$|\psi\rangle = i\alpha|0\rangle + \beta|1\rangle.$$ Does $\alpha$ and $\beta$ represent magnitude and $i$...
• 313
144 views

### Outer Product Intution [duplicate]

Please, help me understand this statement. The outer product notation for matrices also gives an intuitive input-output relation for them. For instance, the matrix |0⟩ ⟨1| + |1⟩ ⟨0| can be read as &...
2k views

### Non-layperson explanation of why a qubit is more useful than a bit?

I have a computer science and mathematics degree and am trying to wrap my head around quantum computing and it just doesn't seem to make sense from the very beginning. I think the problem is the ...
5k views

• 79
1 vote
448 views

### Can Dirac notation be used with 2 or more gates?

Can Dirac notation be used with 2 or more gates? I've been trying to do the math with the $X$ and $Z$ ($X\otimes Z$) gates but I'm not getting the answer I should. In fact, the answer makes no sense. ...
• 45
523 views

### How do I apply a matrix to a ket state?

If we have the following matrix: $$\frac{1}{\sqrt{2}}\begin{pmatrix}1&1&0&0\\ 1&-1&0&0\\ 0&0&1&-1\\ 0&0&1&1\end{pmatrix}$$ How do we find the output for ...
• 173
245 views

### Where is the factor of $-i$ in rotation gates coming from?

As I understand it the Pauli-X, Y and Z gates are the same as their rotational gates with a rotation of $\pi$. But given the expression for those gates, I find that there is a factor of $-i$ in each ...
• 53
232 views

### Why do $n$ inputs to a ket give a vector of dimension $(2^n,1)$?

NB - notation from Octave. I understand that ket([0]) is the $(1,0)$ in a $(x,y)$ plane. But when I try a ket with three numbers I get a column vector of dimension $(8,1)$. I assume that comes ...
122 views