Linked Questions

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1answer
179 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 $i$...
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1answer
56 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 &...
7
votes
4answers
705 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 ...
4
votes
1answer
1k views

How are the Pauli $X$ and $Z$ matrices expressed in bra-ket notation? [duplicate]

For example: $$\rm{X=\sigma_x=NOT=|0\rangle\langle 1|+|1\rangle\langle 0|=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}}$$ $$\rm{Z=\sigma_Z=signflip=|0\rangle\langle 0|-|1\rangle\langle 1|=\...
6
votes
2answers
539 views

How to translate matrix back into Dirac notation?

In Circuit composition and entangled states section of Wikipedia's article on Quantum logic gates the final result of a combined Hadamard gate and identity gate on $|\Phi^{+}\rangle$ state is: $ M \...
3
votes
1answer
254 views

How to read Dirac notation (without algebra)?

I have no idea how to read Dirac notation. $$\left|↑↑ \right\rangle \tag{1}$$ $$\left|↑↓\right\rangle+\left|↓↑\right\rangle \tag{2}$$ $$\left|↑↓\right\rangle-\left|↓↑\right\rangle \tag{3}$$ $$\left|↓...
1
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1answer
437 views

Measurement of a qubit and storage of the information on a bit

Suppose we have the quantum circuit below with a quantum register of 2 qubits and a classical register of 2 bits. The Hadamard gates and CNOT gate are not important for the question. When we measure a ...
2
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2answers
178 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 ...
5
votes
1answer
167 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 ...
3
votes
2answers
64 views

For two-qubit systems, do we have $\langle 01|01\rangle = \langle 0|0\rangle\langle 1|1\rangle$?

I am new to quantum computing and I want to know the following: If I have a 2 qubit system in state e.g. $\left|01\right>$ and I want to calculate the probability of measuring e.g. $\left<01\...
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3answers
61 views

How to prove that the transpose operation maps an arbitrary qubit to its complex conjugate?

How to prove that the transpose operation maps an arbitrary qubit to its complex conjugate, $|\psi^*\rangle \rightarrow |\psi\rangle$
1
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1answer
97 views

What is the difference between the states $i|1\rangle$ and $|+i\rangle$?

I am new to Quantum computing. I see $|\mbox{+}i\rangle$ state maps to y-axis on bloch sphere ($\theta = 90$ degree and $\phi = 90$ degree) while $i|1\rangle$ maps on x-axis, $i|1\rangle$ is stated as ...
0
votes
2answers
104 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 ...
1
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2answers
87 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. ...
1
vote
1answer
91 views

How to write the map $\mathbb C\ni z\mapsto zv$ in bra-ket notation?

As part of a course, I've been asked to write a map $C\rightarrow H,z \rightarrow zv$ for $v \in H=C^3\otimes C^2$, $v=[1, 0, 0, 1, 0, 1]$ in bra-ket notation. However, I never written such a map ...