# Questions tagged [notation]

For questions about the usage of, origin of or reasons for specific notation used in the context of quantum computing.

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### How does bra-ket notation work?

Quantum algorithms frequently use bra-ket notation in their description. What do all of these brackets and vertical lines mean? For example: $|ψ⟩=α|0⟩+β|1⟩$ While this is arguably a question about ...
3k views

### Quantum states are unit vectors… with respect to which norm?

The most general definition of a quantum state I found is (rephrasing the definition from Wikipedia) Quantum states are represented by a ray in a finite- or infinite-dimensional Hilbert space over ...
210 views

### What do double wires mean in quantum circuits, and how do they relate to if statements?

The circuit can be translated to the following code: ...
306 views

### What does quantum error correction code notation stand for?

I understand the notation for classical error correcting codes. E.g., "Hamming(7,4)" stands for a Hamming code that uses 7 bits to encode blocks of 4 bits. What does the notation for quantum error ...
594 views

### How to compute the average value $\langle X_1 Z_2\rangle$ for a two-qubit system?

Show that the average value of the observable $X_1Z_2$ in a two-qubit system measured in the state $(|00\rangle + |11\rangle)/\sqrt{2}$ is zero. How would we approach this question? I understand ...
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### Writing the notation when gates act on non successive registers

Suppose I have registers $|a\rangle^{l}|b\rangle^{l} |c\rangle^{l}$ and want an adder mod $l$ gate between the $a$ and $c$ registers. Let $R$ be the adder mod $l$ gate. So is this the correct ...
58 views

### Confusing notation in Wikipedia's quantum channel article

In the Wikipedia's Quantum channel article, it is said that a purely quantum channel $\phi$ (it's not exactly the same phi calligraphy but it's close), in the Schrodinger picture, is a linear map ...
246 views

### Notation for two qubit composite product state

In my lecture notes on quantum information processing my lecturer gives an example of composite systems as $|\phi\rangle=|0\rangle |0\rangle=|00\rangle$. I understand that if we have two qubits then ...
115 views

### What does the notation $\lvert \underline{x} \rangle$ mean?

I recently read hand-written notes about the "secret mask" or "secret string" algorithm (which I can't share here) with the following notation $\lvert \underline{x} \rangle$, i.e. a letter with a line ...
96 views

### Interpretation of specific Hamiltonian operator

In the paper https://arxiv.org/abs/1909.05820 the authors introduce several Hamiltonians. For example they define $$H_G = A^\dagger \left( \mathbb{I} - \vert b \rangle \langle b \vert \right) A$$ in ...
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### Convention for expressing measurement in non-standard basis

If we're measuring in common bases like $|0\rangle$, $|1\rangle$ or $|+\rangle$, $|-\rangle$ we express this by saying we're measuring with $\sigma_z$ or $\sigma_x$, or measuring in the computational ...
107 views

### What is the notational convention for the single-qubit states $\lvert0\rangle\pm i\lvert1\rangle$?

The features of major search engines (looking at you, google!) prevent me from searching for an answer to this question, so I will poll the community here. Is the state $|{\pm} i\rangle$ generally ...
42 views

### What does the notation $\sigma_j^z$ mean for Pauli matrices?

In multiples papers or online article on the QAOA algorithm (such as this one), I found notation for the Hamiltonian similar to this one : $$\sum_{ij} \frac{1}{2} (I-\sigma_i^z \sigma_j^z)$$ I don'...
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### A question about notation for quantum states

I am reading an article on representation of digital images using qubits. But I am not able to understand the notations of the article. Can somebody help me: $|0\rangle$: It means the first basis ...
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### Why is correlation in the $X$ basis represented as $X\otimes X = 1$?

As far as I know, correlation of two qubits in the $X$ basis implies that under a simultaneous bit flip, the composite quantum state must be invariant. For instance, $A$ and $B$ can be said to be ...
66 views

### Representing a Bell measurement on non adjacent qubits

I have a state {|\psi\rangle} = s {\Bigl(|1\rangle_1|1\rangle_2-|0\rangle_1|0\rangle_2\Bigr)}\otimes{\Bigl(|0\rangle_3|1\rangle_4-|1\rangle_3|0\rangle_4\Bigr)}\otimes{\Bigl(|0\rangle_5|1\rangle_6-|1\...
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### Which is the correct depiction of a qubit before it collapses?

Which is the correct depiction of a qubit state showing the possibilities before it collapses? Is it like: MODEL 1: 1000 0100 0010 0001 MODEL 2: 1000 0100 0010 0001 0111 1011 1101 1110 MODEL 3: ...
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### 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 ...
I started working in Qiskit, and here is an example of how gates of a circuit are represented graphically in LaTeX format: Obviously, $R_y(\theta)$, is a y rotation by a certain angle. But all the ...
### What are $|+\rangle$ and $|-\rangle$?
On a view places, I've seen kets that look like this $\left|+\right>$ or this $\left|-\right>$ but I don't seem to find any explanation of this base online. Is it just a different notation for \$...