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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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What is the meaning of the state $|1\rangle-|1\rangle$?

I don't understand it. But suppose you have a state of two qubits in superposition and it looks like $|10\rangle-|11\rangle$. Now you have in your circuits two gates one is a controlled-NOT from the ...
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Qiskit gates in LaTeX representation: notation meaning [duplicate]

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 ...
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Is there a place online where I can catch up with all the notational syntax associated with quantum computing?

There is a vast amount of new notations which would be new even to Ph.D. in math. How on Earth can I catch up with all of this? Is there a place online which is devoted to the QC syntax? I would ...
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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|↓...
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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 ...
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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 ...
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Problem with the mathematical formulation of “qubitization”

In this research paper, the authors introduce a new algorithm to perform Hamiltonian simulation. The beginning of their abstract is Given a Hermitian operator $\hat{H} = \langle G\vert \hat{U} \...
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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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Notation for two entangled registers

Suppose I have two registers x and y, of length m and n bits respectively. I want to initialize my system to contain an equal superposition of all $2^{n+m}$ states, then apply an oracle function (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 ...
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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 ...
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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 ...
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What do we mean by the notation $\lvert \mathbf{x}, 0\rangle$?

In quantum computation, a common operation performed between two quantum states is the tensor product, which allows us to create a new and higher-dimensional state from two lower-dimensional states. ...
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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 ...
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Compute average value of 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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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: ...
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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 ...