Questions tagged [terminology-and-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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Why is Dirac notation used for quantum states?

I am thinking that I am using Dirac notation to represent $|0\rangle$ and $|1\rangle$ and we are using column vector but why actually using column vector where first one is $(0 \,1)$ for $|1\rangle$ ...
• 143
179 views

What does the centered dot notation mean in the expression $|+\rangle|+\rangle\otimes(\cdot)$?

In the expression $|+\rangle|+\rangle \otimes(\cdot)$, what does the centered dot represent? I have come across a definition of the centered dot previously, similar to the one given here, but I am ...
• 898
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How to write down product operators acting on non-adjacent subsystems?

Given the following fusion gate (type-2) which is projecting 2 qubits to an even state $$F_{ZZ}=(\langle00|+\langle|11|)$$ I would like to find the operator for the bigger space. For example, if I ...
• 1,452
1 vote
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Meaning of the notation $[d]$ in scientific paper

Here in this paper (and several others), the notation $[d]$ is used. For instance, Lemma 9 of the paper reads: Let $T_d\in R[x]$ be the d-th Chebyshev polynomial of the first kind. Let $Φ\in R_d$ be ...
• 129
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What is fidelity in quantum computing?

As I studied quantum computing, I saw term 'Fidelity' in many papers that related to quantum algorithm. So, I really wonder about following two things. What is the real meaning of 'Fidelity' (As I ...
• 61
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Dirac notation for classic bits?

I'm writing about Quantum Computing, and in my preliminary sections on classical computing, there are too many things going by the names 0 and 1. Would it be awful to denote the values of classical ...
• 53
119 views

In what contexts are different notations used for indicating measurement outcomes?

I have seen a few different notations for denoting measurement outcomes. Does anyone know of which notation is more widely used in various contexts? For instance, I like referring to this Wikipedia ...
• 1,411
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What is the difference between "maximally entangled" and "entangled" states?

when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
• 577
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Why does the condition $\langle \varphi _k\left( t \right) |\dot{\varphi}_l\left( t \right) \rangle =0$ called parallel transport condition?

I'm reading this paper (arXiv) about nonadiabatic holonomic quantum computation. Therein, it is stated that $\langle \varphi_k( t ) |\dot{\varphi}_l( t ) \rangle =0$ Eq.(2) is the parallel transport ...
• 715
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What is dual space, and why is it required?

I recently started QC/QM and came across something called dual space? How do we explain concept of dual space to a layman. why do we need dual space? I tried to read and watch some resources on dual ...
• 577
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What is the correct name of this quantum gate? Possibly state control gate

Let $\vec v \in \mathbb{C}^2$ be the following quantum state:  \vec v = \frac{1}{\sqrt{2}}\begin{bmatrix} v_{1} \\ v_{2} \\ \end{bmatrix},\space \lvert v_1 \rvert = 1,...
186 views

Representation of a vector in the HHL algorithm

Reading about the HHL algorithm, which is used to solve the equation $Ax=b$, on Wikipedia, they say to represent $b$ as $|b\rangle=\sum_{i \mathop =1}^N b_i|i\rangle.$ I'm assuming $b$ is a vector ...
• 43
1 vote
221 views

What is the definition of $n$-local commuting circuit?

In this paper and this one, they talk about commuting quantum circuits that are only composed of "$n$-local commuting circuits", typically for $n=2$ or $n=3$. However they don't provide a ...
• 1,876
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Standard name for CZ gate conjugated by Hadamards?

Is there a standard name for a $CZ$ gate conjugated by $H \otimes H$ gates? See below for circuit
In this paper: ArXiv and PRL links, the authors give the definition of two $d\times d$ qudits to be permutationally invariant states if $\varrho$ is invariant under exchanging the particles. This can ...