Questions tagged [terminology]
For questions about the meaning and usage of vocabulary specific to quantum computing or quantum information.
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Do the following circuits violate the principle of "no fast-forwarding"?
The no fast-forwarding principle states roughly that, given that we can simulate a Hamiltonian for time $t$ using $r$ gates, in order to perform the Hamiltonian simulation for time $2t$, we must in ...
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Clarification defining/finding the relative phase of a qubit
Let the vector $ |V\rangle = r_0 e^{i\theta_0} |0\rangle + r_1 e^{i\theta_1} |1\rangle $ correspond to the state of a qubit where $r_0,r_1,\theta_0,\theta_1 \in \mathbb{R}$.
According to p. 22 of ...
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Notation for Lindblad operators
I was reading the paper Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation
. The claim is that universal quantum computation can be achieved using the ...
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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 ...
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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 ?
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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 about nonadiabatic holonomic quantum computation and met the condition eq.(2) states that $\langle \varphi _k\left( t \right) |\dot{\varphi}_l\left( t \right) \rangle =0$ is the ...
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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 ...
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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,...
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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 ...
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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
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What is meant by "local isometry" in this paper?
I apologize for such a basic question here. I've been reading this paper, and I am wondering what is the usage of the term "local isometry" in the paper? The paper is open access, so you can ...
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What is the difference between "permutationally invariant" and "symmetric" states?
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 ...
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What is (formally) a transversal operator?
This question concerns about a formal definition of transversal operator.
I understood that transversal operator are a group of operators which are efficient in terms of circuit depth and can be used ...
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What is a "maximally mixed state"?
What is meant by maximally mixed states? Does this mean that there are partially mixed states?
For example, consider $\rho_{GHZ} = \left| {GHZ} \right\rangle \left\langle {GHZ} \right|$ and $\rho_W =...
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What are "unbounded loss functions" and "unbounded operators"?
I am reading this paper: Quantum Generative Training Using Rényi Divergences. In it, the authors mention the following multiple times:
"...an unbounded loss function can circumvent the existing ...
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Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates?
Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates? Why is it simple for Clifford gates to implement ...
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What is the difference between quantum "system", "register" and "Hilbert space"?
As far as I can tell, these terms are interchangeable but I am not sure of this.
What is meant by each of the terms "quantum system", "quantum register" and "Hilbert space&...
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How is the "space time volume" defined?
In some papers such as this one the "space time volume" of an algorithm implementation is provided. However I am struggling to find a precise definition of that.
How is such quantity defined ...
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What is the name of this "ancilla based" process to implement gates
I just want to know if there is a specific name for the implementation of a gate on the top qubit with the help of the bottom qubit, represented on this image:
It looks like gate teleportation but it ...
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What is a maximal entangled multipartite state?
We know the four Bell states are the maximal entangled states for two-qubit states, and we know if a state cannot be written as the tensor product by its subsets, then it is a entangled state, so is ...
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What is "gate length" in quantum computing?
I am working on adding a new provider to Qiskit, and I have to specify the properties of the backend.
What is "gate length" (in ns) referring to?
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If density matrices are linear operators, what vectors do they operate on?
1. On page 73 of John Watrous' famous book, a quantum channel is defined as a linear map
$$\Phi: L(\mathcal{X})\rightarrow L(\mathcal{Y})$$
Now $L(\mathcal{X})$ stands for $L(\mathcal{X},\mathcal{X})$...
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Why is the first register of $|x,y\oplus f(x)\rangle$ called "data" register?
When talking about quantum parallelism, in Nielsen and Chuang, it's said that:
it is possible to transform this state into $|x, y \oplus f(x)\rangle$, where $\oplus$ indicates addition modulo 2; the ...
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What constitutes a quantum database?
Newb question, I know it's broad. I'm coming here for validated pointers, so I can know what to read. I have QT for CS (Yanofsky, Mannucci) and am reading about Shannon and Von Neumann entropy, but I'...
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Terminology: quantum state vs. quantum system vs. qubit
What are the difference between quantum state, quantum system and qubit(s)?
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Terminology - "Multi-controlled gate": "multiply" or "multiple"
I have a slight notation question on what the "multi" in "multi-controlled" actually stands for. These two published papers are conflicting on whether it means "mutiply" ...
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What does it mean that 1 qubit can do the job of 1 ebit (entanglement bit)? (second Bennett's law)
I just came across Bennett's laws and I wonder what the second law mean. It states that 1 qubit "can do the job" of 1 ebit. However, the definition of ebit (entanglement bit, wiki just ...
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Who was the first to call the phase gates $P(\pi/2)$ and $P(\pi/4)$ the $S$ and $T$ gates, and were they motivated by generators of the modular group?
Within the theory of quantum gates, a common pair of single-qubit phase gates are the $P(\pi/2)=S$ and $P(\pi/4)=T$ gates, with
$$S= \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix},\:T = \begin{...
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Why do we use 'modes' in quantum optics?
In this material, it gives the definition of modes:
The modes are basically defined by the properties of coherence and orthogonality: modes are orthogonal solutions of the wave equation.
Since the ...
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Where is entanglement present and absent in the one clean qubit model of computation?
Based on my limited and poor understanding, a quantum circuit in the "one clean qubit" model of quantum computation generally acts on a single pure (clean) qubit tensored with $n-1$ qubits ...
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What is meant by "perfect state transfer"?
In discussions on many quantum algorithms especially related to quantum walks, I have seen the term "perfect state transfer" used to describe some property apparently related to the ...
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What is the difference between "Shot-Noise-Limit" and "Standard Quantum Limit"?
It seems that in a lot of papers in the field of quantum metrology, there are two terms Shot-Noise-Limit and Standard Quantum Limit which are frequently referred to. What's the difference between them,...
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How is a promise gap related to a spectral gap?
In linear algebra one often concerns oneself with the spectral gap of a given matrix, which may be defined as the difference between the smallest and second-smallest eigenvalue (or, depending on ...
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Is there any difference between "value of a qubit" and its "state"?
Value of a qubit and its state - is there any difference between these two terms in sense of terminology?
For example, can we name this state of a qubit also a value of a qubit:
$$
|\psi\rangle = \...
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What is meant by the term "quantum interference"?
What is meant by the term "quantum interference" in the context of quantum computing and quantum algorithms?
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What is the significance of transpiling time, validating time, in queue time and running time?
What is the significance of different transpiling time, validating time, in queue time, running time for the same circuit run on different quantum systems for same no. of shots in IBM Q experience?
...
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What's the observable when measuring multiple qubits in the computational basis?
In Nielsen and Chuang (Quantum Computing and Quantum Information) the following definition is given to a projective measurement:
Projective measurements are described by an observable $M$:
$$M = \...
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Terminology: what do $|i\rangle$ and $|\mbox{-}i\rangle$ represent?
$|0⟩$ and $|1⟩$ are usually referred as the computational basis. $|+⟩$ and $|-⟩$, the polar basis.
What about $|i\rangle$ and $|\mbox{-}i\rangle$?
And collectively? Orthonormal states?
References are ...
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What is the pseudo threshold of a QECC using stabilizer formalism
Can someone explain what is the threshold and the pseudo threshold of a Quantum Error Correction Code , for instance the 9-qubit code, and how to calculate it using the stabilizer formalism simulation ...
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What are boost and shift operators and why are they called so?
In some texts I see $X$ and $Z$ Pauli operators as being said as boost and shift operators respectively.
But I came across some text that defines its own operators, namely:
$$
X \vert j\rangle = \...
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Why do we say 'classical computer' to mean 'digital computer'?
The term 'classical computer' is always used to mean standard digital computation (Turing model, Boolean circuits or just good old RAM). I have never seen it to mean other models of computation based ...
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Terminology : Are basis states the same as basis vectors?
The question says it all. Explain any difference in terminology that can be encountered across Physics, Quantum Computing and Mathematics. Thanks!
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What is meant with "shot" in quantum computation?
What is a "shot" in relation to quantum computing? I heard it is repeating time, but I don't understand it. Additionally, why is the default number of shots 1,024 in the IBM Q Experience?
One more ...
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What's the difference between T1 and T2?
I learned that T1 is relaxation time (time from $|1\rangle$ to $|0\rangle$) and T2 is coherence time.
The relaxation is a specific case of decoherence.
What's the difference between them and what's ...
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What is a flying qubit?
DiVincenzo criteria for quantum communication mentions flying qubits:
a. The ability to interconvert stationary and flying qubits
b. The ability to faithfully transmit flying qubits between specified ...
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Significance of the term "diffusion" in Grover's diffusion operator
In the context of Grover's algorithm, the diffusion operator is defined as $U_s = 2|s\rangle \langle s| - I$ with $|s\rangle\equiv |+\rangle^{\otimes n}$. What is the significance of the term "...
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What is the difference between relaxation, dephasing, and decoherence?
Many sources seem to loosely use the terms "relaxation", "dephasing", and "decoherence" interchangeably, while others seem to treat certain of them as special cases of another terms, but I can't find ...
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What does fidelity mean?
I am learning qiskit software and this term keeps popping up and I am unable to get a grasp on the technical definition given by wikipedia. For example, the functions state fidelity and process ...
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What is the definition of Bell state on a n-qubit system?
Question 1: The bell state for a 2-qubit system has been defined in Neilsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |...
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Meaning of "diagonal to the computational basis"
I came across the term "diagonal to the computational basis" in my reading recently. I'm not entirely sure what this term means. I know that a diagonal matrix is one with only non-zero elements on the ...
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