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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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What is meant by "Noisy Intermediate-Scale Quantum" (NISQ) technology?

Preskill introduced recently this term, see for example Quantum Computing in the NISQ era and beyond (arXiv). I think the term (and the concept behind it) is of sufficient importance that it deserves ...
agaitaarino's user avatar
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46 votes
5 answers
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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 ...
Ella Rose's user avatar
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43 votes
2 answers
18k views

What is the "surface code" in the context of quantum error correction?

I am studying Quantum Computing and Information, and have come across the term "surface code", but I can't find a brief explanation of what it is and how it works. Hopefully you guys can ...
Ivanovitch's user avatar
36 votes
4 answers
19k views

What is meant by the term "computational basis"?

What is meant by the term "computational basis" in the context of quantum computing and quantum algorithms?
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34 votes
1 answer
11k views

What exactly is an oracle?

What exactly is an "oracle"? Wikipedia says that an oracle is a "blackbox", but I'm not sure what that means. For example, in the Deutsch–Jozsa algorithm,$\hspace{85px}$,is the oracle just the box ...
Marco Fellous-Asiani's user avatar
30 votes
2 answers
6k views

What is postselection in quantum computing?

A quantum computer can efficiently solve problems lying in the complexity class BQP. I have seen a claim that one can (potentially, because we don't know whether BQP is a proper subset or equal to PP) ...
Sir Cornflakes's user avatar
23 votes
2 answers
20k views

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 ...
peachnuts's user avatar
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22 votes
2 answers
3k views

Significance of The Church of the Higher Hilbert space

The term "Church of the Higher Hilbert Space" is used in quantum information frequently when analysing quantum channels and quantum states. What does this term mean (or, alternately, what does the ...
user3483902's user avatar
21 votes
6 answers
6k 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 ...
Adrien Suau's user avatar
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17 votes
2 answers
8k views

What counts as an "ancilla" qubit?

I am getting confused about the meaning of the term "ancilla" qubit. It's use seems to vary a lot in different situations. I have read (in numerous places) that an ancilla is a constant input - but in ...
Quantum spaghettification's user avatar
17 votes
3 answers
7k views

What does "measurement in a certain basis" mean?

In the Wikipedia article about Bell states it is written: Independent measurements made on two qubits that are entangled in Bell states positively correlate perfectly, if each qubit is measured in ...
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14 votes
3 answers
3k views

What is the difference between "code space", "code word" and "stabilizer code"?

I keep reading (e.g. Nielsen and Chuang, 2010; pg. 456 and 465) the following three phases; "code space", "code word" and "stabilizer code" - but am having a difficult time finding definitions of them ...
Quantum spaghettification's user avatar
14 votes
2 answers
2k 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 ...
Alexander Pozdneev's user avatar
14 votes
1 answer
5k views

What does "bipartite" mean?

This is a really easy question, but my mother language is not English and I get confused quite a lot reading Preskill notes. What does a bipartite system mean? Is this just that it "lives" in a ...
CFRedDemon's user avatar
12 votes
3 answers
1k views

When was the first use of the word Entanglement?

Schrödinger wrote a letter to Einstein after the 1935 EPR paper, and in that letter Schrödinger used the German word "Verschränkung" which translates into "entanglement", but when was the word first ...
user1271772 No more free time's user avatar
11 votes
2 answers
3k views

Is qsphere an actual term representing 5 qubits?

I'm a total beginner, I've been brought here by the featured stackoverflow blog post so I started studying. Watching this youtube video (A Beginner’s Guide To Quantum Computing (3:58), I saw this ...
Adelin's user avatar
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11 votes
2 answers
1k views

What is the relation between POVMs and observables (as Hermitian operators)?

Let $\renewcommand{\calH}{{\mathcal{H}}}\calH$ be a finite-dimensional Hilbert space. An observable $A$ is here a Hermitian operator, $A\in\mathrm{Herm}(\calH)$. A POVM is here a collection of ...
glS's user avatar
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11 votes
1 answer
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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 ...
Amitabh Srivastava's user avatar
11 votes
1 answer
5k views

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 ...
tparker's user avatar
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11 votes
1 answer
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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{...
Mark Spinelli's user avatar
10 votes
2 answers
2k views

What is the difference between a qubit and a quantum state?

In general, a qubit is mathematically represented as a quantum state of the form $\lvert \psi\rangle = \alpha \lvert 0\rangle + \beta \lvert 1\rangle$, using the basis $\{ \lvert 0\rangle, \lvert 1\...
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10 votes
1 answer
983 views

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,...
narip's user avatar
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9 votes
4 answers
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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 ...
Eesh Starryn's user avatar
9 votes
3 answers
458 views

What is quantum computing vs. what is not quantum computing

That is to say, what are some common or popular misconceptions about what constitutes quantum computing? and how are those things misconceptions? It could help in explaining to frame this while ...
PowerLuser's user avatar
9 votes
2 answers
2k views

What does it mean to "measure an operator"?

I was reading a book and then I found this statement. I will put the text as well as a screenshot of the text. The expectation value of an operator is the mean or average value of that operator with ...
user27286's user avatar
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9 votes
2 answers
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Do any specific types of qudits other than qubits and qutrits have a name?

For example, has anyone seen something like: "quqrit" for a 4-level system[1], or "qupit" for a 5-level system[2] ? 1 From "quad" or "quart" since "tetra" would be qutrit, which is already a 3-level ...
user1271772 No more free time's user avatar
9 votes
1 answer
479 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: ...
R. Chopin's user avatar
  • 1,199
8 votes
3 answers
6k views

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 =...
Bekaso's user avatar
  • 285
8 votes
2 answers
776 views

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 ...
Daniele Cuomo's user avatar
8 votes
3 answers
263 views

Is there a convention for denoting $Y$ eigenstates?

Two common shorthands for eigenstates of the $Z$ operator are $\{|0\rangle,|1\rangle\}$ and $\{|1\rangle,|-1\rangle\}$, where in the first case we have $Z|z\rangle=(-1)^z|z\rangle$ and in the second ...
Jahan Claes's user avatar
8 votes
1 answer
3k views

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 ...
Wang's user avatar
  • 119
8 votes
2 answers
242 views

What exactly is "matrix sparsity" $s$?

In many sources (like on Page 30 here), I found that the complexity of the original Harrow Hassidim Lloyd is stated as $\mathcal{O}(\log (N) s^2 \kappa^2/\epsilon)$ where $s$ is said to be the "matrix ...
Sanchayan Dutta's user avatar
8 votes
2 answers
4k views

What do we mean by parity of qubits?

I am currently reading "Quantum Computation and Quantum Information" by Nielsen and Chuang. In the section about Quantum Simulation, they give an illustrative example (section 4.7.3), which I don't ...
brzepkowski's user avatar
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8 votes
1 answer
1k views

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, |...
John Jacob's user avatar
8 votes
2 answers
234 views

Use of the term "dimension" in this description of Simon's algorithm?

In Kaye, Laflamme and Mosca (2007) pg106 they write the following (in the context of Simon's algorithm): ...where $S=\{\mathbf{0},\mathbf{s}\}$ is a $2$-dimensional vector space spanned by $\mathbf{...
Quantum spaghettification's user avatar
7 votes
1 answer
157 views

Elementary question: is $\langle a|b \rangle$ the same as $\langle a||b\rangle$?

In trying to learn more about quantum computing, one of the first things encountered is a definition of the inner product $\langle a|b\rangle$. If I interpret it correctly, and looking near the bottom ...
mhucka's user avatar
  • 203
7 votes
2 answers
661 views

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 "...
Sanchayan Dutta's user avatar
7 votes
3 answers
2k views

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 = \...
nathan raynal's user avatar
7 votes
1 answer
296 views

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 ...
Mark Spinelli's user avatar
7 votes
1 answer
189 views

In qubit/qudit terms, where is the experimental limit between S=3/2 and 2·S=1/2?

This question is inspired by "What is the difference between a qudit system with d=4 and a two-qubit system?", as an experimental follow-up. Consider for illustration these two particular cases: ...
agaitaarino's user avatar
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6 votes
3 answers
3k views

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 ...
김동민's user avatar
  • 907
6 votes
3 answers
299 views

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 ...
luciano's user avatar
  • 5,763
6 votes
2 answers
2k 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 that ...
Alk's user avatar
  • 163
6 votes
2 answers
1k views

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 = \...
Divy's user avatar
  • 61
6 votes
2 answers
1k views

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 ...
Woody1193's user avatar
  • 331
6 votes
1 answer
534 views

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 ...
Mark Spinelli's user avatar
6 votes
1 answer
268 views

In Dirac notation, why do we have $\langle cf|g\rangle = c^*\langle f\vert g\rangle$?

A Hilbert Space has this property $$\langle cf,g\rangle=c\langle f,g\rangle$$ where $f$ and $g$ are the vectors in the Hilbert Space and $c$ is a complex number. In Dirac Notation, $$\langle cf|g\...
HYW's user avatar
  • 207
6 votes
1 answer
648 views

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} \...
Adrien Suau's user avatar
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5 votes
2 answers
968 views

What would be the meaning of an $i$ in a qubit state $i\alpha|0\rangle+\beta|1\rangle$?

I do not know if the question is not too easy, but I'll put it here, because I'm interested in it. So the state of a qubit is often stated in this form: $$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$...
P_Gate's user avatar
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5 votes
2 answers
3k views

What does it mean to express a gate in Dirac notation?

When discussing the Dirac notation of an operator, for example, let's just say we have the bit flip gate $X$ if we want to write this in the Dirac notation does that just mean writing it as follows? $...
bhapi's user avatar
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