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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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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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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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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
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
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
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 ...
user avatar
53 votes
2 answers
20k views

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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23 votes
2 answers
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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 ...
peachnuts's user avatar
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21 votes
6 answers
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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 ...
Adrien Suau's user avatar
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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
1 answer
368 views

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
9 votes
2 answers
448 views

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
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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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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3 votes
1 answer
3k views

How to translate the Hadamard gate matrix into Dirac notation?

Hadamard gate matrix is: $$\frac{1}{\sqrt 2}\begin{bmatrix}1 && 1 \\ 1 && -1\end{bmatrix}$$ The Dirac notation for it is: $$\frac{|0\rangle+|1\rangle}{\sqrt 2}\langle0|+\frac{|0\...
Kumar's user avatar
  • 219
3 votes
1 answer
2k views

What is the meaning of writing a state in its Bloch representation?

What is the meaning of writing a state $|\psi\rangle$ in its Bloch representation. Would I be correct in saying it's just writing out its Bloch vector?
bhapi'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
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
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
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
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
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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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
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
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
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
5 votes
1 answer
3k views

What is the difference between signaling and non-signaling quantum correlations, and what is a signaling channel?

This article talks about correlation and causality in quantum mechanics. In the abstract, under Framework for local quantum mechanics, it says (emphasis mine): The most studied, almost epitomical, ...
fr_andres's user avatar
  • 754
4 votes
1 answer
3k views

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 ?
Vinay Sharma's user avatar
4 votes
2 answers
357 views

What is the relation between observables (as defined in the measure-theoretic framework) and POVMs?

A POVM is typically defined as a collection of operators $\{\mu(a)\}_{a\in\Sigma}$ with $\mu(a)\in\mathrm{Pos}(\mathcal X)$ positive operators such that $\sum_{a\in\Sigma}\mu(a)=I$, where I take here $...
glS's user avatar
  • 25k
4 votes
1 answer
132 views

What mathematical object is the set of quantum states of a qudit? How should one write this?

It is tempting to write $|\psi\rangle \in \mathbb{C}^d$ for a qudit state, but this isn't very precise because of global phases. What's a better notation for the set of states of a qudit?
shashvat's user avatar
  • 805
4 votes
1 answer
412 views

Difference between change of basis in bra-ket notation and matrix notation

In matrix notation, say I have the vector $\begin{bmatrix} 1 \\ 0 \end{bmatrix}$. It is currently represented in the computational basis $\{\begin{bmatrix} 1 \\ 0\end{bmatrix}, \begin{bmatrix} 0 \\ 1\...
Mahathi Vempati's user avatar
4 votes
2 answers
948 views

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 ...
El-Mo's user avatar
  • 103
3 votes
2 answers
198 views

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 ...
Marco Fellous-Asiani's user avatar
3 votes
1 answer
278 views

Notation question: How would one read $|0\rangle (|0\rangle+|0\rangle)$?

For example in Deutsch's Algorithm, we apply $H$ to $|0\rangle$ and $|1\rangle$ respectively. I have seen the notation this result in the state: $$\frac{1}{2}(|0\rangle+|1\rangle)(|0\rangle-|1\rangle)$...
csstundent's user avatar
3 votes
1 answer
530 views

What is the "phase" of a state in terms of the Bloch sphere?

I am pretty new to Quantum Computing and am not exactly sure what the phase is. Could you please explain in terms of the Bloch sphere and point out how to mathematically calculate and represent the ...
abhobe's user avatar
  • 73
2 votes
4 answers
774 views

What is the name for quantum gates that can be reversed?

Sorry if this question sounds too basic. But I can't find a word for those quantum gates than can be reversed (exchanging the target qubit with the control qubit) and still performs the same operation....
Alex's user avatar
  • 183
2 votes
1 answer
341 views

Circuit construction and Dirac notation of the following operation

I have a state $$ |\tilde{\Phi_2}\rangle =\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |x\rangle^{\otimes l}\otimes |y\rangle^{\otimes l}\...
Upstart's user avatar
  • 1,420
2 votes
1 answer
270 views

What is the "quantum phase" of a quantum state?

On this page IMBQ docs, until the sentence '..and since the global phase of a quantum state is not detectable..' I follow everything. However 'quantum phase' is introduced without any explaination? ...
Tim's user avatar
  • 21
2 votes
1 answer
140 views

How does this expression from the VQLS paper result in a CZ-gate?

I am reading the VQLS paper and equation C2 on page 10 they have: $ \delta_{ll'}^j = \beta_{ll'} + \langle0|V^\dagger A_{l'}^\dagger U(Z_j \otimes I_\bar{j}) U^\dagger A_lV|0\rangle $ Here they define ...
thespaceman's user avatar
1 vote
1 answer
105 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\...
Upstart's user avatar
  • 1,420
1 vote
1 answer
153 views

How does the graphical notation used to denote doubly-controlled gates work?

$\qquad$ $\qquad$ What is the difference between solid and hollow? How to express the corresponding matrix of these figures? In addition, if they are not adjacent, what should be done in the middle of ...
Despriobaby's user avatar
0 votes
2 answers
74 views

Why are slice states called so?

The "slice" states are defined by equation 50 in this (freely available) article. I wonder why they call them so!
User101's user avatar
  • 598