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

When we talk about quantum computers, we usually mean fault-tolerant devices. These will be able to run Shor's algorithm for factoring, as well as all the other algorithms that have been developed ...
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34 votes
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What exactly is an oracle?

An oracle (at least in this context) is simply an operation that has some property that you don't know, and are trying to find out. The term "black box" is used equivalently, to convey the idea that ...
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  • 46.2k
24 votes
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What is postselection in quantum computing?

"Postselection" refers to the process of conditioning on the outcome of a measurement on some other qubit. (This is something that you can think of for classical probability distributions and ...
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23 votes
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Significance of The Church of the Higher Hilbert space

The church of the larger (or higher, or greater) Hilbert space is just a trick that some people like (myself included) for rewriting some operations. The most general operations that you can write ...
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  • 46.2k
21 votes

What is 'Surface Code'? (Quantum Error Correction)

The terminology of 'surface code' is a little bit variable. It might refer to a whole class of things, variants of the Toric code on different lattices, or it might refer to the Planar code, the ...
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  • 46.2k
18 votes
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What is 'Surface Code'? (Quantum Error Correction)

The surface codes are a family of quantum error correcting codes defined on a 2D lattice of qubits. Each code within this family has stabilizers that are defined equivalently in the bulk, but differ ...
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14 votes
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What's the difference between T1 and T2?

T2 is so-called dephasing time. It describes how long the phase of a qubit stays intact. In your words, it is time from $|+\rangle= \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ to $|-\rangle= \frac{1}{\...
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14 votes

What's the difference between T1 and T2?

Slight correction to Martin Vesely's answer: $T_2$ is not the (decay constant) time after which an initial state $|+\rangle$ will necessarily switch to the state $|-\rangle$. If it were, then error ...
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  • 2,057
13 votes

What is meant by the term "computational basis"?

Quantum computing deals (mostly) with finite-dimensional quantum systems called qubits. If you know basic quantum mechanics then you know that the Hilbert space of a qubit is $\mathbb{C}^2$, i.e., the ...
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12 votes
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What is the difference between a qubit and a quantum state?

There are a few things to distinguish here, which are often conflated by experts because we're using these terms quickly and informally to convey intuitions rather than in the way that would be most ...
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12 votes
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Is qsphere an actual term representing 5 qubits?

The qsphere is a way of representing multi-qubit states. So it could be used for 5 qubit states, but it could also be used for any other number. It could also be used for just one qubit. But in this ...
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11 votes
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What is the difference between "code space", "code word" and "stabilizer code"?

Code spaces and code-words A quantum error correcting code is often identified with the code-space (Nielsen & Chuang certainly seem to do so). The code space $\mathcal C$ of e.g. an $n$-...
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11 votes

What is a flying qubit?

Preliminary - The DiVincenzo criteria for a 'normal' quantum computer The DiVincenzo criteria, as originally proposed by DiVincenzo, are $5$ criteria that he originally proposed in his seminal 2000 ...
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10 votes

What is postselection in quantum computing?

As the other answer conveyed (and to which I am just trying to provide some clarification), post-selection is about just looking at a subset of possible measurement outcomes. To my mind, this falls ...
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  • 46.2k
10 votes

What is meant by the term "computational basis"?

The "computational basis" is just a basis that is "most natural" in a given context, and is conventionally denoted with $|0\rangle$ and $|1\rangle$ in the case of qubits. To give a ...
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10 votes
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What is a "maximally mixed state"?

The maximally mixed state is a quantum state whose density matrix is proportional to the identity matrix. Physically, it may be interpreted as a uniform mixture of states in an orthonormal basis. The ...
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9 votes

Is there any difference between "value of a qubit" and its "state"?

I'm not aware of any widespread technical distinction between the "value" and "state" of qubits. I'd expect any paper or textbook or presentation using such a distinction to define ...
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8 votes
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What counts as an "ancilla" qubit?

The general meaning of ancilla in ancilla qubit is auxiliary. In particular, when people write about "constant input" what they mean is that, for a given algorithm -which has a purpose, such as ...
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  • 3,587
8 votes
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What exacty is "matrix sparsity" $s$?

You have the definitions in your paper you link page 12. Simply said, it is a matrix with many 0s. As an example take N = 16, and the polynomial function is just a simple function like 1.5*X, then ...
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  • 4,554
7 votes

Significance of The Church of the Higher Hilbert space

"Church of the higher hilbert space" is a term coined by John Smolin. According to quantiki it is: for the dilation constructions of channels and states, which [...] provide a neat characterization ...
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  • 3,281
7 votes
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What is meant by the term "computational basis"?

When we have just one qubit, there's nothing particularly special about the computational basis; it's just nice to have a canonical basis. In practice you could think that first you implement a gate $...
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7 votes
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When was the first use of the word Entanglement?

I managed to get access to the paper mentioned in the question. Schrödinger in 1935 (the same year the original EPR paper was published) wrote in English: "By the interaction the two representatives (...
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7 votes

Do any specific types of qudits other than qubits and qutrits have a name?

There is no standard name for a qudit for $d>3$. The community has mostly settled on the term qudit (but you will still find qunit or quNit, for example, using $n$ or $N$ instead of $d$ in some ...
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  • 46.2k
7 votes

What is quantum computing vs. what is not quantum computing

The difficulty with explaining quantum computing is that quantum objects and processes have no direct classical analogue; they're an entirely new ontological category. For example, you might have ...
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  • 3,888
7 votes
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What does fidelity mean?

It might be worth mentioning the physical motivation for these definitions and the concept of fidelity itself. Unlike the classical computers we all know and love, quantum computers are ...
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  • 186
7 votes
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Significance of the term "diffusion" in Grover's diffusion operator

I had forwarded this question to Dr. Lov Grover and received the following response. I guess inversion about average is a better name for the $\mathrm{W}\mathbb I_0\mathrm{W}$ transformation. When I ...
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7 votes
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How is a promise gap related to a spectral gap?

The spectral gap is pretty much independent of the promise gap. (First off, my feeling is that "promise gap" is a little bit misleading, though formally correct: What it really refers to, in ...
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6 votes

'Rectilinear' and 'Diagonal' Basis in BB84 Protocol

Talking about bases such as $\left|0\rangle\langle0\right|$ and $\left|1\rangle\langle1\right|$ (or the equivalent vector notation $\left|0\right>$ and $\left|1\right>$, which I'll use in this ...
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  • 3,397
6 votes

Is qsphere an actual term representing 5 qubits?

Is qsphere an actual term representing 5 qubits? If it is, it is not widely used. I claim this because I looked around in arXiv, a repository of electronic preprints of research articles, and found ...
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