47
votes
Accepted
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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37
votes
Accepted
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 ...
- 54.5k
29
votes
Accepted
What is the "surface code" in the context of 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 ...
- 11.1k
28
votes
What is the "surface code" in the context of 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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24
votes
Accepted
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 ...
- 54.5k
24
votes
Accepted
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 ...
- 11.7k
23
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 ...
- 2,561
19
votes
Accepted
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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16
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 ...
- 1,803
13
votes
Accepted
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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12
votes
Accepted
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
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 ...
- 54.5k
12
votes
Accepted
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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12
votes
Accepted
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 ...
- 20k
11
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 ...
glS♦
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11
votes
Accepted
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 ...
- 356
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 ...
- 5,289
9
votes
Accepted
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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9
votes
Accepted
What is the difference between relaxation, dephasing, and decoherence?
Decoherence is the very general term which, more or less, is anything resulting in a loss of purity during the evolution of a system. Sometimes, when people are being a bit non-specific, they might ...
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9
votes
Accepted
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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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 ...
- 32.5k
9
votes
What is (formally) a transversal operator?
Based on informal conversations: there is no actually agreed upon definition of a transversal operator. People use it to mean different things. Typically it refers to either the operation being fast ...
- 32.5k
8
votes
Accepted
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 ...
- 3,747
8
votes
What does "measurement in a certain basis" mean?
Qubits are essentially quantum objects from which you can extract a bit. But there are different ways that this can be done, and the answer you get depends on the measurement you choose.
If you qubit ...
- 11.1k
8
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 ...
- 3,379
8
votes
Accepted
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 $...
- 369
8
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 ...
- 54.5k
8
votes
Accepted
What exactly 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 ...
- 4,644
8
votes
Clifford gates are transversal What exactly does this transversal mean? What is the difference between non-Clifford gates and Clifford gates?
Transversal and Clifford are not as closely linked as your question would seem to imply.
Transversal gates are those for which an error-correcting code can achieve the transformation on a logical ...
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