48 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 ...
James Wootton's user avatar
38 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 ...
DaftWullie's user avatar
  • 57.1k
30 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 ...
James Wootton's user avatar
28 votes
Accepted

How does bra-ket notation work?

As already explained by others, a ket $\left|\psi\right>$ is just a vector. A bra $\left<\psi\right|$ is the Hermitian conjugate of the vector. You can multiply a vector with a number in the ...
Sir Cornflakes's user avatar
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 ...
DaftWullie's user avatar
  • 57.1k
26 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 ...
tparker's user avatar
  • 2,691
25 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 ...
Niel de Beaudrap's user avatar
25 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 ...
DaftWullie's user avatar
  • 57.1k
23 votes

How does bra-ket notation work?

You could think of $|0\rangle$ and $|1\rangle$ as two orthonormal basis states (represented by "ket"s) of a quantum bit which resides in a two dimensional complex vector space. The lines and brackets ...
Sanchayan Dutta's user avatar
22 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}{\...
Martin Vesely's user avatar
19 votes

How does bra-ket notation work?

What do all of these brackets and vertical lines mean? The notation $\left \lvert v \right \rangle$ means exactly the same thing as $\vec{v}$ or $\textbf{v}$, i.e. it denotes a vector whose name is "...
DanielSank's user avatar
  • 1,193
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 ...
keisuke.akira's user avatar
16 votes

How does bra-ket notation work?

The ket notation $|\psi\rangle$ means a vector in whatever vector space we're working in, such as the space of all complex linear combinations of the eight 3-bit strings $000$, $001$, $010$, etc., as ...
Squeamish Ossifrage's user avatar
14 votes

How does bra-ket notation work?

This leads me to conclude that there is some difference/reason why bra-ket is especially handy for denoting quantum algorithms. There's already an accepted answer and an answer that explains 'ket', '...
snulty's user avatar
  • 591
14 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 ...
Adam Zalcman's user avatar
  • 21.7k
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 $n$-...
Niel de Beaudrap's user avatar
13 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 ...
DaftWullie's user avatar
  • 57.1k
13 votes
Accepted

What does "bipartite" mean?

What does a bipartite system mean? I'll summarize the main definitions below (adapted from Quantiki). Bipartite system and states: If Alice's subsystem is described by the Hilbert space $\mathcal{H}...
Sanchayan Dutta's user avatar
13 votes
Accepted

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

One way of looking at the relationship between POVMs and observables arises from identifying their counterparts in the theory of probability of which quantum mechanics can be thought of as an ...
Adam Zalcman's user avatar
  • 21.7k
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 ...
James Wootton's user avatar
12 votes
Accepted

What do double wires mean in quantum circuits, and how do they relate to if statements?

The double lines are one common convention for classical bits in quantum circuit diagrams. In this case, they represent the bits arising from the measurements of the qubits ...
Niel de Beaudrap's user avatar
12 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's user avatar
  • 24.1k
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 ...
Niel de Beaudrap's user avatar
12 votes
Accepted

What is the meaning of the state $|1\rangle-|1\rangle$?

The second approach is to take the state after the CNOT $|11\rangle-|10\rangle$ and just as I did with the CNOT I would apply $\operatorname{H}$ gate only on the first qubit which is $|1\rangle-|1\...
Sanchayan Dutta's user avatar
12 votes
Accepted

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

Your understanding is correct. $\langle a | b \rangle$ is shorthand for $\langle a||b\rangle$. Here is a good resource for linear algebra and Dirac notation for quantum computing.
epelaez's user avatar
  • 2,875
11 votes
Accepted

How to compute the average value $\langle X_1 Z_2\rangle$ for a two-qubit system?

I suggest two different ways of trying to solve this, which will give you experience of different bits of the formulation of Quantum Information Theory. I'll give examples that are closely related to ...
DaftWullie's user avatar
  • 57.1k
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 ...
MMK1137's user avatar
  • 366
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 ...
JSdJ's user avatar
  • 5,409
10 votes
Accepted

What does quantum error correction code notation stand for?

An $[\![n,k,d]\!]$ code is a quantum error correction code which encodes $ k$ qubits in an $ n$-qubit state, in such a way that any operation which maps some encoded state to another encoded state ...
Niel de Beaudrap's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible