Quantum statistics

Enzyme inhibitor

Cleanroom

{c}
{wiki=Controlled_NOT_gate}

= Controlled NOT gate
{synonym}
{title2}

The <CNOT gate> is a <controlled quantum gate> that operates on two <qubits>, flipping the second (operand) <qubit> if the first (control) <qubit> is set.

This gate is the first example of a <controlled quantum gate> that you should study.

$$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0
\end{bmatrix}
$$
{title=<CNOT gate> <matrix>}

\Image[https://upload.wikimedia.org/wikipedia/commons/4/4e/CNOT_gate.svg]
{title=<CNOT gate> symbol}
{description=The symbol follow the generic symbol convention for <controlled quantum gates> shown at <image Generic controlled quantum gate symbol>, but replacing the generic "U" with the <image Quantum NOT gate symbol>.}

To understand why the gate is called a CNOT gate, you should think as follows.

First let's produce a generic <quantum state> vector where the control qubit is certain to be 0.

On the standard basis:
$$
\ket{00} \\
\ket{01} \\
\ket{10} \\
\ket{11} \\
$$
we see that this means that only $\ket{00}$ and $\ket{01}$ should be possible. Therefore, the state must be of the form:
$$
\begin{bmatrix}
x \\
y \\
0 \\
0
\end{bmatrix}
$$
where $x$ and $y$ are two <complex numbers> such that $|x| + |y| = 1.0$

If we operate the <CNOT gate> on that state, we obtain:
$$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0
\end{bmatrix}

\times

\begin{bmatrix}
x \\
y \\
0 \\
0
\end{bmatrix}

=

\begin{bmatrix}
x \\
y \\
0 \\
0
\end{bmatrix}
$$
and so the input is unchanged as desired, because the control qubit is 0.

If however we take only states where the control qubit is for sure 1:
$$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0
\end{bmatrix}

\times

\begin{bmatrix}
0 \\
0 \\
x \\
y
\end{bmatrix}

=

\begin{bmatrix}
0 \\
0 \\
y \\
x
\end{bmatrix}
$$

Therefore, in that case, what happened is that the probabilities of $\ket{10}$ and $\ket{11}$ were swapped from $x$ and $y$ to $y$ and $x$ respectively, which is exactly what the <quantum NOT gate> does.

So from this we understand more concretelly what "the gate only operates if the first <qubit> is set to one" means.

Now go and study the <Bell state> and understand intuitively how this gate is used to produce it.


CNOT gate

TODO. Can't find it easily. Anyone?

This is closely linked to the <Pauli exclusion principle>.

What does a particle even mean, right? Especially in <quantum field theory>, where two electrons are just vibrations of a single electron field.

Another issue is that if we consider <magnetism>, things only make sense if we add <special relativity>, since <Maxwell's equations require special relativity>, so a non approximate solution for this will necessarily require full <quantum electrodynamics>.

As mentioned at <david tong s 2009 quantum field theory lectures at the perimeter institute/lecture 1> https://youtube.com/watch?video=H3AFzbrqH68&t=555[], <special relativity>[relativistic] quantum mechanical theories like the <Dirac equation> and <Klein-Gordon equation> make no sense for a "single particle": they must imply that particles can pop in out of existence.

Bibliography:
* https://www.youtube.com/watch?v=Og13-bSF9kA&list=PLDfPUNusx1Eo60qx3Od2KLUL4b7VDPo9F "Advanced quantum theory" by <Tobias J. Osborne> says that the course will essentially cover multi-particle quantum mechanics!
* https://physics.stackexchange.com/questions/54854/equivalence-between-qft-and-many-particle-qm "Equivalence between QFT and many-particle QM"
* Course: Quantum Many-Body Physics in Condensed Matter by Luis Gregorio Dias (2020) from <course: Quantum Many-Body Physics in Condensed Matter by Luis Gregorio Dias (2020)> give a good introduction to non-interacting particles


Solutions of the Schrodinger equation for two electrons

Crystal

City in the Netherlands

{c}
{wiki}

= DNA fingerprinting
{c}
{synonym}


DNA profiling

L-Amino acid

{wiki}

They split up from the rest of the <mammals> after the <monotremes>.

Every other mammal has a <placenta>.

This baby in pouch thing just feels like a pre-<placenta> stage.


Marsupial

Calendar

Phenotype

Science communication

Cellular compartment

Electromagnetic spectrum

Mine

{disambiguate=genetics}

= Promoter
{synonym}

A <DNA> sequence that marks the start of a <transcription> area.


Promoter

{wiki}

An artificial <metabolic pathway>{parent} using <synthetic biology> technology.


Synthetic biological circuit

2D rigid body dynamics simulator

{c}
{title2=evil soccer player}
{wiki}

= 高俅
{synonym}
{title2}

The ball game is named <cuju>.

He is extremely despicable and petty, enjoys <art>[only useless things], and is vengeful and disloyal. <Rooting for sport teams is stupid>.

Surely his family name 俅 is a pun on the same sounding character 求 for ball.


Title	Author	Created	Updated
Quantum statistics	Ciro Santilli 32	1970-01-01	1970-01-01
Enzyme inhibitor	Ciro Santilli 32	1970-01-01	1970-01-01
Cleanroom	Ciro Santilli 32	1970-01-01	1970-01-01
CNOT gate	Ciro Santilli 32	1970-01-01	1970-01-01
Solutions of the Schrodinger equation for two electrons	Ciro Santilli 32	1970-01-01	1970-01-01
Crystal	Ciro Santilli 32	1970-01-01	1970-01-01
City in the Netherlands	Ciro Santilli 32	1970-01-01	1970-01-01
DNA profiling	Ciro Santilli 32	1970-01-01	1970-01-01
L-Amino acid	Ciro Santilli 32	1970-01-01	1970-01-01
Marsupial	Ciro Santilli 32	1970-01-01	1970-01-01
Calendar	Ciro Santilli 32	1970-01-01	1970-01-01
Phenotype	Ciro Santilli 32	1970-01-01	1970-01-01
Science communication	Ciro Santilli 32	1970-01-01	1970-01-01
Cellular compartment	Ciro Santilli 32	1970-01-01	1970-01-01
Electromagnetic spectrum	Ciro Santilli 32	1970-01-01	1970-01-01
Mine	Ciro Santilli 32	1970-01-01	1970-01-01
Promoter	Ciro Santilli 32	1970-01-01	1970-01-01
Synthetic biological circuit	Ciro Santilli 32	1970-01-01	1970-01-01
2D rigid body dynamics simulator	Ciro Santilli 32	1970-01-01	1970-01-01
Gao Qiu	Ciro Santilli 32	1970-01-01	1970-01-01

Ciro Santilli (@cirosantilli, 32)