Pauli gate

{wiki=Quantum_logic_gate\#Controlled_gates}

<Controlled quantum gates> are gates that have two types of input qubits:
* control <qubits>
* operand <qubits> (terminology made up by <Ciro Santilli> just now)
These gates can be understood as doing a certain <unitary operation> only if the control qubits are enabled or disabled.

The first example to look at is the <CNOT gate>.

\Image[https://upload.wikimedia.org/wikipedia/commons/d/dc/Controlled_gate.svg]
{title=Generic <controlled quantum gate> symbol}
{description=
The black dot means "control qubit", and "U" means an arbitrary <Unitary operation>.

When the operand has a conventional symbol, e.g. the <image Quantum NOT gate symbol> for the <quantum NOT gate> to form the <CNOT gate>, that symbol is used in the operand instead. 
}


Controlled quantum gate

Evening raga

\Video[https://www.youtube.com/watch?v=jPIl2G88w_A]
{title=Raag Puriya Dhanashri performed on the <Sitar> by Shahid Parvez}


Puriya

Ungulate subclade

Information Engineering group of the University of Oxford

{c}
{wiki=Quantum_logic_gate\#Hadamard_gate}

The <Hadamard gate> takes $\ket{0}$ or $\ket{1}$ (<quantum states> with probability 1.0 of measuring either 0 or 1), and produces states that have equal probability of 0 or 1.

$$
H = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}
$$
{title=<Hadamard gate> <matrix>}

\Image[https://upload.wikimedia.org/wikipedia/commons/1/1a/Hadamard_gate.svg]
{title=<Hadamard gate> symbol}


Hadamard gate

Some authors use the convention of:
* filled black circle: conventional <controlled quantum gate>, i.e. operate if control qubit is active
* empty (White) circle: operate if control qubit is inactive


Empty circle control qubit notation

Alps

Raga

Raga by time of the day

Ustad

Ungulate

Area of mathematics

Recreational mathematics

Additive number theory

Additive basis

{disambiguate=mathematics}

A <theorem> that is not very important on its own, often an intermediate step to proving something that the author feels deserves the name "<theorem>".


Lemma

Lemma (mathematics)

Additive basis theorem

Ciro Santilli @cirosantilli 40