\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

python/numpy/fft_cheat.py

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

{wiki=List_of_unsolved_problems_in_mathematics}


Open problem in mathematics

https://math.stackexchange.com/questions/2382011/computational-complexity-of-modular-exponentiation-from-rosens-discrete-mathem mentions:
$$
b^n mod m
$$
can be calculated in:
$$
log(m)^2 log(n)
$$
Remember that $log(m)$ and $log(n)$ are the lengths in bits of $m$ and $n$, so in terms of the length in bits $M$ and $N$ we'd get:
$$
M^2 N
$$


Ciro Santilli @cirosantilli 40