Let a bit aa be an Element of either 0 or 1

a∈{0,1}a\in\{0,1\}

Let a system be nn bits represented in a String. This is also known as the state

z∈{0,1}nz\in \{0,1\}^n

A model of computation for Classical Computer and Quantum Computer

We can think of circuits as functions.

Let there be a circuit ff. It accepts a Variable zinz_{in} and outputs a variable zoutz_{out}

zout=f(zin)z_{out}=f(z_{in})

Gates

What can ff be?

NOT GATE

NOT(a)=1−aNOT(a) = 1 - a

NAND GATE

NAND(a,b)=1−abNAND(a,b) = 1-ab

TYPICAL GATE

f(z1,z2,...)=zoutf(z_1, z_2, ...)=z_{out}