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【Two characteristics of quantum computers to keep in mind】

Designed according
to the rules of quantum mechanics

There are two main rules

・Various calculation processes
　can be "superimposed"

・Measurement results
　are obtained "probabilistically"

【Measurement in quantum mechanics】

In quantum physics,
measurement is the testing
or manipulation
of a physical system
to yield a numerical result.

The predictions that
quantum physics makes are
in general probabilistic.

【Quantum error correction】

Quantum error correction (QEC) is
used in quantum computing
to protect quantum information
from errors due to decoherence
and other quantum noise.

Quantum error correction is essential
if one is to achieve fault-tolerant
quantum computation.

【Logical equivalence】

In logic and mathematics,
statements p and q
are said to be logically equivalent
if they have the same truth value
in every model

The logical equivalence of p and q
is sometimes expressed
as p 三 q, p::q or p <==> q,
depending the on notation being used

【Quantum Classical Logic】

In the late nineteenth century George Boole
realized that certain parts of logic
could be treated algebraically-that there were laws
of logic that could be expressed in terms of algebra

We adopt the now standard way of introducing
boolean logic.

【Using the CNOT Gate to Entangle Qubits】

The controlled NOT gate (also C-NOT or CNOT) is
a quantum logic gate that is an essential component
in the construction of a gate-based quantum computer.

It can be used to entangle and disentangle Bell states.

【Orthonormal Bases】

The word "Orthonormal" has two parts,

Ortho from orthogonal, and normal from normalized which

in this instance, means unit.

If we are working with two-dimensional kets,
an orthonormal basis will consist of a set of n unit kets
that are mutually.

【Bra-kets and Orthogonality】

The key result is:

Two kets |a> and |b> are orthogonal
if and only if <a|b> = 0.

They're couple.

And, we can say crealy

This number equals ||a>^2 + ||b>^2
if and only if 2<a|b> = 0.

【Shor's algorithm】

Shor's algorithm is
a polynomial-time quantum computer algorithm for integer factorization. Informally,

it solves the following problem:
Given an integer, find its prime factors.

It was discovered in 1994 by the American mathematician Peter Shor.

【Quantum Decoherence】

This usually means isolating the system
from its environment as interactions
with the external world cause
the system to decohere.

Other sources of decoherence also exist.

Examples
- include the quantum gate
- the lattice vibrations
- background