## Quantum Information Science

There are various different theoretical fields of conventional information science: theory of computation, information theory, cryptography, logical circuit, formal language, operation system, network communication, artificial intelligence, ...etc. All these fields share the same assumption that behavior of hardware can be explained by the classical mechanics. On the other hand, development of nano technology makes semiconductor devices smaller and smaller. Nowadays, the size of physical areas on chip which represents a single bit can be 10 nano meter, which may consists of just a hundred of atoms. On this scale, physics can not be explained only by classical mechanics. In order to understand the physics on such scale, we need quantum mechanics, which is physics for microscopic systems like atoms, molecules and photons.

As long as we use conventional theory of information science, quantumness of such small devices may merely be considered as noise, because conventional theory assumes that the devices do not have quantumness. On the other hand, if we rebuild theory of information science which assumes that devices are governed by quantum mechanics, we may use quantumness of the devices for making a new information processing which never be developed on conventional information science. Actually, quantum information science is the new field of information science which remakes theory of information science based on quantum mechanics aimed at developing groundbreaking software by utilizing quantumness of hardware.

In this 20 years, various different quantum information processing protocols are developed. They are represented by quantum algorithms, which is algorithm utilizing quantumness of hardware and should be run on quantum computers, and quantum cryptography, which is cryptography utilizing quantumness of hardware, and may be implemented without quantum computers

## Quantum Mechanics

Quantum mechanics is physics for microscopic systems like atoms and molecule, photons, and electron. Quantum mechanics is developed in 1920's, and is foundation for most of modern physical theories and experiments: quantum mechanics is essential to understand not only microscopic systems, but also more large systems like biological systems, stars and the universe. Quantum mechanics contributed to modern information technology: semiconductor devices on PC and optical communication using laser are never understood without quantum mechanics.

Classical mechanics gives deterministic description of
physical systems. For example, if initial position and velocity
of a particle is given, we can completely determine its future
evolution in principle; that is, we can calculate the position
and velocity at time t=t_{1} from the position and
velocity at time t=0. In general, the future can be predicted
with a unit probability by classical mechanics when we know all
information about the present world. On the other hand, quantum
mechanics does not give description of physical system in such a
way. That is, Even though we know all the information of a given
physical system at t=0, we can only predict the probability in
which particular outcome of measurements occurs at the different
points at the future. For example, we can only predict the
probability in which a particular value of velocity is observed
by measuring a particle at time t. Historically, because of this
non-deterministic property, Albert Einstein did not accept
quantum mechanics as a *complete theory of physical systems*.
However, from various different experiments performed in this
100 years, quantum mechanics has been certified with great
accuracy.