# Syllabus

**Source**::**Instructor**:: *Sergey Sysoev*

# # Syllabus

- Introduction
- Why quantum computers are so powerful?
- Why is it so hard to implement them?

- The Origins of the Mathematical Model
- The Language of
*Quantum Mechanics* - Quantum Cryptography and Teleportation

# # Notes

In this course, we are going to focus more on the physical nature of a *quantum computer* instead of algorithms and mathematics.

- To create something as powerful as a quantum computer, we have to satisfy the following requirements:
- Continuum of states
- Satisfied by a Qubit.

- True randomness
- Interference
- To avoid unintended changes before interference, computing process must be:
- Fast
- Cold
- Isolated

- To avoid unintended changes before interference, computing process must be:

- Continuum of states
- The position of a particle in the space is connected to the notion of a wavefunction.
- The integral of the
*probability distribution*over the whole interval must be equal to one.- The integral of the squared wavefunction over the whole space must be finite.

- From the quantum mechanical point of view, the position of a particle is not an exact point in space. It is defined by the probability distribution, which itself is proportional to the square of the wave function of a particle.
- For any well-defined wave function $f$, multiplication of it by any scalar
*except zero*does not change its physical meaning, i.e., it would represent the same particle state. - A
*basis*is the set of vectors which generate the whole Vector Space.- It means that any vector from this space can be represented as some weighted sum of the basis vectors.
- There are infinite number of basis you can choose for the same space. But all of them share one important parameter. They’ll have the same number of elements. The number of elements of the vector space basis is called the
*dimensionality of the space*. - There are special basis which are called the
*orthonormal basis*. These are the basis in which elements (basis vectors) has the length of one and are mutually perpendicular to each other.

- The dimensionality of the vector space of square integrable functions is infinite.
- The set of possible outcomes which forms the basis in the wave function vector space and defines the characteristics of our measurement procedure is called an observable.

## # Week 4: The Language of Quantum Mechanics

*Inner product*