Fundamentals of quantum information

Learning outcomes:
-Offer the students a general overview of the quantum theory of information. The students must be able to:
-Know the mathematical formalism that underlies quantum mechanics
-To understand the formal issues that are addressed in the classical theory of information.
-To understand the operation of elementary quantum circuits and be able to execute some simple cases in a simulator or in a quantum computer.
- Understand the basic concepts that are used in communication theory.
- Know safe quantum compression and encryption protocols.
-To understand and model the physical limitations inherent in a generic implementation (decoherence, quantum error correction, etc.).
-To know the state of the technologies that compete to implement computing (IBM, Dwave, Microsoft, ...) and quantum communications.

1 Formalism of Quantum Mechanics
Axioms, States and operators. States pure and mix. Measurements Density operator. Fidelity. Tensor product and multipartite states. Interlacing and decomposition of Schmidt. Partial trace and purification.

2-Qubits
Sphere of Bloch. Manipulation of qubits. Correlations, Bell inequality and GHZ inequality.

3-Quantum computing
Reversibility. Elementary doors. Quantum parallelism Algorithms of Deutsh and Grover. Quantum Fourier Transform Period of a function. Phase estimation. Algorithm of Shor. Principles of adiabatic computing. Classic simulation programs.

4-Quantum communication
Non-cloning theorem. Simple applications: dense coding, teleportation. Secret communication: private and public keys.

5-Quantum information
Entropies of Shannon and von Neumann. Entrophies combined. Data compression. Open quantum systems. Noisy channels. Decoherence Quantum correction of errors.

-M. Nielsen, I. Chuang, Quantum Computation and Quantum information, Cambridge
University Press, 2000.
-M. Le Bellac, A short introduction to quantum information and quantum computation,
Cambridge University Press, 2006.
-M. Nakahara, T. Ohmi, Quantum Computing, CRC Press, 2008.
-G. Benenti, G. Casati, G. Strini, Principles of quantum computation and information, World
Scientific 2004.

In this subject the student will acquire and practice a series of basic competences, desirable.
in any basic degree, and specific competences in the field of quantum information theory. Among the specific competencies, it is worth noting:

- Perform simple calculations of quantum logic circuits.
- Understand the place of quantum computing in the current field of information technologies.
- Program simple quantum algorithms in a classic Python simulator.
- Be able to send processes to the IBM Quantum Experience.
- Understand the concept of quantum simulation, and the one of adiabatic quantum computation.

Class hours will be given according to the official Master's calendar, which will be taught.
They will explain, using all the audiovisual media of which they may be available, the
Contents of the subject, introducing exercises and illustrative problems of said contents.

It will be provided to students by providing a material that covers both the
Development of theoretical contents as statements of exercises and problems. They will exist
Self-assessment tests with which the student can supervise self-development.
learning At the same time, the corresponding tutoring hours will be available.

The Virtual Campus of the USC will be used. In order to be able to be used, English will be used as a vehicle language.

Scenarios 2 and/or 3: see contingency plan in section Observations

The course will be imparted preferably in spanish, but it can be taught in english if needed by any participant.

The evaluation of the subject will basically consist of the continuous evaluation in
It has the following aspects:

Attendance to classes and realization of exercises 60%.
Presentation of specific projects or projects. 40%

The subject consists of 3 ECTS, which means that the total number of hours of work of the student, including the evaluation activities, is 75 hours, structured in:

- 20 hours of expositive class.
- 10 hours of interactive class.
- 1 hour of tutoring.
- 44 hours of personal work of the student.

No prior knowledge is required beyond the one acquired in the regular courses of the Degree in Physics.