A university program designed for people who wish to balance their professional responsibilities with a quality education” 

The development of Quantum Sciences will mean a breakthrough for human beings in practically all productive sectors. Thus, work is already underway to create quantum computers that allow transmitting information at higher speeds and in a secure manner. However, the potential of quantum computing goes beyond this, and its applications can be reflected in transportation management, in the creation of batteries with higher energy density, or in the creation of materials with a better strength-to-weight ratio. 

Engineering professionals are faced here with a challenge and a range of possibilities for innovation and progress of possibilities for innovation and the advancement of today's Industry 4.0: a favorable scenario for progress in a booming field, where companies are increasingly demanding highly qualified personnel. For this reason, TECH offers this Postgraduate diploma in Quantum Sciences, where in just 6 months the students will obtain the necessary learning to progress in their careers. 

A 100% online program, where students can delve into the main essential mathematical methods, to later delve more easily into quantum field theory and quantum computation. In addition, the multimedia teaching resources will provide greater dynamism to the content and facilitate the acquisition of knowledge. 

Thus, the engineering professionals can obtain a university qualification that is at the cutting edge, and which can be accessed easily, whenever and wherever they wish. The students only require a computer, tablet or cell phone with Internet connection to be able to access, at any time, the syllabus hosted on the virtual platform. Also, the Relearning method, will allow you to progress through this Postgraduate diploma in a much more agile way and reduce the long hours of study.  

 This is an excellent opportunity to advance in your professional career thanks to this Postgraduate diploma in Quantum Sciences. Enroll now”

This Postgraduate diploma in Quantum Sciences contains the most complete and up-to-date program on the market. The most important features include:

• Practical case studies are presented by experts in Physics 
• The graphic, schematic, and practical contents with which they are created, provide scientific and practical information on the disciplines that are essential for professional practice
• Practical exercises where the self-assessment process can be carried out to improve learning 
• Its special emphasis on innovative methodologies 
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments 
• Content that is accessible from any fixed or portable device with an Internet connection  

Enroll now in a university program that you can easily access from your computer or tablet with Internet connection"

The program includes, in its teaching staff, professionals from the sector who bring to this program the experience of their work, in addition to recognized specialists from prestigious reference societies and universities.

Its multimedia content, developed with the latest educational technology, will allow professionals to learn in professionals a situated and contextual learning, i.e., a simulated environment that will provide immersive education programmed to prepare in real situations.

The design of this program focuses on Problem-Based Learning, by means of which professionals must try to solve the different professional practice situations that arise during the academic course. For this purpose, students will be assisted by an innovative interactive video system developed by renowned experts.

Video summaries, detailed videos or essential readings will allow you to go deeper into the Klein-Gordon and Dirac theories"

Access the most relevant information on quantum theory of light-matter interaction at any time"

The syllabus of this program has been designed to offer the engineering professionals the most advanced knowledge on Quantum Sciences. For this reason, the specialized teaching team of this university program has designed a 3-module program that will allow to obtain a solid and essential learning in this field. Thus, delve into mathematical methods, students will delve into quantum field theory and quantum information and computation. The video summaries of each topic, the videos in detail or the case studies will allow to advance in a much more dynamic way through this online program. 

The case studies provided by specialists in quantum physics will allow you acquiring a closer knowledge of Quantum Science" 

Module 1. Mathematical Methods

1.1. Prehibertian Spaces

1.1.1. Vector Spaces
1.1.2. Positive Hermitian Scalar Product
1.1.3. Single Vector Module
1.1.4. Schwartz Inequality
1.1.5. Minkowsky Inequality
1.1.6. Orthogonality
1.1.7. Dirac Notation

1.2. Topology of Metric Spaces

1.2.1. Definition of Distance
1.2.2. Definition of Metric Space
1.2.3. Elements of Topology of Metric Spaces
1.2.4. Convergent Successions
1.2.5. Cauchy Successions
1.2.6. Complete Metric Space

1.3. Hilbert Spaces

1.3.1. Hilbert Spaces: Definition
1.3.2. Herbatian Base
1.3.3. Schrödinger vs. Heisenberg. Lebesgue Integral
1.3.4. Continuous Frames of a Hilbert Space
1.3.5. Change of Basis Matrix

1.4. Linear Operations

1.4.1. Linear Operators: Basic Concepts
1.4.2. Inverse Operator
1.4.3. Adjoint Operator
1.4.4. Self-Adjoint Operator
1.4.5. Positive Definite Operator
1.4.6. Unitary Operator I: Change of Basis
1.4.7. Antiunitary Operator
1.4.8. Projector

1.5. Stumr-Liouville Theory

1.5.1. Eigenvalue Theorem
1.5.2. Eigenvector Theorem
1.5.3. Sturm-Liouville Problem
1.5.4. Important Theorems for Sturm-Liouville Theory

1.6. Introduction to Group Theory

1.6.1. Definition of Group and Characteristics
1.6.2. Symmetries
1.6.3. Study of SO (3), SU(2) and SU(N) Groups
1.6.4. Lie Algebra
1.6.5. Groups I and Quantum Physics

1.7. Introduction to Representations

1.7.1. Definitions
1.7.2. Fundamental Representation
1.7.3. Adjoint Representation
1.7.4. Unitary Representation
1.7.5. Product of Representation
1.7.6. Young Tables
1.7.7. Okubo Theorems
1.7.8. Applications to Particle Physics

1.8. Introduction to Tensors

1.8.1. Definition of Covariant and Contravariant Tensors
1.8.2. Kronecker Delta
1.8.3. Levi-Civita Tensor
1.8.4. Study of SO(N) i SO (3)
1.8.5. Study of SO(N)
1.8.6. Relation between tensors and representations

1.9. Group Theory Applied to Physics

1.9.1. Translation Group
1.9.2. Lorentz Group
1.9.3. Discrete Groups
1.9.4. Continuous Groups

1.10. Representations and Particle Physics

1.10.1. Representations of SU(N) Groups
1.10.2. Fundamental Representations
1.10.3. Multiplication of Representations
1.10.4. Okubo Theorem and Eightfold Ways

Module 2. Quantum Field Theory

2.1. Classical Field Theory

2.1.1. Notation and Conventions
2.1.2. Lagrangian Formulation
2.1.3. Euler Lagrange Equations
2.1.4. Symmetries and Conservation Laws

2.2. Klein-Gordon Field

2.2.1. Klein-Gordon Equations
2.2.2. Klein-Gordon Field Quantization
2.2.3. Lorentz Invariance in theKlein-Gordon Field 
2.2.4. Vacuum Vacuum and Fock States
2.2.5. Vacuum Energy
2.2.6. Normal Arrangement: Agreement
2.2.7. Energy and Momentum of States
2.2.8. Study of Causality 
2.2.9. Klein-Gordon propagator

2.3. Dirac Field

2.3.1. Dirac Equation
2.3.2. Dirac Matrices and their Properties
2.3.3. Representation of Dirac Matrices
2.3.4. Dirac Lagrangian
2.3.5. Solution to Dirac Equation: Plane Waves
2.3.6. Commuting and Anticommuting
2.3.7. Quantification of Dirac Field
2.3.8. Fock Space
2.3.9. Dirac Propagator

2.4. Electromagnetic Field

2.4.1. Classical Field Electromagnetic Theory
2.4.2. Quantization of the Electromagnetic Field and its Problems
2.4.3. Fock Space
2.4.4. Gupta-Bleuler Formalism
2.4.5. Photon Propagator

2.5. S-Matrix Formalism

2.5.1. Lagrangian and Hamitonian of Interaction
2.5.2. S Matrix: Definition and Properties
2.5.3. Dyson Expansion
2.5.4. Wick Theorem
2.5.5. Dirac Picture

2.6. Feinman Diagrams in the Position Space

2.6.1. How to Draw Feynman Diagrams? Rules Utilities
2.6.2. First Order
2.6.3. Second Order
2.6.4. Dispersion Processes with Two Particles

2.7. Feynman Rules

2.7.1. Normalization of States in Fock Space
2.7.2. Feynman Amplitude
2.7.3. Feynman Rules for QED
2.7.4. Gauge Invariance in the Amplitudes
2.7.5. Examples

2.8. Cross Section and Decay Rates

2.8.1. Definition of Cross Sections
2.8.2. Definition of Decay Rate
2.8.3. Example with Two Bodies in Final State
2.8.4. Unpolarized Cross Section
2.8.5. Summation on Fermion Polarization
2.8.6. Summation on Photon Polarization
2.8.7. Examples

2.9. Study of Muons and Other Charged Particles

2.9.1. Muons
2.9.2. Charged Particles
2.9.3. Scalar Charged Particles
2.9.4. Feynman Rules for Scalar Quantum Electrodynamics Theory

2.10. Symmetries

2.10.1. Parity
2.10.2. Load Conjugation
2.10.3. Time Reversal
2.10.4. Violation of Some Symmetries
2.10.5. CPT Symmetry

Module 3. Information and Quantum Computing

3.1. Introduction: Mathematics and Quantum

3.1.1. Complex Vector Spaces
3.1.2. Linear Operators
3.1.3. Scalar Products and Hilbert Spaces
3.1.4. Diagonalization
3.1.5. Tensor Product
3.1.6. The Role of Operators
3.1.7. Important Theorems on Operators
3.1.8. Checked Quantum Mechanics Postulates

3.2. Statistical States and Samples

3.2.1. The Qubit
3.2.2. Density Matrix
3.2.3. Two-Part System
3.2.4. Schmidt Decomposition
3.2.5. Statistical Interpretation of the Mixing States

3.3. Measurements and Temporary Evolution

3.3.1. Von Neumann Measurements
3.3.2. Generalized Measurements
3.3.3. Neumark Theorem
3.3.4. Quantum Channels

3.4. Interwoven and its Applications

3.4.1. ERP States
3.4.2. Dense Coding
3.4.3. State Teleportation
3.4.4. Density Matrix and its Representations

3.5. Classic and Quantum Information

3.5.1. Introduction to Probability
3.5.2. Information
3.5.3. Shannon Entropy and Mutual Information
3.5.4. Communication

3.5.4.1. The Bynary Symmettric Channel
3.5.4.2. Channel Capacity

3.5.5. Shannon Theorems
3.5.6. Difference between Classic and Quantum Information
3.5.7. Von Neumann Entropy
3.5.8. Schumacher Theorem
3.5.9. Holevo Information
3.5.10. Accessible Information and Holevo Limit

3.6. Quantum Computing

3.6.1. Turing Machines
3.6.2. Circuits and Classification of Complexity
3.6.3. Quantum Computer
3.6.4. Quantum Logic Gates
3.6.5. Deutsch-Josza and Simon´s Algorithm
3.6.6. Unstructured Search; Grover´s Algorithm
3.6.7. RSA Encryption Method
3.6.8. Factorizatión: Shor Algorithm

3.7. Quantum Theory of the Light-Matter Interaction

3.7.1. Two-Level Atom
3.7.2. AC-Stark Splitting
3.7.3. Rabi Oscillations
3.7.4. Light dipole force

3.8. Quantum Theory of the Light-Matter Interaction

3.8.1. Quantum States of the Electromagnetic Field
3.8.2. Jaynes-Cummings Model
3.8.3. The Problem of Decoherence
3.8.4. Treatment of Weisskopf-Wigner Model of Spontaneous Emission

3.9. Quantum Communication

3.9.1. Quantum Cryptography: BB84 and Ekert91 protocols
3.9.2. Bell Inequalities
3.9.3. Generation of Individual Photons
3.9.4. Propagation of Individual Photons
3.9.5. Detection of Individual Photons

3.10. Quantum Computing and Simulation

3.10.1. Neutral Atoms in Dipolar Traps
3.10.2. Cavity Quantum Electrodynamics
3.10.3. Ions in Paul Tramps
3.10.4. Superconducting Cubits

A 100% online program that will allow you to delve, through multimedia resources, into the latest developments in quantum cryptography"