Master in Quantum Computing

For profiles with no prior knowledge or less familiarity with the Python programming language, this leveling prework provides the foundations you need to begin this master. You will learn this language and practice with dynamic, self-correcting hands-on material, with access to the IT Specialist Python certification (ITS-303).

Introduction to programming Introduction to Python Data types Variables Basic input and output operations Basic operators Boolean values Conditional execution

Loops Lists Bitwise operations Lists Functions Tuples and dictionaries Exceptions

This topic presents the fundamentals of quantum computing and how it differs from classical computing, introducing essential concepts such as qubits, superposition and entanglement, along with their disruptive applications and current challenges.

Classical vs. quantum computing The concept of the qubit and fundamental phenomena (superposition, entanglement) Examples of potential applications: cryptography, simulation, AI Current technological limitations and challenges

Quantum vs. classical parallel computing Quantum computing in the cloud Impact on industry and society Practical case: basic simulation with Qiskit

This topic reviews the mathematical framework needed to understand quantum computing systems, focusing on linear algebra, bra-ket notation and operators in Hilbert spaces.  The goal is to give the student the mathematical tools required to model, analyze and apply the fundamental concepts of quantum computing.

Essential linear algebra for quantum computing Hilbert spaces and column vectors Bra-ket notation and its interpretation Tensor product of qubits and joint operations

Linear operators and unitary matrices Orthogonality, norm and transformation Hermitian operators and projection Practical case: representing qubits in code

This topic teaches the essential foundations of quantum mechanics needed to understand how quantum computing works. It shows how principles such as superposition, entanglement and quantum measurement translate into unique computational behaviors. The goal is not a complete physics education, but an operational, applied understanding of the key concepts from a computational perspective.

Basic principles applied to computing Quantum computing states and wave functions Unitary evolution and reversibility Superposition and quantum measurement Entanglement as a computational resource

State collapse and observables Postulates and interpretations Practical case: visualizing states and collapses with Qiskit

This topic introduces the student to the current ecosystem for programming quantum solutions, with particular emphasis on its main frameworks such as Qiskit, Cirq and Amazon Braket. It explores their features, functionalities and use cases, as well as how they make it possible to simulate, visualize and run quantum computing algorithms in both local and cloud environments. Through a hands-on approach, the student will take their first steps in building circuits and programming basic operations on qubits.

Most widely used languages and frameworks Introduction to Qiskit, Cirq and Braket Comparison of syntax and functions Simulation vs. real hardware

Installation and initial execution Basic circuits in Qiskit Visualizing states and measurements Practical case: your first circuit in Qiskit

This topic introduces how information is represented and transformed in quantum computing through gates and operations on qubits. The frameworks covered in the previous topic will also be used to implement quantum gates.

The qubit as the fundamental unit of information Basis states |0⟩, |1⟩ and linear combinations Unitary matrices and operations on qubits Basic quantum gates: X, H, Z

The CNOT gate and controlled operations Composing gates into circuits Physical implication of each operation Programming quantum gates in Qiskit and Cirq

This topic teaches how to design and analyze quantum circuits by combining multiple qubits and quantum gates. It shows how to represent these circuits visually, understand the flow of qubits and how the sequence of operations affects the final state of the system. It also covers the measurement process and how it influences the computational result. The goal is for the student to be able to build and simulate basic circuits that form the basis of quantum computing algorithms.

Visual and logical design of quantum circuits Information flow between qubits Gate sequencing and cumulative effects Entanglement across circuits Measurement and collapse at runtime

Interpreting outputs and probabilities Simulation of real circuits Practical case: programming and simulating simple circuits

This topic covers the first algorithms and fundamental phenomena of quantum computing, which laid the groundwork for the field. Through paradigmatic examples such as quantum teleportation, superdense coding and Deutsch's algorithm, students learn to interpret and build complete quantum circuits, identifying the characteristic properties and phenomena that arise in them, such as entanglement or interference.

An important aspect of this topic is phase kickback, a mechanism by which the phase of one qubit is transferred to another within a circuit. This phenomenon is essential to the correct operation of many quantum algorithms, since it makes it possible to harness quantum interference as a computational resource. Understanding it gives students a first look at how small circuit blocks form the basis of more advanced algorithms in the discipline.

No-cloning principle Quantum teleportation Superdense coding

Phase kickback Deutsch's algorithm

This topic teaches the different models that exist for describing quantum computing. It shows how each model offers a different perspective on quantum computing, from the circuit model to alternative models such as adiabatic computing and topological computing. The goal is for the student to understand that quantum computing is not limited to a single way of operating, and that different approaches may be more suitable depending on the problem or the physical technology used.

Circuit model: the standard approach Adiabatic quantum computing Topological computing and anyons Comparison of models by applicability Theoretical similarities between models

Choosing a model based on hardware Real use cases by model type Practical case: simple example of adiabatic simulation

QUBO formulations are an essential mathematical framework in quantum computing for modeling combinatorial optimization problems. This topic introduces the fundamentals of QUBO, its relationship with quantum computing algorithms such as QAOA (Quantum Approximate Optimization Algorithm) and adiabatic computing, and its application to real-world problems such as logistics optimization, machine learning and planning.

Introduction to QUBO Definition and mathematical structure of QUBO formulations Transforming real-world problems into QUBO formulations Practical examples (e.g., graph partitioning, scheduling).

Relationship with quantum computing algorithms Use of QUBO in QAOA and adiabatic quantum computing Practical implementation: how to formulate and solve QUBO problems in environments such as D-Wave or classical simulators Applications: use cases in optimization and industrial problems

This topic covers the main physical technologies currently used to implement qubits in quantum hardware. It shows how different approaches—such as superconducting qubits, trapped ions, quantum dots, and photons—present unique advantages and challenges. The current state of industrial and academic development of each technology is also discussed. The goal is for students to understand what makes a qubit physically viable, how it is controlled and measured, and which factors determine the scalability of a quantum computing platform.

Superconducting qubits: advantages and limitations Trapped ions and high fidelity Quantum dots and scalability Photonic qubits: communication and networks Diamond defects and stability

Comparison between technologies Current state of development Practical case: evaluating the characteristics of different technologies

Students gain in-depth experience with the leading development environments for quantum computing solutions, simulating and running real circuits.

A closer look at the main frameworks: Qiskit, Cirq, Braket Key differences between platforms Creating and running circuits Connecting to real hardware in the cloud

State visualization and analysis Debugging quantum computing errors Local vs. remote simulation Case study: comparison of frameworks.

This topic focuses on programming quantum computing algorithms and projects, with practical exercises that guide algorithm implementation step by step. Students work with tools such as Qiskit and Cirq, developing personal projects and evaluating their performance on simulators.

Step-by-step guided practical exercises Implementing classical and quantum computing algorithms Integration between tools (Qiskit, Cirq) Creating personal projects Performance evaluation on simulators

Presentation of experimental results Working in multidisciplinary teams Case study: developing a quantum computing project

This topic covers how the errors affecting qubits during computation are detected, mitigated, and corrected. It shows the difference between classical and quantum computing errors, and how controlling quantum computing systems requires specialized techniques to prevent the loss of coherence. Correction codes such as Shor, Steane, and surface codes are also studied, along with concepts such as logical error and quantum redundancy. The goal is to give students a practical and theoretical understanding of how to achieve fault-tolerant quantum computing.

The nature of quantum computing errors Decoherence and information loss Detection and control techniques Shor code Steane code and efficiency

Surface codes The concept of fault tolerance Case study: error simulation and basic correction

This topic covers the first quantum computing algorithms developed that show advantages over classical computing on specific tasks. It shows how algorithms such as Deutsch-Jozsa and Grover work, and which quantum principles they exploit. These algorithms are presented step by step, with circuit diagrams and simulations. The goal is for students to understand how a quantum computing algorithm is structured and what makes it different from its classical counterpart.

Introduction to quantum advantage Deutsch-Jozsa algorithm Grover's algorithm and efficient search Applied quantum interference Comparison with classical algorithms

Circuit representation Step-by-step analysis Case study: full implementation of Grover's algorithm and results visualization

This topic covers how Shor's algorithm works, one of the best-known quantum computing algorithms because of its ability to factor integers efficiently, which threatens classical RSA-based cryptography. It shows how the algorithm leverages quantum phase estimation and the quantum Fourier transform to solve the factorization problem, and analyzes its implications for digital security. It also introduces quantum cryptography, including the BB84 protocol, and how it offers secure communication methods based on quantum computing principles. The goal is to understand both the threats and the opportunities that quantum computing presents for cybersecurity.

Description of Shor's algorithm Using the quantum Fourier transform (QFT) Quantum phase estimation Implications for RSA cryptography Introduction to quantum cryptography BB84 protocol

Secure communication with qubits Future risks and benefits Case study: simulating QFT and BB84 keys

This topic covers more advanced quantum computing algorithms that extend and generalize the concepts seen in earlier topics. It shows how algorithms such as Simon's algorithm, the Quantum Fourier Transform (QFT), and iterative search are structured. It also covers fundamental quantum computing subroutines that serve as building blocks for complex algorithms. The goal is for students to recognize common patterns and learn to combine quantum computing techniques to solve more sophisticated problems.

Simon's algorithm Quantum Fourier transform Subroutines as reusable blocks Modularity in algorithm design

Efficient iterative search Relation to structure problems Case study: composing subroutines for complex tasks

This topic focuses on the use of quantum techniques to model and simulate complex dynamic systems, which are fundamental in fields such as physics, chemistry, mechanics, and engineering. Throughout the course, students learn how quantum algorithms can be used to simulate the time evolution of systems that, due to their complexity and size, are intractable with classical methods. This approach is key to understanding natural phenomena, optimizing industrial processes, and developing new technologies.

Fundamentals of quantum computing dynamic systems Time evolution of quantum states Simulating systems that follow Schrödinger equations Simulation algorithms in quantum computing (HHL, Trotterization, and QPE)

Modeling and mapping dynamic systems: techniques and applications Solving ODE systems Molecular simulation Chemical reactions and complex materials

This topic explores the main areas where quantum computing promises to have a significant impact. It shows how this technology can transform sectors such as cryptography, the simulation of materials and chemical reactions, complex optimization, machine learning, and logistics. Real use cases and feasibility studies are also discussed. 

Scientific, industrial, and technological applications Transformation of key sectors and data Post-quantum cryptography Quantum machine learning Real cases at technology companies

New frontiers and emerging uses Emerging opportunities by sector Case study: developing and analyzing a prototype quantum computing solution applied to logistics optimization in the transportation sector

This topic covers how quantum computing can be integrated with machine learning to create new hybrid approaches. It shows how quantum computing algorithms can accelerate tasks such as classification, regression, and dimensionality reduction. The goal is for students to understand the fundamentals and potential of quantum machine learning (QML).

Introduction to QML and its applications Hybrid quantum-classical models Variational quantum circuits (VQC) Classification and clustering with qubits Quantum dimensionality reduction

Available frameworks: PennyLane, Qiskit ML Comparison with classical ML Case study: training a basic QML model

This topic covers where quantum computing is heading in the coming years, showing which challenges must be overcome to achieve practical quantum supremacy, which advances are expected in hardware, software, and algorithms, and how integration with other disciplines (such as artificial intelligence and communications) can generate new synergies. It also reflects on the ethical, social, and economic implications of this emerging technology, including security, equity of access, and sustainability. The goal is to encourage a critical, responsible view of the future of quantum computing. 

Expected advances in hardware and software The path toward quantum supremacy Integration with Artificial Intelligence Quantum computing networks and the future of communication Equity and global access

Technological sustainability Ethics in emerging quantum computing technologies Discussion: social and economic impacts