Quantum computing represents a significant paradigm shift in how we approach computation. This subject aims to provide a foundational understanding of quantum computing principles, algorithms, and hardware. By building on prior knowledge from classical computing and introducing the concepts unique to quantum mechanics, students will gain the skills necessary to engage with this cutting-edge field.

The course will begin with an introduction to quantum mechanics and its application to computation. We will then explore quantum algorithms, such as Grover's and Shor's algorithms, which demonstrate the potential of quantum computers to solve certain problems more efficiently than classical computers. The final part of the course will cover quantum hardware, including quantum gates, qubits, and error correction methods and some state-of-the-art tropics such as quantum machine learning and quantum communications. Practical sessions will include programming quantum algorithms using tools like Qiskit and real IBM quantum computers.

• Understand the fundamental principles of quantum mechanics as they apply to quantum computing.

• Comprehend the operation and structure of quantum bits (qubits) and quantum gates.

• Analyze and implement basic quantum algorithms, including Grover's and Shor's algorithms.

• Understand the concepts of quantum entanglement and superposition and their implications for computation.

• Gain familiarity with quantum programming environments and develop simple quantum programs.

• Understand the challenges of quantum error correction and decoherence.

• Understand and apply quantum algorithms to machine learning problems.

• Understand and implement secure quantum communication protocols, including quantum key distribution and quantum teleportation, to ensure data security in quantum networks.

Theoretical Quantum Computing

1. Mathematical foundations of Quantum Computing

1.1. Complex numbers

1.2. Complex vector spaces

2. Introduction to Quantum Computing

2.1. Basics of Quantum Mechanics

2.2. Quantum states and qubits

2.3. Quantum superposition and entanglement

3. Quantum gates and circuits

3.1. Single qubit gates

3.2. Multi-qubit gates and circuits

3.3. Quantum measurement

4. Quantum algorithms

4.1. Deustch algorithm

4.2. Grover's algorithm for search

4.3. Quantum period finding

4.4. Quantum Fourier transform

4.5. Shor's algorithm for factoring

5. Quantum Hardware

5.1. Qubit implementation technologies

5.2. Quantum error correction

5.3. Quantum decoherence

6. Advanced Topics

6.1. Quantum cryptography

6.2. Quantum machine learning

6.3. Quantum internet and networking

Practical Quantum Computing

1. Introduction to Qiskit

1.1. Overview of Qiskit

1.2. Installation and setup

1.3. Basic Qiskit commands and structures

2. Writing and simulating quantum algorithms

2.1. Building quantum circuits with Qiskit

2.2. Simulating circuits on classical hardware

2.3. Analyzing results and debugging

3. Running Algorithms on real quantum hardware

3.1. Accessing IBM quantum experience

3.2. Submitting jobs to real quantum devices

3.3. Interpreting real quantum hardware results



This content structure provides a comprehensive foundation in quantum computing, balancing theoretical concepts with practical applications. The inclusion of advanced topics allows for exploration beyond the basics and the evolving nature of the field.

During the development of classes and labs, systematic group work, discussions, and presentation of exercise results will be conducted to encourage direct participation in the course and to encourage student motivation.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Los sistemas de evaluación y sus porcentajes se especifican en los siguientes apartados (%): 100

There are two ways to pass the subject in the ordinary call:

a) Continuous assessment (ongoing study): This is the default mode of assessment and applies only to the first call. It involves active and continuous participation in course activities: attendance at classes and labs, submission of exercises and assignments, evaluation tests, etc. If these conditions are not met, the global evaluation procedure will be used.

The subject will be assessed as follows in this mode:

◦ Theoretical topics 1 to 3: 3 points (1 point exam + 2 points exercises)

◦ Theoretical topics 4 to 6: 3 points (3 points exam)

◦ Practical work (Project): 4 points (related to theoretical topics 4 to 6)

To pass the subject, in addition to obtaining a grade higher than 5, it is necessary to obtain at least 4 points (out of 10) in each of the evaluable activities, i.e., exercises, exams, practical work, and project. Students who, meeting the conditions to continue with continuous assessment, decide to opt for global evaluation, must inform the course instructor by email before the 14th week of the course.

b) Final assessment: If it is not possible to continue with continuous assessment due to low performance or personal choice, the subject will be evaluated globally as follows:

◦ Written exam (all topics): 6 points

◦ Practical work (related to theoretical topics 4 to 6): 4 points

In this case, to pass the subject, in addition to obtaining a grade higher than 5, it is necessary to obtain at least 4 points in both the written exam and the practical work.

In the extraordinary call, the assessment will be performed as follows:

◦ Written exam (all topics): 6 points

◦ Practical work (related to theoretical topics 4 to 6): 4 points

In this case, to pass the subject, in addition to obtaining a grade higher than 5, it is necessary to obtain at least 4 points in both the written exam and the practical work.

The course materials, transparencies, and/or readings are available on eGela.

Basic bibliography

Primary Textbooks

• Yanofsky, N. S., & Mannucci, M. A. (2008). Quantum Computing for Computer Scientists. Cambridge University Press.

• Nielsen, M. A., & Chuang, I. L. (2011). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.

In-depth bibliography

Supplementary Books
• Jack D. Hidary. Quantum Computing: An Applied Approach (2019). Springer.
• Scott Aaronson. Quantum Computing Since Democritus (2013). Cambridge University Press.

Web addresses

Online Resources and Documentation
• IBM Quantum Documentation. (2024). https://docs.quantum.ibm.com/
• IBM Quantum Platform. (2024). https://quantum.ibm.com/
• Quantum Algorithm Zoo. (2024). https://quantumalgorithmzoo.org/
• Shtetl-Optimized-The Blog of Scott Aaronson. https://scottaaronson.blog/