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Quantum Information

Code: 100182
Credits: 6
2026/2027
Degree programme Type Course
Physics OP 4

Contact lecturer

Name :
Gael Sentís Herrera
Email :
gael.sentis@uab.cat

Teaching staff

Gael Sentís Herrera
Alessio Celi
Mani Zartab

Group languages

You can consult this information at the end of the document.

Prerequisites

It is advisable to have a good command of algebra, especially of vector spaces and, preferably, of complex Euclidean spaces. Notions of quantum mechanics. of course. are recommended, but the course is quite self-contained. Knowledge of quantum optics is complementary and recommended, but not essential.

Objectives

The course offers an introduction to the modern perspective of quantum mechanics and its paradigms. With today’s available technology, many of the most paradoxical quantum effects have moved beyond academic curiosities and have become powerful resources that form the basis of quantum technologies, with numerous and surprising practical applications. Some of these applications will be presented in this course: teleportation, dense coding, quantum cryptography, quantum computation and simulation, etc.
The course is designed for physicists, but also for mathematicians, computer scientists, and engineers. Since it is a self-contained course, it includes an introduction to the fundamentals of quantum mechanics, classical information theory, classical cryptography and computation, to allow students to understand the contributions of their quantum counterparts.
The course also has an applied component closely linked to quantum optics. It includes an introduction to the semiclassical and quantum theory of light-matter interaction, as well as a description of the principles and their implementation in concrete physical systems for quantum communication and quantum computation/simulation.
The goal of the course is not only to provide an overview of the advances in quantum information but also to equip students with the basic tools necessary to pursue graduate-level education in this field, should they be interested.

Learning outcomes

  1.  Carry out academic work independently using bibliography (especially in English), databases and through collaboration with other professionals
  2. Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
  3. Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
  4. Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
  5. Working in groups, assume shared responsibilities and interact professionally and constructively with others, showing absolute respect for their rights.
  6. Apply the axioms of quantum mechanics to problems of information processing.
  7. Differentiate between pure quantum states and statistical mixture.
  8. Apply quantum measurement in the context of information theory.
  9. Describe the concept of quantum entanglement state, its characterization and its use in quantum information.
  10. Describe the similarities and differences between cryptography and classical computation, their quantum versions and their relationship to the physical principles underlying the latter.
  11. Describe the bases of light-matter interaction necessary to understand the physical implementations of cryptography and quantum computing.
  12. Establish the main protocols of quantum cryptography.
  13. Describe the main implementations of quantum computing.
  14. Demonstrate an understanding of Schmidt's decomposition of bipartite quantum states.
  15. Formulate the statistical interpretation of mixed quantum states.
  16. Demonstrate an understanding of both Von Neumann's measurement and generalized measurements.
  17. Demonstrate an understanding of EPR states and formulate Bell's inequalities.
  18. Demonstrate an understanding of the quantum algorithms of Deutsch-Józsa, Shor and Grover.
  19. Demonstrate an understanding of Shannon's concept of entropy, channel capacity and corresponding theorems.
  20. Demonstrate an understanding of the quantum versions of the said concepts and theorems.
  21. Demonstrate an understanding of the BB84 and Eckert91 protocols for quantum cryptography.
  22. Demonstrate an understanding of physical implementations for one- and two-qubit quantum logic gates.
  23. Use the concept of state mixture to solve simple problems with open systems.
  24. Apply the concept of quantum measurement (Von Neumann or generalized) to simple problems of optimization, discrimination, estimation and quantum communication.
  25. Use the semiclassical theory of light-matter interaction to understand the cooling and trapping of particles, in addition to the implementation of single-qubit logic gates.
  26. Use the quantum theory of light-matter interaction to understand the characteristics of quantum light sources.
  27. Contrast classical information theory with that of quantum theory.
  28. Relate the fundamentals of quantum information with the principal current physical implementations of cryptography and quantum computing.
  29. Apply the matrix formulation of quantum mechanics to quantum protocols and algorithms.
  30. Solve problems on the characterization of entanglement in quantum states by Schmidt decomposition.
  31. Carry out a project that relates the concepts of quantum information and computation studied with current innovative issues and present the results.
  32. Identify situations in which a change or improvement is needed.
  33. Identify the social, economic and environmental implications of academic and professional activities within one's own area of knowledge.

Contents

Part I (Theoretical Aspects)


  1. Operational Quantum Physics
  2. Quantum States
  3. Vectors in Hilbert Space
  4. Density Matrices and Mixed States
  5. Bloch Sphere
  6. Distance and Fidelity Between Mixed States
  7. Quantum Measurements
  8. Observables and Projective Measurements
  9. Generalized Measurements
  10. Applications
  11. Composite Systems
  12. The Tensor Product
  13. Combining Systems
  14. Entanglement of Pure States
  15. Superdense Coding
  16. Quantum Teleportation
  17. Quantum Processes
  18. Partial Trace and Purification
  19. Ancillary Systems and Kraus Operators
  20. Completely Positive Maps
  21. Entanglement of Mixed States
  22. LOCC
  23. The Peres–Horodecki Criterion
  24. Entanglement Witnesses
  25. Quantum Communication and Computation
  26. Classical Information Theory
  27. Shannon Entropy
  28. Joint and Relative Entropy; Mutual Information
  29. The Binary Symmetric Channel; Channel Capacity
  30. Shannon’s Theorems
  31. Quantum Information Theory
  32. von Neumann Entropy
  33. Quantum Relative Entropy
  34. Holevo Information, Accessible Information, and the Holevo Bound
  35. Classical Computation
  36. Turing Machines
  37. The Halting Problem
  38. Computational Complexity
  39. Complexity Classes
  40. The Circuit Model
  41. Oracle-Based Quantum Algorithms
  42. Oracles
  43. Deutsch Algorithm
  44. Deutsch–Jozsa Algorithm
  45. Simon’s Problem
  46. Grover’s Algorithm
  47. The Quantum Circuit Model of Computation
  48. Single-Qubit Gates
  49. Two-Qubit and Multi-Qubit Gates
  50. Implementation of Oracle Unitaries
  51. A Universal Gate Set
  52. Arbitrary Quantum Computations
  53. Quantum Computational Complexity
  54. Shor’s Algorithm




Part II (Physical Implementation)


  1. Brief Review of Light–Matter Interaction
  2. Semiclassical Theory of Light–Matter Interaction
  3. The Two-Level Atom
  4. AC Stark Splitting
  5. Rabi Oscillations
  6. The Optical Dipole Force
  7. Quantum Theory of Light–Matter Interaction
  8. States of the Quantum Electromagnetic Field
  9. The Jaynes–Cummings Model
  10. The Decoherence Problem
  11. Quantum Communication
  12. Quantum Cryptography: BB84 and Ekert91 Protocols
  13. Bell Inequalities
  14. Single-Photon Generation
  15. Single-Photon Propagation
  16. Single-Photon Detection
  17. Quantum Computing and Simulation
  18. Neutral Atoms (Ground-State and Rydberg) in Optical Dipole Traps
  19. Cavity Quantum Electrodynamics (Cavity QED)
  20. Ions in Paul Traps
  21. Superconducting Qubits


Learning activities and methodology

Title Hours ECTS Learning outcomes
Exercises lectures 16 0.64 2, 5, 6, 7, 8, 23, 24, 25, 26, 29, 30, 32, 33
Solving exercises 40 1.6 3, 4, 6, 7, 8, 23, 24, 29, 30
Exercises to deliver 3 0.12 1, 2, 4, 5, 6, 7, 8, 23, 24, 25, 26, 29, 30, 31, 32, 33
Theory lectures 33 1.32 3, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 27, 28, 32, 33
Study of the theoretical background 49 1.96 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 27, 28

The course is structured into theory classes, problem classes, and continuous assessment activities.


Theory classes are held in two formats: chalkboard sessions and presentations with a projector. There will be some classes/seminars on certain topics from the course, which will be presented by researchers in the field of Quantum Information.

Problem classes are usually done on the board and consist of solving the most significant problems, the problem statements of which are made available to students through the Virtual Campus.

There will be two two-hour seminar sessions dedicated to autonomous group problem-solving. Solutions must be submitted at the end of the session and will be graded.

All materials—problem sets, supplementary teaching materials, detailed solutions to some exercises, as well as news related to the course's operation—are made available to students through the Virtual Campus.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Retake oral exam on theoretical concepts 56 0.5 0.02 2, 3, 6, 7, 8, 9, 14, 15, 16, 18, 19, 20, 23, 24, 27, 29, 30
Multiple-choice test on quantum tecnologies 15 1 0.04 10, 11, 12, 13, 17, 21, 22, 25, 26, 28
Oral final exam on theoretical concepts 35 0.5 0.02 2, 3, 6, 7, 8, 9, 14, 15, 16, 18, 19, 20, 23, 24, 27, 29, 30
Multiple-choice test on quantum technologies 9 1 0.04 10, 11, 12, 13, 17, 21, 22, 25, 26, 28
Delivery of exercises done by groups in class (autonomous work) 20 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 18, 19, 20, 24, 27, 31, 32, 33
Retaken test on quantum tecnologies 24 1 0.04 10, 11, 12, 13, 17, 21, 22, 25, 26, 28
Partial exam on theoretical concepts 21 2 0.08 2, 3, 6, 7, 8, 9, 14, 15, 16, 18, 19, 20, 23, 24, 27, 29, 30

The evaluation consists of the following activities:

  1. Submission of exercises completed in class autonomously by groups, worth 20%. Two class sessions (3 hours in total) will be dedicated to this activity.
  2. A midterm exam on theoretical concepts, worth 21%
  3. A multiple-choice quiz on quantum technologies, worth 9%
  4. An oral final exam on theoretical concepts, worth 35%
  5. A multiple-choice final exam on quantum technologies, worth 15%


It is necessary to have been evaluated on both of the theoretical concepts/quantum technologies tests in order to be eligible for the corresponding make-up exams. A student who has only completed activity 1 will be considered ungraded.

Bibliography

The Virtual Campus provides students with notes on the subject in pdf format and a copy of the Keynote/Powerpoint of the course. The following bibliography is recommended for further information:

Basic

Theory

  • J. Preskill. Lectures notes on Quantum Computation. Es pot obtenir gratuïtament a la direcció: http://www.theory.caltech.edu/people/preskill/ph229.
  • M.A. Nielsen; S.L. Chuang. Quantum Computation and Quantum Information. Cambridge Univ. Press, Cambridge 2000.
  • S.M. Barnett, Quatum Information, Oxford University Press, 2009.

• A. Peres. Quantum Theory: Concepts and Methods. Kluwer, Dordrecht 1995.
• D. Applebaum. Probability and Information. Cambridge Univ. Press, Cambridge 1996.
• D. Boumeester; A. Eckert; A. Zeilinger. The Physics of Quantum Information. Springer 2000.
• D. Heiss. Fundamentals of Quantum Information. Springer 2002.

Exercises

  • Steeb, Willi-Hans, and Yorick Hardy. Problems and solutions in quantum computing and quantum information. World Scientific Publishing Company, 2018.
  • C. P. Williams; S. Clearwater. Exploration in Quantum Computing. Springer 1998

 

Advanced

• R. A. Bertlmann; A. Zeilinger. Quantum (Un)speakables. Springer 2002. 
• A. Ekert; R. Jozsa. Quantum Computation and Shor’s Factoring Algorithm. Rev. Mod. Phys. 68 (1996) 733.

  • T.A. Cover; J.A Thomas, Elements of Information Theory, John Wiley 2006.

Software

Qiskit (IBM Quantum programming language)

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 English second semester afternoon
(PAUL) Classroom practices 1 English second semester afternoon