Quantum Information and Computing
A.Y. 2024/2025
Learning objectives
The course introduces the basics of the quantum paradigm and its application to the field of computing. The student will discover main differences between the classical and quantum paradigm, consolidating knowledge both in the suitable mathematical framework and by designing quantum software.
Expected learning outcomes
The student will be able to understand the premises of the quantum paradigm and the motivations for its application within different fields of computer science. She/He will acquire the ability to solve elementary problems in quantum mechanics that are of interest for the physical implementation of quantum devices for communication and computation. She/He will also learn the working principles of some paradigmatic algorithms of quantum key distribution and of some of the most important algorithms in quantum computing.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Introduction: physics and computation
Qbit
· Mathematical interpretation
· Dirac notation
· Geometrical interpretation
· Physical interpretation
Quantum register
· Tensor product
· Entangled states
Basics of linear algebra
· Inner product and Hilbert space
· Orthonormal basis
· Linear operators and outer product
· Eigenvalues and eigenvectors
· Adjoint and Hermitian operators
Quantum mechanics
· Postulates, Schroedinger equation
· Quantum measurement
Porte logiche quantistiche
· Linear operator representation
· Unitary matrices
· Single-qbit quantum gates
· Multiple-qbit quantum gates
Quantum circuits
· No cloning theorem
· Examples of quantum circuits
· Bell states
· Quantum teleportation
· Superdense coding
Introduction to quantum algorithms
· Classical computations
· Quantum parallelism
· Deutsch algorithm
· Deutsch-Josza algorithm
Classical and quantum computational complexity
· Elements of classical complexity: problem classes P, NP, BPP, complete problems
· Elements of quantum complexity: the problem class BQP
Quantum Fourier transform (QFT) and algorithms
· Unitary matrix eigenvalue evaluation
· Computing number order: the quantum algorithm
· Continued fractions
· Integer factoring: Shor's algorithm
Quantum search algorithms
· Grover's algorithm
A practical framework for quantum circuit design and analysis
· A Python's quick overview
· Qibo (open-source middleware for quantum computing)
A simple quantum computer: finite state automa
· Deterministic and probabilistic finite state automata
· Quantum finite state automata
· Strength and weakness of quantum and classical finite state automata
· Physical implementation of quantum finite state automata
Qbit
· Mathematical interpretation
· Dirac notation
· Geometrical interpretation
· Physical interpretation
Quantum register
· Tensor product
· Entangled states
Basics of linear algebra
· Inner product and Hilbert space
· Orthonormal basis
· Linear operators and outer product
· Eigenvalues and eigenvectors
· Adjoint and Hermitian operators
Quantum mechanics
· Postulates, Schroedinger equation
· Quantum measurement
Porte logiche quantistiche
· Linear operator representation
· Unitary matrices
· Single-qbit quantum gates
· Multiple-qbit quantum gates
Quantum circuits
· No cloning theorem
· Examples of quantum circuits
· Bell states
· Quantum teleportation
· Superdense coding
Introduction to quantum algorithms
· Classical computations
· Quantum parallelism
· Deutsch algorithm
· Deutsch-Josza algorithm
Classical and quantum computational complexity
· Elements of classical complexity: problem classes P, NP, BPP, complete problems
· Elements of quantum complexity: the problem class BQP
Quantum Fourier transform (QFT) and algorithms
· Unitary matrix eigenvalue evaluation
· Computing number order: the quantum algorithm
· Continued fractions
· Integer factoring: Shor's algorithm
Quantum search algorithms
· Grover's algorithm
A practical framework for quantum circuit design and analysis
· A Python's quick overview
· Qibo (open-source middleware for quantum computing)
A simple quantum computer: finite state automa
· Deterministic and probabilistic finite state automata
· Quantum finite state automata
· Strength and weakness of quantum and classical finite state automata
· Physical implementation of quantum finite state automata
Prerequisites for admission
Mathematical and algorithmic skills typically acquired after the first two years. Familiarity with elementary topics of linear algebra and probability is welcome.
Teaching methods
The course basically consists of traditional lectures, aiming to introduce to quantum computing from both a theoretical and a practical viewpoint. First, the theoretical foundations of quantum computing will be introduced, within the suitable mathematical background. Then, a framework for developing quantum software (Qibo) will be presented, aiming to put into practice theoretical basis. This combined theoretical/practical approach will enable to consolidate knowledge on the quantum paradigm.
Teaching Resources
Textbooks and other material
· Slides and handouts by instructors.
· M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010.
Websites
· Ariel: https://myariel.unimi.it/course/view.php?id=3259
· Qibo: https://qibo.science
· Slides and handouts by instructors.
· M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010.
Websites
· Ariel: https://myariel.unimi.it/course/view.php?id=3259
· Qibo: https://qibo.science
Assessment methods and Criteria
Essentially, the final exam will consist of a written test, structured into open questions on theoretical topics and exercises, with contents and difficulties like those faced during lectures. Two hours will be devoted to this test. Together with students, small software projects and scientific presentations could be envisioned as well. The exam will be rated from 1 to 30. An evaluation between 18 and 23 indicates an appropriate level of knowledge of basics of quantum computing, an evaluation between 24 and 27 indicates a good knowledge of such basics, higher evaluations indicate a very good knowledge and originality in applying basics of quantum computing.
INF/01 - INFORMATICS - University credits: 6
Lessons: 48 hours
Professors:
Mereghetti Carlo, Palano Beatrice Santa
Professor(s)
Reception:
On appointment, via email
Uff. S 6008, VI floor, Dip. Informatica "Giovanni Degli Antoni", via Celoria 18, 20133 Milano, Italy