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ELEMENTS OF QUANTUM COMPUTING

CODE 98389
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 3nd year of 8759 INFORMATICA (L-31) - GENOVA
  • 6 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR FIS/02
    LANGUAGE Italian
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course is an introduction to quantum information and computation. The theorical part is followed by an applicative one aimed to show the more recent developments of the field.

    AIMS AND CONTENT

    PREREQUISITES

    There are no particular prerequisites for the mathematics and physics.
    The mathematical tools needed will be introduced during the course.

     

    TEACHING METHODS

    Theoretical lectures supported by more applicative ones focused on the quantum computers languages (Qiskit by IBM, CIRQ by Google, Braket by Amazon)

    SYLLABUS/CONTENT

    1. Physics of computation
      1. Basic concepts in Informatics: logical gates, universal and reversible logical gates
      2. Billiard ball and DNA computers
    2. Mathematical tools
      1. Vector spaces and operations
      2. Tensor product
      3. Hermitian operators, eigenvectors and eigenvalues and matrix representation of an operator
    3. Introduction to quantum phenomena
      1. Double slit and light polarization experiments
      2. Quantum state, quantum superposition and quantum bit (qubit)
      3. Quantum measurement
      4. Composite quantum systems and entanglement
      5. Unitary transformations, logical gates with one and two qubits
      6. Pauli operators and Bloch sphere representation
    4. Introduction to quantum information
      1. Quantum parallelism, no-cloning theorem, super-dense coding and quantum teleportation
      2. Quantum algorithms: Deutch, Deutch-Joza, Bernstein-Vazirani and Simon
    5. Quantum cryptography
      1. Fundamental concepts in classical cryptography: public and private key cryptography
      2. Quantum cryptography protocols: Bennett-Brassard (BB84) and Ekert91
    6. Quantum algorithm for the search in a database: (Grover’s algorithm)
      1. Fundamental concepts in database search algorithms
      2. Grover’s algorithm
    7. Introduction to error correcting codes
      1. Fundamental concepts in the classical case and differences with the quantum case
      2. Composite observables and their eigenvalues
      3. Quantum error correcting codes (bit-flip, small errors and phase errors)
      4. Shor’s protocol for error correcting code
    8. Introduction to quantum games
      1. Introduction to game theory: classical and quantum
      2. spin-flip in star trek
      3. Prisoner dilemma: quantum and classical case
      4. Mermin’s game
    9. Elitzur-Vaidman bomb tester
    10. Quantum Fourier transform and quantum phase estimation algorithm
      1. Mathematical tools and classical Fourier transform
      2. Quantum Fourier transform
      3. Quantum phase estimation algorithm
      4. Applications: quantum counting algorithm
    11. Advanced quantum algorithms
      1. Shor’s algorithm for factorizing integer numbers
      2. Harrow-Hassidim-Lloyd (HHL) algorithm
      3. Applications of HHL algorithm: linear algebra and quantum machine learning
    12. Nonlocality and entanglement in quantum mechanics
      1. Nonlocality in quantum mechanics
      2. Einstein, Podolsky, and Rosen paradox
      3. Bell’s inequality and Aspet’s experiment
      4. Greenberger–Horne–Zeilinger  nonlocal states and Zeilinger’s experiment
    13. Quantum algorithms, quantum protocol and quantum experiments implementations with the IBM quantum computers

    RECOMMENDED READING/BIBLIOGRAPHY

    P. Solinas – Notes: “Introduzione all’Informatica quantistica”

    M. A. Nielsen e I. L. Chuang "Quantum Computation and Quantum Information", Cambridge University Press (2011)
     
    N. S. Yanofsky e M. A. Mannucci  "Quantum Computing for Computer Scientists", Cambridge University Press (2008)

    E. G. Rieffel and W. H. Polak "Quantum Computing: A Gentle Introduction (Scientific and Engineering Computation)"
    The MIT Press (2011)

    TEACHERS AND EXAM BOARD

    Exam Board

    PAOLO SOLINAS (President)

    PIERANTONIO ZANGHI'

    ALESSANDRO VERRI (Substitute)

    LESSONS

    LESSONS START

    The lectures will start according to the academic calendar

     

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    The exam is composed by an oral examination and a home assignment.
    In home assignment the student will be asked to solve a simple problem by writing a code for a quantum computer and he/she will be asked to write a short report.

     

    Exam schedule

    Date Time Location Type Notes
    18/01/2023 09:00 GENOVA Orale
    06/02/2023 09:00 GENOVA Orale
    09/06/2023 09:00 GENOVA Orale
    04/07/2023 09:00 GENOVA Orale
    07/09/2023 09:00 GENOVA Orale