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)