LEARNING OUTCOMES

This course aims to introduce the key concepts and methods of Quantum Information and Computation. The first part will provide the operational elements of quantum mechanics and quantum information: superposition principle, quantum entanglement, the quantum bit (qubit) and quantum logical gates. The second part will introduce the basic quantum algorithms and applications to informatics such as quantum database search algorithm, quantum teleportation and superdense coding.The final part will deal with some possible applications to robotics. It will be shown as the above ideas and concepts can be introduced in software architecture for robots that exploit quantum-inspired perception, reasoning and action techniques.

AIMS AND LEARNING OUTCOMES

The course aims to bring the students updated with the recent and fast-developing field of quantum technologies, quantum information, and computation.
The students will learn the fundamental ideas of quantum mechanics which form the basis for the applications of quantum technologies and information.
The most important innovations and applications to informatics (such as quantum teleportation and cryptography) and computation (database search algorithm) will be presented. Some of the more recently proposed applications to Robotics engineering will be discussed.
The students will also learn the most used quantum programming languages (such as IBM-Qiskit) and apply the knowledge to solve prototypical simple problems.

PREREQUISITES

There are no particular prerequisites for 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. Mathematical tools
   1. Vector spaces and operations
   2. Tensor product
   3. Hermitian operators, eigenvectors and eigenvalues and matrix representation of an operator
2. 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
3. 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
4. Quantum cryptography
   1. Fundamental concepts in classical cryptography: public and private key cryptography
   2. Quantum cryptography protocols: Bennett-Brassard (BB84) and Ekert91
5. Quantum algorithm for the search in a database: (Grover’s algorithm)
   1. Fundamental concepts in database search algorithms
   2. Grover’s algorithm
6. 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
7. Introduction to quantum programming languages
   1. IBMQ - Qiskit
   2. Pennylane
   3. Google Cirq and Amazon Braket
8. Possible applications to Robotics engineering
   1. Quantum devices as sensors in robots
   2. Quantum information and robotics applications

RECOMMENDED READING/BIBLIOGRAPHY

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)