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01HEJUU

A.A. 2024/25

Course Language

Inglese

Degree programme(s)

Master of science-level of the Bologna process in Quantum Engineering - Torino

Course structure

Teaching | Hours |
---|---|

Lezioni | 60 |

Lecturers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Carbone Anna Filomena | Professore Ordinario | PHYS-04/A | 30 | 0 | 0 | 0 | 2 |

Co-lectures

Espandi

Riduci

Riduci

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut |
---|---|---|---|---|---|---|

De Gregorio Paolo Mario | Professore Associato | MATH-04/A | 30 | 0 | 0 | 0 |

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

FIS/03 MAT/05 |
3 3 |
F - Altre attività (art. 10) B - Caratterizzanti |
Altre conoscenze utili per l'inserimento nel mondo del lavoro Ingegneria elettronica |

2024/25

The course “Quantum Information” bridges the knowledge of quantum mechanics to information theory thus accompanying the student beyond classical information Shannon theory. Indeterminism and uncertainty are founding concepts of quantum mechanics which do not arise due to loss of information or imprecise measurement capability as in the classical information theory, but rather are intrinsically related to the quantum phenomena. Classical Information Theory aims at quantifying the ultimate compressibility of information and the ultimate ability for a sender to transmit information reliably to a receiver. The uncertainty in classical information theory relies upon probability theory. The “classical” uncertainty, arising from our lack of total information about any given scenario, is ubiquitous throughout all information-processing tasks. “Quantum” uncertainty is inherent in the nature itself of quantum phenomena and thus require new physical knowledge and tools that will be the focus of the course.

The course “Quantum Information” bridges the knowledge of quantum mechanics to information theory thus accompanying the student beyond classical Shannon information theory. Indeterminism and uncertainty are founding concepts of quantum mechanics which do not arise due to loss of information or imprecise measurement capability as in the classical information theory, but rather are intrinsically related to the quantum phenomena. Classical Information Theory aims at quantifying the ultimate compressibility of information and the ultimate ability for a sender to transmit information reliably to a receiver. The uncertainty in classical information theory relies upon probability theory. The “classical uncertainty”, arising from our lack of total information about any given scenario, is ubiquitous throughout all information-processing tasks. “Quantum uncertainty” is inherent in the nature itself of quantum phenomena and thus requires new physical knowledge and tools that are the focus of the course.

The student will understand and quantify: (i) the information about a quantum state and the error affecting that state; (ii) the transmission of quantum information over quantum channels, considering the case of a noiseless channel and the case of noisy channel; (iii) the complementary approaches and technologies related to quantum error correcting codes and quantum error mitigation strategies for noiseless and noisy intermediate quantum devices. The student will also tackle key quantum engineering issues such as: noise effects with and without quantum error correction; noise performance of quantum devices for practical applications.

The student will understand and quantify: (i) the information about a quantum state and the error affecting that state; (ii) the transmission of quantum information over quantum channels, considering both noiseless and noisy channels; (iii) the complementary approaches related to quantum error correcting codes and quantum error mitigation strategies for noiseless and noisy intermediate quantum devices. The student will also tackle key quantum engineering issues such as: noise effects with and without quantum error correction; quantum noise in some practical cases.

Classical bits, gates, parity and data compression. Computational complexity, randomness, classical error correction. Quantum bits, superposition states, quantum measurements. Single-qubit Hilbert space: linear operators. orthonormal bases and basis changes, qubit rotations, Bloch sphere. Dirac notation for qubits and operation. Expectation values and variance of measurement results. Classical and Quantum Statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein). The density matrix. Pure states vs mixed states. Composite systems.

Classical bits, gates, parity and data compression. Computational complexity, randomness, classical error correction. Quantum bits, superposition states, quantum measurements. Single-qubit Hilbert space: linear operators. orthonormal bases and basis changes, qubit rotations, Bloch sphere. Dirac notation for qubits and operation. Expectation values and variance of measurement results. Classical and Quantum Statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein).

Fundamentals of Quantum Information (1.0 CFU Brief Recalls): Multiqubit Hilbert space and operators. Tensor product spaces and combinatorial complexity. Reversible and irreversible evolution. Quantum channels. Entanglement. Bell states. Nonlocality. No signaling. No cloning theorem. Teleportation.
Quantum Information Measures (2.0 CFU): Thermodynamics entropy vs information entropy. Statistical Ensembles. Shannon entropy. Data compression. Mutual information. Kullback-Leibler (relative) entropy. Fisher entropy. The noisy channel coding theorem. Von Neumann Entropy. Quantum Renyi entropy. Quantum Data Compression. Holevo information. Holevo Bound. Information measures for pure states and for mixed states. Relative quantum entropy. Accessible information.
Quantum errors (1.5 CFU): Quantum states distinguishability, the PeresWootters method. Helstrom’s minimum error decoder. Fidelity. Quantum channel distinguishability. Quantum error correction. Quantum error correctability. Knill-Laflamme method.
Quantum noise sources (1.5 CFU): Classical noise and quantum noise. Physical noise sources in qubits (superconductor, quantum dots, ion traps)

Fundamentals of Quantum Information (1.5 CFU) Density matrix. Pure states vs mixed states. Composite systems. Multiqubit Hilbert space and operators. Tensor product and combinatorial complexity. Reversible and irreversible evolution. Quantum channels. Entanglement. Bell states. Nonlocality. No signaling. No cloning theorem. Teleportation.
Quantum Information Measures (1.5 CFU): Thermodynamics entropy vs information entropy. Statistical Ensembles. Shannon entropy. Data compression. Mutual information. Kullback-Leibler (relative) entropy. The noisy channel coding theorem. Von Neumann Entropy. Information measures for pure states and for mixed states. Relative quantum entropy. Quantum Data Compression. Holevo information. Holevo Bound. Accessible information.
Quantum errors (2.0 CFU): Quantum states distinguishability, positive operator-valued measures, purifications, quantum operations. The PeresWootters method. Helstrom’s minimum error decoder. Fidelity. Quantum channel distinguishability. Quantum error correction. Quantum error correctability. Knill-Laflamme method.
Quantum noise (1.0 CFU): Classical noise and quantum noise. Classical and quantum Langevin equation. Noise sources in qubits in equilibrium and quasi-equilibrium conditions. Nyquist noise, shot noise, Brownian particle paths, harmonic oscillator.

The course is organized into theoretical lectures and exercise classes (approximately 40hours lectures and 20hours exercises). Exercises classes are aimed at applying concepts and methods presented during the lectures. Part of the practical classes will be dedicated to computer simulations. During practical classes, the active participation of the students is required.

The course is organized into theoretical lectures and exercise classes (approximately 40hours lectures and 20hours exercises). Exercises classes are aimed at applying concepts and methods presented during the theoretical lectures. The active participation of the students is required during practical classes.

"Quantum Computation and Quantum Information"
by Michael A. Nielsen, Isaac L. Chuang
Cambridge University Press; Anniversary edition (2011)
"Quantum Information Theory"
by Mark M. Wilde
Cambridge University Press (2013)
"Quantum Information Processing, Quantum Computing, and Quantum Error Correction. An Engineering Approach”
by Ivan Djordjevic
Academic Press (2021)

"Quantum Computation and Quantum Information"
by Michael A. Nielsen, Isaac L. Chuang
Cambridge University Press; Anniversary edition (2011)
"Quantum Information Theory"
by Mark M. Wilde
Cambridge University Press (2013)
"Quantum Information Processing, Quantum Computing, and Quantum Error Correction. An Engineering Approach”
by Ivan Djordjevic
Academic Press (2021)
“Elements of Information Theory”
by Thomas M. Cover, Joy A. Thomas
2nd Edition,
Wiley Series in Telecommunications and Signal Processing (2006)

Slides; Libro di testo; Libro di esercitazione; Esercizi; Esercizi risolti;

Lecture slides; Text book; Practice book; Exercises; Exercise with solutions ;

...
The exam consists of a written part and an oral part. The written part contains 10 multiple-choice questions (both literal and numerical) related to the theoretical parts and exercises of the course. The total time allotted for the written test is one hour. The written test is considered passed if a total grade of at least 18/30 is obtained. Passing the written test is followed by the oral test, which consists of a few questions on the theoretical parts of the course.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The evaluation (exam) consists of a written part and an oral part.
Written Part: The written exam contains 10 multiple-choice questions (both theoretical and numerical) related to the theoretical and applicative topics of the course and exercises. The total time allotted for the multiple-choice test is half an hour. The correct answer receives a score of 3 points. No penalties are assigned to the wrong or unanswered questions. The written test is considered passed if a total grade of at least 18/30 is obtained.
The second part consists of a general question on the theoretical and applicative topics of the course. The general question is split in three sub-questions. Each sub-question receives a maximum score of 10 points. The general question is considered satisfactorily answered if a score of at least 18/30 is obtained.
Oral Part: The content of the written exam is discussed during the oral. One or two more questions will be asked during the oral.
The final score will be the averaged sum of the scores of the: (a) multiple-choice test, (b) the general question and (c) the oral discussion.
During the course, a couple of classes will be devoted to the solution of multiple-choice test and to address general questions to familiarize with those proposed at the exams.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.