Theoretical Chemistry with Elements of Quantum Computing
A.Y. 2025/2026
Learning objectives
This course aims to provide students with a solid understanding of quantum mechanical methods applied to the structure of matter, with particular emphasis on quantum dynamics. Additionally, fundamental concepts of quantum computing will be introduced, including key algorithms and their potential applications. Additionally, fundamental concepts of quantum computing will be introduced, including key algorithms and their potential applications. The goal is to equip students with the theoretical and practical tools necessary to tackle quantum problems in theoretical chemistry, with both traditional techniques and those of the emerging field of quantum information.
Expected learning outcomes
By the end of the course, students will have mastered the resolution of quantum problems in chemistry, both static and dynamic. +Additionally, they will gain insight into the potential of quantum computing, become familiar with quantum gates, and be able to develop basic algorithms for simple quantum applications.
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
1 States and Observables in Quantum Mechanics. Projection-valued measurement, Heisenberg uncertainty principle.
2 Schrödinger Equation and Time Evolution Operator. Dynamical (or Heisenberg) derivative and applications. Descriptions: Schrödinger, Heisenberg, Dirac (or Interaction) pictures. Time-dependent perturbation theory.
3 Statistical Operator and Liouville-von Neumann Equation. Rays, gauge invariance, and absolute dynamics.
4 Open Systems (overview): Dissipation and decoherence. Thermodynamic equilibrium. Modern measurement theory. Linear response theory. Generalized susceptibilities. Correlations. Fluctuation-dissipation theorem. Onsager reciprocity.
5 Numerical Methods for Solving the Schrödinger Equation. Variational principle.
6 Molecules. Exact factorization theory. Born-Oppenheimer approximation, adiabatic approximation.
7 Classification of Quantum Mechanical States: Factorized states and entangled states.
8 Classical Computing (bits and logic gates). The qubit: fundamental element of quantum computing. The use of multiple qubits and quantum logic gates. Description of the "philosophy" underlying methods based on a quantum computing approach.
9 The Wonders of the Quantum World: Quantum teleportation, the no-cloning theorem, the Deutsch algorithm.
10Two Fundamental Algorithms in Quantum Computing: Quantum Fourier transform and quantum phase estimation algorithm.
11 Applications of Quantum Computing Methods: Wavefunction determination, database search, and Shor's algorithm in cryptography.
2 Schrödinger Equation and Time Evolution Operator. Dynamical (or Heisenberg) derivative and applications. Descriptions: Schrödinger, Heisenberg, Dirac (or Interaction) pictures. Time-dependent perturbation theory.
3 Statistical Operator and Liouville-von Neumann Equation. Rays, gauge invariance, and absolute dynamics.
4 Open Systems (overview): Dissipation and decoherence. Thermodynamic equilibrium. Modern measurement theory. Linear response theory. Generalized susceptibilities. Correlations. Fluctuation-dissipation theorem. Onsager reciprocity.
5 Numerical Methods for Solving the Schrödinger Equation. Variational principle.
6 Molecules. Exact factorization theory. Born-Oppenheimer approximation, adiabatic approximation.
7 Classification of Quantum Mechanical States: Factorized states and entangled states.
8 Classical Computing (bits and logic gates). The qubit: fundamental element of quantum computing. The use of multiple qubits and quantum logic gates. Description of the "philosophy" underlying methods based on a quantum computing approach.
9 The Wonders of the Quantum World: Quantum teleportation, the no-cloning theorem, the Deutsch algorithm.
10Two Fundamental Algorithms in Quantum Computing: Quantum Fourier transform and quantum phase estimation algorithm.
11 Applications of Quantum Computing Methods: Wavefunction determination, database search, and Shor's algorithm in cryptography.
Prerequisites for admission
No specific prerequisites are required, except for Chimica Quantistica.
Teaching methods
6 ECTS (teoria, 48 h)
The course is structured around chalkboard lectures, providing a rigorous and detailed exposition of theoretical concepts.
The course is structured around chalkboard lectures, providing a rigorous and detailed exposition of theoretical concepts.
Teaching Resources
Reference textbooks include:
"Quantum Mechanics" - Albert Messiah, Dover Publications
"Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems" - A. Nitzan, Oxford University Press, 2006
Additional teaching materials, including lecture notes and slides, will be provided for specific topics.
"Quantum Mechanics" - Albert Messiah, Dover Publications
"Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems" - A. Nitzan, Oxford University Press, 2006
Additional teaching materials, including lecture notes and slides, will be provided for specific topics.
Assessment methods and Criteria
The exam consists of a written test focused on the general formulation of quantum mechanics and another dedicated to quantum computing.
CHIM/02 - PHYSICAL CHEMISTRY - University credits: 6
Lessons: 48 hours
Professors:
Martinazzo Rocco, Sironi Maurizio
Professor(s)