Computational quantum physics
Summary
The numerical simulation of quantum systems plays a central role in modern physics. This course gives an introduction to key simulation approaches, through lectures and practical programming exercises. Simulation methods based both on classical and quantum computers will be presented.
Content
1. Single-particle Problems: Numerical solutions of the Schroedinger equation, Numerov's integration, the split operator method
2. Quantum Spin Models: Choice and representations of basis sets for the many-body problem, the Trotter decompososition for real and imaginary-time evolution
3. Electronic Structure: Second Quantization, Full Configuration Interaction, Hartree-Fock, Density Functional Theory
4. Variational Methods: Variational Monte Carlo. Machine Learning Based Techniques, Time-dependent Variational Approaches
5. Quantum Monte Carlo Methods: Path Integral Monte Carlo at finite and zero temperature
6. Quantum Computing: Quantum simulation on a quantum computer, Adiabatic State preparation, Variational Quantum Eigensolver
Keywords
Quantum simulation, Variational Monte Carlo, Machine Learning in Physics, Density Functional Theory, Lanczos, Path Integral Monte Carlo, Quantum Computing, Second Quantization, Time-Dependent Variational Principle
Learning Prerequisites
Required courses
A solid understanding of quantum mechanics (I and II) is required.
Students should have a good working knowledge of at least one common programming language (Python, C, C++, Fortran, Julia...). Knowledge of Matlab is typically sufficient, but it is strongly advised to be familiar with Python, since the exercises will be typically presented and discussed in Python.
Recommended courses
The following courses are recommended but not compulsory
PHYS-403 - Computer simulation of physical systems I, highly recommended to get an introduction to simulation paradigms for physical systems
PHYS-467 - Machine learning for physicists, highly recommended to get an introduction to modern machine learning, since part of the course will make us of machine learning to study quantum systems
PHYS-641 - Quantum Information and Quantum Computing, also highly recommended since part of the course will cover quantum algorithms
To have a broader view of the importance of the problems attacked during the course, it is also suggested to attend the following courses
PHYS-419 - Solid State Physics III
PHYS-426 - Quantum Physics IV
Learning Outcomes
By the end of the course, the student must be able to:
- Model a quantum problem through numerical tools
- Identify suitable algorithms to solve or approximately solve a certain quantum problem
- Discuss the limitations of a given algorithm
- Carry out computer simulations of physical systems
Teaching methods
Ex cathedra with exercises
Expected student activities
Practical assignments will be given every week.
Solutions to the assignements will be handed out and the homework will not be graded.
It is strongly advised however to make the effort to do the homework weekly, since the final exam will also evaluate the understanding of the practical implementation aspects of the computational methods.
Assessment methods
The course is graded through an oral exam.
The oral exam will assess both the general theory as well as the understanding of the practical implementation of the algorithms, as presented during the practical weekly exercises.
Resources
Bibliography
Suggested books to acquire a broader view on the topics discussed in the lecture notes
"Quantum Monte Carlo Approaches for Correlated Systems", F. Becca & S. Sorella, (Cambridge University Press, 2017)
"Computational Physics", J. M. Thijssen, (Cambridge University Press)
"Statistical Mechanics: Algorithms and Computations", W. Krauth, (Oxford Master Series in Physics)
Ressources en bibliothèque
- Computational Physics / Thijssen
- Quantum Monte Carlo Approaches for Correlated Systems / Becca
- Statistical Mechanics: Algorithms and Computations / Krauth
Notes/Handbook
Detailed Lecture Notes will be provided
Moodle Link
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Computational quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional