Lecture

Stochastic Numerical Methods for Quantum Systems

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

PHYS-744: Advanced Topics in Quantum Sciences and Technologies

This course provides an in-depth treatment of the latest experimental and theoretical topics in quantum sciences and technologies, including for example quantum sensing, quantum optics, cold atoms, theory of quantum measurements and open dissipative quantu ...

Description

This lecture covers topics such as exact diagonalization, iterative diagonalization, real-time dynamics, quantum information, mean field states, matrix product state form, Metropolis-Hastings algorithm, and computing properties as stochastic averages. The instructor discusses the practical implementation in Python and provides examples related to many-body quantum systems.

Instructors (5)

Zoë Holmes

Teaching & PhD PhD Students Ricard Puig, Sacha Lerch, Reyhaneh Aghaei Saem, Shao Hen Chiew, Weijie Xiong, Marc Sanz Drudis, Mehrad Sahebi, Manuel Rudolph Courses Quantum information theory PHYS-550 After recapping the basics of quantum theory from an informationtheoretic perspective, we will cover more advanced topics inquantum information theory. This includes introducing measures of quantum information, and developing a more advanced understanding quantum states, channels and measurement

Vincenzo Savona

Vincenzo Savona studied physics in Pisa at the Scuola Normale Superiore and the University of Pisa, prior to completing his PhD at the EPFL's Institute of Theoretical Physics. Subsequently he did post-doctoral work, first at the EPFL and then in the physics department of the Humboldt University of Berlin. In 2002, he returned to the EPFL to create his own research group, receiving a "professeur boursier" fellowship from the Swiss National Science Foundation. In 2006, he was appointed tenure-track assistant professor at the EPFL and joined the NCCR for Quantum Photonics. In 2010 he was appointed associate professor. Currently he directs the Laboratory of Theoretical Physics of Nanosystems.

Jean-Philippe Brantut

I did my PhD at the Institut d'Optique under the direction of Philippe Bouyer and Alain Aspect, before moving to ETHZ in the group of Tilman Esslinger, first as a post-doc then as a senior scientist. There I developed in particular the method allowing for a quantum simulation of nano-electronic devices with ultracold quantum gases.Since september 2016, I hold the Fondation Sandoz chair in physics of quantum gases at EPFL. There, my group has developed the first cold atoms machine combining Fermi gases with cavity-quantum electrodynamics. We use it to explore new ways of measuring and manipulating quantum matter.

Christophe Marcel Georges Galland

I studied at Ecole Polytechnique in Paris (X2003) and received my PhD in 2010 from ETH Zürich for a thesis in solid-state quantum optics with individual carbon nanotubes, in the Quantum Photonics Group of Prof. Ataç Imamoglu. As a postdoctoral researcher at Los Alamos National Lab (USA) I studied the photophysics of individual nanocrystal quantum dots in the groups of Victor Klimov and Han Htoon. I was investigating the mechanisms responsible for fluorescence fluctuations and how to control them. I then moved to the University of Delaware in the group of Michael Hochberg to work in the emerging field of integrated quantum optics. I was leading international projects such as the realisation of an on-chip source of quantum correlated photons integrating optical filters and demultiplexers. From 2013 to 2016, I was working at EPFL in the group of Prof. Kippenberg in the field of quantum optomechanics with an Ambizione Fellowship of the Swiss National Science Foundation (SNSF). My work focused on the creation of non-classical vibrational states of mesoscopic oscillators and on the amplification of vibrations in molecules. Since May 2017, I am leading the Laboratory of Quantum and Nano-Optics at EPFL as an SNSF-funded professor in the Institute of Physics. My team investigates two main phenomena: (i) the vibrational dynamics of molecules embedded in nanoscale plasmonic cavities, and (ii) non-classical correlations mediated by individual quanta of crystal vibrations at room-temperature. We employ state-of-the-art spectroscopic tools such as femtosecond lasers and single-photon counters to get new insights into sub-nanometer scale dynamics.

Official source

Related concepts (32)

Quantum information

Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields.

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Jacobi method

In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.

Quantum information science

Quantum information science is a field that combines the principles of quantum mechanics with information science to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information.

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Related lectures (62)

Quantum Information Theory: Basics and Quantum States

Covers the basics of quantum information theory, focusing on classical and quantum states, evolutions, and measurements.

Quantum Information: Density Matrices

Explores density matrices, quantum states representation, and entropy in quantum information.

Quantum Information: Young's Double-Slit Experiment

Explores Young's double-slit experiment and the behavior of quantum particles.

Quantum Information Principles

Covers the mathematical principles of quantum physics, including Hilbert spaces and quantum bits.

Quantum Entropy: Markov Chains and Bell States